{
  "version": 3,
  "sources": ["../node_modules/zod/lib/index.mjs", "../node_modules/drand-client/node_modules/@noble/hashes/src/crypto.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/utils.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/utils.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/modular.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/hash-to-curve.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/curve.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/weierstrass.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/bls.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/tower.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/_u64.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/sha3.ts", "../node_modules/drand-client/node_modules/@kevincharm/noble-bn254-drand/dist/src/bn254.js", "../node_modules/drand-client/node_modules/@kevincharm/noble-bn254-drand/dist/src/index.js", "../node_modules/drand-client/node_modules/base64-js/index.js", "../node_modules/drand-client/node_modules/ieee754/index.js", "../node_modules/drand-client/node_modules/buffer/index.js", "../node_modules/drand-client/lib/version.ts", "../node_modules/drand-client/lib/util.ts", "../node_modules/drand-client/lib/http-caching-chain.ts", "../node_modules/drand-client/lib/http-chain-client.ts", "../node_modules/drand-client/lib/speedtest.ts", "../node_modules/drand-client/lib/fastest-node-client.ts", "../node_modules/drand-client/lib/multi-beacon-node.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/crypto.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/utils.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/_md.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/_u64.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/sha2.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/utils.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/modular.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/hash-to-curve.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/curve.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/weierstrass.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/bls.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/abstract/tower.ts", "../node_modules/drand-client/node_modules/@noble/curves/src/bls12-381.ts", "../node_modules/drand-client/lib/beacon-verification.ts", "../node_modules/drand-client/node_modules/@noble/hashes/src/sha3.ts", "../node_modules/drand-client/lib/defaults.ts", "../node_modules/drand-client/lib/index.ts", "../node_modules/@modelcontextprotocol/sdk/src/types.ts", "../node_modules/@modelcontextprotocol/sdk/src/shared/protocol.ts", "../node_modules/@modelcontextprotocol/sdk/src/server/index.ts", "../node_modules/zod-to-json-schema/dist/esm/Options.js", "../node_modules/zod-to-json-schema/dist/esm/Refs.js", "../node_modules/zod-to-json-schema/dist/esm/errorMessages.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/any.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/array.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/bigint.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/boolean.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/branded.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/catch.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/date.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/default.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/effects.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/enum.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/intersection.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/literal.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/string.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/record.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/map.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/nativeEnum.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/never.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/null.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/union.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/nullable.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/number.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/object.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/optional.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/pipeline.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/promise.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/set.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/tuple.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/undefined.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/unknown.js", "../node_modules/zod-to-json-schema/dist/esm/parsers/readonly.js", "../node_modules/zod-to-json-schema/dist/esm/selectParser.js", "../node_modules/zod-to-json-schema/dist/esm/parseDef.js", "../node_modules/zod-to-json-schema/dist/esm/zodToJsonSchema.js", "../node_modules/@modelcontextprotocol/sdk/src/server/completable.ts", "../node_modules/@modelcontextprotocol/sdk/src/server/mcp.ts", "../node_modules/@modelcontextprotocol/sdk/src/server/stdio.ts", "../node_modules/@modelcontextprotocol/sdk/src/shared/stdio.ts", "../src/index.ts"],
  "sourcesContent": ["var util;\n(function (util) {\n    util.assertEqual = (val) => val;\n    function assertIs(_arg) { }\n    util.assertIs = assertIs;\n    function assertNever(_x) {\n        throw new Error();\n    }\n    util.assertNever = assertNever;\n    util.arrayToEnum = (items) => {\n        const obj = {};\n        for (const item of items) {\n            obj[item] = item;\n        }\n        return obj;\n    };\n    util.getValidEnumValues = (obj) => {\n        const validKeys = util.objectKeys(obj).filter((k) => typeof obj[obj[k]] !== \"number\");\n        const filtered = {};\n        for (const k of validKeys) {\n            filtered[k] = obj[k];\n        }\n        return util.objectValues(filtered);\n    };\n    util.objectValues = (obj) => {\n        return util.objectKeys(obj).map(function (e) {\n            return obj[e];\n        });\n    };\n    util.objectKeys = typeof Object.keys === \"function\" // eslint-disable-line ban/ban\n        ? (obj) => Object.keys(obj) // eslint-disable-line ban/ban\n        : (object) => {\n            const keys = [];\n            for (const key in object) {\n                if (Object.prototype.hasOwnProperty.call(object, key)) {\n                    keys.push(key);\n                }\n            }\n            return keys;\n        };\n    util.find = (arr, checker) => {\n        for (const item of arr) {\n            if (checker(item))\n                return item;\n        }\n        return undefined;\n    };\n    util.isInteger = typeof Number.isInteger === \"function\"\n        ? (val) => Number.isInteger(val) // eslint-disable-line ban/ban\n        : (val) => typeof val === \"number\" && isFinite(val) && Math.floor(val) === val;\n    function joinValues(array, separator = \" | \") {\n        return array\n            .map((val) => (typeof val === \"string\" ? `'${val}'` : val))\n            .join(separator);\n    }\n    util.joinValues = joinValues;\n    util.jsonStringifyReplacer = (_, value) => {\n        if (typeof value === \"bigint\") {\n            return value.toString();\n        }\n        return value;\n    };\n})(util || (util = {}));\nvar objectUtil;\n(function (objectUtil) {\n    objectUtil.mergeShapes = (first, second) => {\n        return {\n            ...first,\n            ...second, // second overwrites first\n        };\n    };\n})(objectUtil || (objectUtil = {}));\nconst ZodParsedType = util.arrayToEnum([\n    \"string\",\n    \"nan\",\n    \"number\",\n    \"integer\",\n    \"float\",\n    \"boolean\",\n    \"date\",\n    \"bigint\",\n    \"symbol\",\n    \"function\",\n    \"undefined\",\n    \"null\",\n    \"array\",\n    \"object\",\n    \"unknown\",\n    \"promise\",\n    \"void\",\n    \"never\",\n    \"map\",\n    \"set\",\n]);\nconst getParsedType = (data) => {\n    const t = typeof data;\n    switch (t) {\n        case \"undefined\":\n            return ZodParsedType.undefined;\n        case \"string\":\n            return ZodParsedType.string;\n        case \"number\":\n            return isNaN(data) ? ZodParsedType.nan : ZodParsedType.number;\n        case \"boolean\":\n            return ZodParsedType.boolean;\n        case \"function\":\n            return ZodParsedType.function;\n        case \"bigint\":\n            return ZodParsedType.bigint;\n        case \"symbol\":\n            return ZodParsedType.symbol;\n        case \"object\":\n            if (Array.isArray(data)) {\n                return ZodParsedType.array;\n            }\n            if (data === null) {\n                return ZodParsedType.null;\n            }\n            if (data.then &&\n                typeof data.then === \"function\" &&\n                data.catch &&\n                typeof data.catch === \"function\") {\n                return ZodParsedType.promise;\n            }\n            if (typeof Map !== \"undefined\" && data instanceof Map) {\n                return ZodParsedType.map;\n            }\n            if (typeof Set !== \"undefined\" && data instanceof Set) {\n                return ZodParsedType.set;\n            }\n            if (typeof Date !== \"undefined\" && data instanceof Date) {\n                return ZodParsedType.date;\n            }\n            return ZodParsedType.object;\n        default:\n            return ZodParsedType.unknown;\n    }\n};\n\nconst ZodIssueCode = util.arrayToEnum([\n    \"invalid_type\",\n    \"invalid_literal\",\n    \"custom\",\n    \"invalid_union\",\n    \"invalid_union_discriminator\",\n    \"invalid_enum_value\",\n    \"unrecognized_keys\",\n    \"invalid_arguments\",\n    \"invalid_return_type\",\n    \"invalid_date\",\n    \"invalid_string\",\n    \"too_small\",\n    \"too_big\",\n    \"invalid_intersection_types\",\n    \"not_multiple_of\",\n    \"not_finite\",\n]);\nconst quotelessJson = (obj) => {\n    const json = JSON.stringify(obj, null, 2);\n    return json.replace(/\"([^\"]+)\":/g, \"$1:\");\n};\nclass ZodError extends Error {\n    get errors() {\n        return this.issues;\n    }\n    constructor(issues) {\n        super();\n        this.issues = [];\n        this.addIssue = (sub) => {\n            this.issues = [...this.issues, sub];\n        };\n        this.addIssues = (subs = []) => {\n            this.issues = [...this.issues, ...subs];\n        };\n        const actualProto = new.target.prototype;\n        if (Object.setPrototypeOf) {\n            // eslint-disable-next-line ban/ban\n            Object.setPrototypeOf(this, actualProto);\n        }\n        else {\n            this.__proto__ = actualProto;\n        }\n        this.name = \"ZodError\";\n        this.issues = issues;\n    }\n    format(_mapper) {\n        const mapper = _mapper ||\n            function (issue) {\n                return issue.message;\n            };\n        const fieldErrors = { _errors: [] };\n        const processError = (error) => {\n            for (const issue of error.issues) {\n                if (issue.code === \"invalid_union\") {\n                    issue.unionErrors.map(processError);\n                }\n                else if (issue.code === \"invalid_return_type\") {\n                    processError(issue.returnTypeError);\n                }\n                else if (issue.code === \"invalid_arguments\") {\n                    processError(issue.argumentsError);\n                }\n                else if (issue.path.length === 0) {\n                    fieldErrors._errors.push(mapper(issue));\n                }\n                else {\n                    let curr = fieldErrors;\n                    let i = 0;\n                    while (i < issue.path.length) {\n                        const el = issue.path[i];\n                        const terminal = i === issue.path.length - 1;\n                        if (!terminal) {\n                            curr[el] = curr[el] || { _errors: [] };\n                            // if (typeof el === \"string\") {\n                            //   curr[el] = curr[el] || { _errors: [] };\n                            // } else if (typeof el === \"number\") {\n                            //   const errorArray: any = [];\n                            //   errorArray._errors = [];\n                            //   curr[el] = curr[el] || errorArray;\n                            // }\n                        }\n                        else {\n                            curr[el] = curr[el] || { _errors: [] };\n                            curr[el]._errors.push(mapper(issue));\n                        }\n                        curr = curr[el];\n                        i++;\n                    }\n                }\n            }\n        };\n        processError(this);\n        return fieldErrors;\n    }\n    static assert(value) {\n        if (!(value instanceof ZodError)) {\n            throw new Error(`Not a ZodError: ${value}`);\n        }\n    }\n    toString() {\n        return this.message;\n    }\n    get message() {\n        return JSON.stringify(this.issues, util.jsonStringifyReplacer, 2);\n    }\n    get isEmpty() {\n        return this.issues.length === 0;\n    }\n    flatten(mapper = (issue) => issue.message) {\n        const fieldErrors = {};\n        const formErrors = [];\n        for (const sub of this.issues) {\n            if (sub.path.length > 0) {\n                fieldErrors[sub.path[0]] = fieldErrors[sub.path[0]] || [];\n                fieldErrors[sub.path[0]].push(mapper(sub));\n            }\n            else {\n                formErrors.push(mapper(sub));\n            }\n        }\n        return { formErrors, fieldErrors };\n    }\n    get formErrors() {\n        return this.flatten();\n    }\n}\nZodError.create = (issues) => {\n    const error = new ZodError(issues);\n    return error;\n};\n\nconst errorMap = (issue, _ctx) => {\n    let message;\n    switch (issue.code) {\n        case ZodIssueCode.invalid_type:\n            if (issue.received === ZodParsedType.undefined) {\n                message = \"Required\";\n            }\n            else {\n                message = `Expected ${issue.expected}, received ${issue.received}`;\n            }\n            break;\n        case ZodIssueCode.invalid_literal:\n            message = `Invalid literal value, expected ${JSON.stringify(issue.expected, util.jsonStringifyReplacer)}`;\n            break;\n        case ZodIssueCode.unrecognized_keys:\n            message = `Unrecognized key(s) in object: ${util.joinValues(issue.keys, \", \")}`;\n            break;\n        case ZodIssueCode.invalid_union:\n            message = `Invalid input`;\n            break;\n        case ZodIssueCode.invalid_union_discriminator:\n            message = `Invalid discriminator value. Expected ${util.joinValues(issue.options)}`;\n            break;\n        case ZodIssueCode.invalid_enum_value:\n            message = `Invalid enum value. Expected ${util.joinValues(issue.options)}, received '${issue.received}'`;\n            break;\n        case ZodIssueCode.invalid_arguments:\n            message = `Invalid function arguments`;\n            break;\n        case ZodIssueCode.invalid_return_type:\n            message = `Invalid function return type`;\n            break;\n        case ZodIssueCode.invalid_date:\n            message = `Invalid date`;\n            break;\n        case ZodIssueCode.invalid_string:\n            if (typeof issue.validation === \"object\") {\n                if (\"includes\" in issue.validation) {\n                    message = `Invalid input: must include \"${issue.validation.includes}\"`;\n                    if (typeof issue.validation.position === \"number\") {\n                        message = `${message} at one or more positions greater than or equal to ${issue.validation.position}`;\n                    }\n                }\n                else if (\"startsWith\" in issue.validation) {\n                    message = `Invalid input: must start with \"${issue.validation.startsWith}\"`;\n                }\n                else if (\"endsWith\" in issue.validation) {\n                    message = `Invalid input: must end with \"${issue.validation.endsWith}\"`;\n                }\n                else {\n                    util.assertNever(issue.validation);\n                }\n            }\n            else if (issue.validation !== \"regex\") {\n                message = `Invalid ${issue.validation}`;\n            }\n            else {\n                message = \"Invalid\";\n            }\n            break;\n        case ZodIssueCode.too_small:\n            if (issue.type === \"array\")\n                message = `Array must contain ${issue.exact ? \"exactly\" : issue.inclusive ? `at least` : `more than`} ${issue.minimum} element(s)`;\n            else if (issue.type === \"string\")\n                message = `String must contain ${issue.exact ? \"exactly\" : issue.inclusive ? `at least` : `over`} ${issue.minimum} character(s)`;\n            else if (issue.type === \"number\")\n                message = `Number must be ${issue.exact\n                    ? `exactly equal to `\n                    : issue.inclusive\n                        ? `greater than or equal to `\n                        : `greater than `}${issue.minimum}`;\n            else if (issue.type === \"date\")\n                message = `Date must be ${issue.exact\n                    ? `exactly equal to `\n                    : issue.inclusive\n                        ? `greater than or equal to `\n                        : `greater than `}${new Date(Number(issue.minimum))}`;\n            else\n                message = \"Invalid input\";\n            break;\n        case ZodIssueCode.too_big:\n            if (issue.type === \"array\")\n                message = `Array must contain ${issue.exact ? `exactly` : issue.inclusive ? `at most` : `less than`} ${issue.maximum} element(s)`;\n            else if (issue.type === \"string\")\n                message = `String must contain ${issue.exact ? `exactly` : issue.inclusive ? `at most` : `under`} ${issue.maximum} character(s)`;\n            else if (issue.type === \"number\")\n                message = `Number must be ${issue.exact\n                    ? `exactly`\n                    : issue.inclusive\n                        ? `less than or equal to`\n                        : `less than`} ${issue.maximum}`;\n            else if (issue.type === \"bigint\")\n                message = `BigInt must be ${issue.exact\n                    ? `exactly`\n                    : issue.inclusive\n                        ? `less than or equal to`\n                        : `less than`} ${issue.maximum}`;\n            else if (issue.type === \"date\")\n                message = `Date must be ${issue.exact\n                    ? `exactly`\n                    : issue.inclusive\n                        ? `smaller than or equal to`\n                        : `smaller than`} ${new Date(Number(issue.maximum))}`;\n            else\n                message = \"Invalid input\";\n            break;\n        case ZodIssueCode.custom:\n            message = `Invalid input`;\n            break;\n        case ZodIssueCode.invalid_intersection_types:\n            message = `Intersection results could not be merged`;\n            break;\n        case ZodIssueCode.not_multiple_of:\n            message = `Number must be a multiple of ${issue.multipleOf}`;\n            break;\n        case ZodIssueCode.not_finite:\n            message = \"Number must be finite\";\n            break;\n        default:\n            message = _ctx.defaultError;\n            util.assertNever(issue);\n    }\n    return { message };\n};\n\nlet overrideErrorMap = errorMap;\nfunction setErrorMap(map) {\n    overrideErrorMap = map;\n}\nfunction getErrorMap() {\n    return overrideErrorMap;\n}\n\nconst makeIssue = (params) => {\n    const { data, path, errorMaps, issueData } = params;\n    const fullPath = [...path, ...(issueData.path || [])];\n    const fullIssue = {\n        ...issueData,\n        path: fullPath,\n    };\n    if (issueData.message !== undefined) {\n        return {\n            ...issueData,\n            path: fullPath,\n            message: issueData.message,\n        };\n    }\n    let errorMessage = \"\";\n    const maps = errorMaps\n        .filter((m) => !!m)\n        .slice()\n        .reverse();\n    for (const map of maps) {\n        errorMessage = map(fullIssue, { data, defaultError: errorMessage }).message;\n    }\n    return {\n        ...issueData,\n        path: fullPath,\n        message: errorMessage,\n    };\n};\nconst EMPTY_PATH = [];\nfunction addIssueToContext(ctx, issueData) {\n    const overrideMap = getErrorMap();\n    const issue = makeIssue({\n        issueData: issueData,\n        data: ctx.data,\n        path: ctx.path,\n        errorMaps: [\n            ctx.common.contextualErrorMap, // contextual error map is first priority\n            ctx.schemaErrorMap, // then schema-bound map if available\n            overrideMap, // then global override map\n            overrideMap === errorMap ? undefined : errorMap, // then global default map\n        ].filter((x) => !!x),\n    });\n    ctx.common.issues.push(issue);\n}\nclass ParseStatus {\n    constructor() {\n        this.value = \"valid\";\n    }\n    dirty() {\n        if (this.value === \"valid\")\n            this.value = \"dirty\";\n    }\n    abort() {\n        if (this.value !== \"aborted\")\n            this.value = \"aborted\";\n    }\n    static mergeArray(status, results) {\n        const arrayValue = [];\n        for (const s of results) {\n            if (s.status === \"aborted\")\n                return INVALID;\n            if (s.status === \"dirty\")\n                status.dirty();\n            arrayValue.push(s.value);\n        }\n        return { status: status.value, value: arrayValue };\n    }\n    static async mergeObjectAsync(status, pairs) {\n        const syncPairs = [];\n        for (const pair of pairs) {\n            const key = await pair.key;\n            const value = await pair.value;\n            syncPairs.push({\n                key,\n                value,\n            });\n        }\n        return ParseStatus.mergeObjectSync(status, syncPairs);\n    }\n    static mergeObjectSync(status, pairs) {\n        const finalObject = {};\n        for (const pair of pairs) {\n            const { key, value } = pair;\n            if (key.status === \"aborted\")\n                return INVALID;\n            if (value.status === \"aborted\")\n                return INVALID;\n            if (key.status === \"dirty\")\n                status.dirty();\n            if (value.status === \"dirty\")\n                status.dirty();\n            if (key.value !== \"__proto__\" &&\n                (typeof value.value !== \"undefined\" || pair.alwaysSet)) {\n                finalObject[key.value] = value.value;\n            }\n        }\n        return { status: status.value, value: finalObject };\n    }\n}\nconst INVALID = Object.freeze({\n    status: \"aborted\",\n});\nconst DIRTY = (value) => ({ status: \"dirty\", value });\nconst OK = (value) => ({ status: \"valid\", value });\nconst isAborted = (x) => x.status === \"aborted\";\nconst isDirty = (x) => x.status === \"dirty\";\nconst isValid = (x) => x.status === \"valid\";\nconst isAsync = (x) => typeof Promise !== \"undefined\" && x instanceof Promise;\n\n/******************************************************************************\r\nCopyright (c) Microsoft Corporation.\r\n\r\nPermission to use, copy, modify, and/or distribute this software for any\r\npurpose with or without fee is hereby granted.\r\n\r\nTHE SOFTWARE IS PROVIDED \"AS IS\" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH\r\nREGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY\r\nAND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,\r\nINDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM\r\nLOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR\r\nOTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR\r\nPERFORMANCE OF THIS SOFTWARE.\r\n***************************************************************************** */\r\n\r\nfunction __classPrivateFieldGet(receiver, state, kind, f) {\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a getter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot read private member from an object whose class did not declare it\");\r\n    return kind === \"m\" ? f : kind === \"a\" ? f.call(receiver) : f ? f.value : state.get(receiver);\r\n}\r\n\r\nfunction __classPrivateFieldSet(receiver, state, value, kind, f) {\r\n    if (kind === \"m\") throw new TypeError(\"Private method is not writable\");\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a setter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot write private member to an object whose class did not declare it\");\r\n    return (kind === \"a\" ? f.call(receiver, value) : f ? f.value = value : state.set(receiver, value)), value;\r\n}\r\n\r\ntypeof SuppressedError === \"function\" ? SuppressedError : function (error, suppressed, message) {\r\n    var e = new Error(message);\r\n    return e.name = \"SuppressedError\", e.error = error, e.suppressed = suppressed, e;\r\n};\n\nvar errorUtil;\n(function (errorUtil) {\n    errorUtil.errToObj = (message) => typeof message === \"string\" ? { message } : message || {};\n    errorUtil.toString = (message) => typeof message === \"string\" ? message : message === null || message === void 0 ? void 0 : message.message;\n})(errorUtil || (errorUtil = {}));\n\nvar _ZodEnum_cache, _ZodNativeEnum_cache;\nclass ParseInputLazyPath {\n    constructor(parent, value, path, key) {\n        this._cachedPath = [];\n        this.parent = parent;\n        this.data = value;\n        this._path = path;\n        this._key = key;\n    }\n    get path() {\n        if (!this._cachedPath.length) {\n            if (this._key instanceof Array) {\n                this._cachedPath.push(...this._path, ...this._key);\n            }\n            else {\n                this._cachedPath.push(...this._path, this._key);\n            }\n        }\n        return this._cachedPath;\n    }\n}\nconst handleResult = (ctx, result) => {\n    if (isValid(result)) {\n        return { success: true, data: result.value };\n    }\n    else {\n        if (!ctx.common.issues.length) {\n            throw new Error(\"Validation failed but no issues detected.\");\n        }\n        return {\n            success: false,\n            get error() {\n                if (this._error)\n                    return this._error;\n                const error = new ZodError(ctx.common.issues);\n                this._error = error;\n                return this._error;\n            },\n        };\n    }\n};\nfunction processCreateParams(params) {\n    if (!params)\n        return {};\n    const { errorMap, invalid_type_error, required_error, description } = params;\n    if (errorMap && (invalid_type_error || required_error)) {\n        throw new Error(`Can't use \"invalid_type_error\" or \"required_error\" in conjunction with custom error map.`);\n    }\n    if (errorMap)\n        return { errorMap: errorMap, description };\n    const customMap = (iss, ctx) => {\n        var _a, _b;\n        const { message } = params;\n        if (iss.code === \"invalid_enum_value\") {\n            return { message: message !== null && message !== void 0 ? message : ctx.defaultError };\n        }\n        if (typeof ctx.data === \"undefined\") {\n            return { message: (_a = message !== null && message !== void 0 ? message : required_error) !== null && _a !== void 0 ? _a : ctx.defaultError };\n        }\n        if (iss.code !== \"invalid_type\")\n            return { message: ctx.defaultError };\n        return { message: (_b = message !== null && message !== void 0 ? message : invalid_type_error) !== null && _b !== void 0 ? _b : ctx.defaultError };\n    };\n    return { errorMap: customMap, description };\n}\nclass ZodType {\n    get description() {\n        return this._def.description;\n    }\n    _getType(input) {\n        return getParsedType(input.data);\n    }\n    _getOrReturnCtx(input, ctx) {\n        return (ctx || {\n            common: input.parent.common,\n            data: input.data,\n            parsedType: getParsedType(input.data),\n            schemaErrorMap: this._def.errorMap,\n            path: input.path,\n            parent: input.parent,\n        });\n    }\n    _processInputParams(input) {\n        return {\n            status: new ParseStatus(),\n            ctx: {\n                common: input.parent.common,\n                data: input.data,\n                parsedType: getParsedType(input.data),\n                schemaErrorMap: this._def.errorMap,\n                path: input.path,\n                parent: input.parent,\n            },\n        };\n    }\n    _parseSync(input) {\n        const result = this._parse(input);\n        if (isAsync(result)) {\n            throw new Error(\"Synchronous parse encountered promise.\");\n        }\n        return result;\n    }\n    _parseAsync(input) {\n        const result = this._parse(input);\n        return Promise.resolve(result);\n    }\n    parse(data, params) {\n        const result = this.safeParse(data, params);\n        if (result.success)\n            return result.data;\n        throw result.error;\n    }\n    safeParse(data, params) {\n        var _a;\n        const ctx = {\n            common: {\n                issues: [],\n                async: (_a = params === null || params === void 0 ? void 0 : params.async) !== null && _a !== void 0 ? _a : false,\n                contextualErrorMap: params === null || params === void 0 ? void 0 : params.errorMap,\n            },\n            path: (params === null || params === void 0 ? void 0 : params.path) || [],\n            schemaErrorMap: this._def.errorMap,\n            parent: null,\n            data,\n            parsedType: getParsedType(data),\n        };\n        const result = this._parseSync({ data, path: ctx.path, parent: ctx });\n        return handleResult(ctx, result);\n    }\n    \"~validate\"(data) {\n        var _a, _b;\n        const ctx = {\n            common: {\n                issues: [],\n                async: !!this[\"~standard\"].async,\n            },\n            path: [],\n            schemaErrorMap: this._def.errorMap,\n            parent: null,\n            data,\n            parsedType: getParsedType(data),\n        };\n        if (!this[\"~standard\"].async) {\n            try {\n                const result = this._parseSync({ data, path: [], parent: ctx });\n                return isValid(result)\n                    ? {\n                        value: result.value,\n                    }\n                    : {\n                        issues: ctx.common.issues,\n                    };\n            }\n            catch (err) {\n                if ((_b = (_a = err === null || err === void 0 ? void 0 : err.message) === null || _a === void 0 ? void 0 : _a.toLowerCase()) === null || _b === void 0 ? void 0 : _b.includes(\"encountered\")) {\n                    this[\"~standard\"].async = true;\n                }\n                ctx.common = {\n                    issues: [],\n                    async: true,\n                };\n            }\n        }\n        return this._parseAsync({ data, path: [], parent: ctx }).then((result) => isValid(result)\n            ? {\n                value: result.value,\n            }\n            : {\n                issues: ctx.common.issues,\n            });\n    }\n    async parseAsync(data, params) {\n        const result = await this.safeParseAsync(data, params);\n        if (result.success)\n            return result.data;\n        throw result.error;\n    }\n    async safeParseAsync(data, params) {\n        const ctx = {\n            common: {\n                issues: [],\n                contextualErrorMap: params === null || params === void 0 ? void 0 : params.errorMap,\n                async: true,\n            },\n            path: (params === null || params === void 0 ? void 0 : params.path) || [],\n            schemaErrorMap: this._def.errorMap,\n            parent: null,\n            data,\n            parsedType: getParsedType(data),\n        };\n        const maybeAsyncResult = this._parse({ data, path: ctx.path, parent: ctx });\n        const result = await (isAsync(maybeAsyncResult)\n            ? maybeAsyncResult\n            : Promise.resolve(maybeAsyncResult));\n        return handleResult(ctx, result);\n    }\n    refine(check, message) {\n        const getIssueProperties = (val) => {\n            if (typeof message === \"string\" || typeof message === \"undefined\") {\n                return { message };\n            }\n            else if (typeof message === \"function\") {\n                return message(val);\n            }\n            else {\n                return message;\n            }\n        };\n        return this._refinement((val, ctx) => {\n            const result = check(val);\n            const setError = () => ctx.addIssue({\n                code: ZodIssueCode.custom,\n                ...getIssueProperties(val),\n            });\n            if (typeof Promise !== \"undefined\" && result instanceof Promise) {\n                return result.then((data) => {\n                    if (!data) {\n                        setError();\n                        return false;\n                    }\n                    else {\n                        return true;\n                    }\n                });\n            }\n            if (!result) {\n                setError();\n                return false;\n            }\n            else {\n                return true;\n            }\n        });\n    }\n    refinement(check, refinementData) {\n        return this._refinement((val, ctx) => {\n            if (!check(val)) {\n                ctx.addIssue(typeof refinementData === \"function\"\n                    ? refinementData(val, ctx)\n                    : refinementData);\n                return false;\n            }\n            else {\n                return true;\n            }\n        });\n    }\n    _refinement(refinement) {\n        return new ZodEffects({\n            schema: this,\n            typeName: ZodFirstPartyTypeKind.ZodEffects,\n            effect: { type: \"refinement\", refinement },\n        });\n    }\n    superRefine(refinement) {\n        return this._refinement(refinement);\n    }\n    constructor(def) {\n        /** Alias of safeParseAsync */\n        this.spa = this.safeParseAsync;\n        this._def = def;\n        this.parse = this.parse.bind(this);\n        this.safeParse = this.safeParse.bind(this);\n        this.parseAsync = this.parseAsync.bind(this);\n        this.safeParseAsync = this.safeParseAsync.bind(this);\n        this.spa = this.spa.bind(this);\n        this.refine = this.refine.bind(this);\n        this.refinement = this.refinement.bind(this);\n        this.superRefine = this.superRefine.bind(this);\n        this.optional = this.optional.bind(this);\n        this.nullable = this.nullable.bind(this);\n        this.nullish = this.nullish.bind(this);\n        this.array = this.array.bind(this);\n        this.promise = this.promise.bind(this);\n        this.or = this.or.bind(this);\n        this.and = this.and.bind(this);\n        this.transform = this.transform.bind(this);\n        this.brand = this.brand.bind(this);\n        this.default = this.default.bind(this);\n        this.catch = this.catch.bind(this);\n        this.describe = this.describe.bind(this);\n        this.pipe = this.pipe.bind(this);\n        this.readonly = this.readonly.bind(this);\n        this.isNullable = this.isNullable.bind(this);\n        this.isOptional = this.isOptional.bind(this);\n        this[\"~standard\"] = {\n            version: 1,\n            vendor: \"zod\",\n            validate: (data) => this[\"~validate\"](data),\n        };\n    }\n    optional() {\n        return ZodOptional.create(this, this._def);\n    }\n    nullable() {\n        return ZodNullable.create(this, this._def);\n    }\n    nullish() {\n        return this.nullable().optional();\n    }\n    array() {\n        return ZodArray.create(this);\n    }\n    promise() {\n        return ZodPromise.create(this, this._def);\n    }\n    or(option) {\n        return ZodUnion.create([this, option], this._def);\n    }\n    and(incoming) {\n        return ZodIntersection.create(this, incoming, this._def);\n    }\n    transform(transform) {\n        return new ZodEffects({\n            ...processCreateParams(this._def),\n            schema: this,\n            typeName: ZodFirstPartyTypeKind.ZodEffects,\n            effect: { type: \"transform\", transform },\n        });\n    }\n    default(def) {\n        const defaultValueFunc = typeof def === \"function\" ? def : () => def;\n        return new ZodDefault({\n            ...processCreateParams(this._def),\n            innerType: this,\n            defaultValue: defaultValueFunc,\n            typeName: ZodFirstPartyTypeKind.ZodDefault,\n        });\n    }\n    brand() {\n        return new ZodBranded({\n            typeName: ZodFirstPartyTypeKind.ZodBranded,\n            type: this,\n            ...processCreateParams(this._def),\n        });\n    }\n    catch(def) {\n        const catchValueFunc = typeof def === \"function\" ? def : () => def;\n        return new ZodCatch({\n            ...processCreateParams(this._def),\n            innerType: this,\n            catchValue: catchValueFunc,\n            typeName: ZodFirstPartyTypeKind.ZodCatch,\n        });\n    }\n    describe(description) {\n        const This = this.constructor;\n        return new This({\n            ...this._def,\n            description,\n        });\n    }\n    pipe(target) {\n        return ZodPipeline.create(this, target);\n    }\n    readonly() {\n        return ZodReadonly.create(this);\n    }\n    isOptional() {\n        return this.safeParse(undefined).success;\n    }\n    isNullable() {\n        return this.safeParse(null).success;\n    }\n}\nconst cuidRegex = /^c[^\\s-]{8,}$/i;\nconst cuid2Regex = /^[0-9a-z]+$/;\nconst ulidRegex = /^[0-9A-HJKMNP-TV-Z]{26}$/i;\n// const uuidRegex =\n//   /^([a-f0-9]{8}-[a-f0-9]{4}-[1-5][a-f0-9]{3}-[a-f0-9]{4}-[a-f0-9]{12}|00000000-0000-0000-0000-000000000000)$/i;\nconst uuidRegex = /^[0-9a-fA-F]{8}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{12}$/i;\nconst nanoidRegex = /^[a-z0-9_-]{21}$/i;\nconst jwtRegex = /^[A-Za-z0-9-_]+\\.[A-Za-z0-9-_]+\\.[A-Za-z0-9-_]*$/;\nconst durationRegex = /^[-+]?P(?!$)(?:(?:[-+]?\\d+Y)|(?:[-+]?\\d+[.,]\\d+Y$))?(?:(?:[-+]?\\d+M)|(?:[-+]?\\d+[.,]\\d+M$))?(?:(?:[-+]?\\d+W)|(?:[-+]?\\d+[.,]\\d+W$))?(?:(?:[-+]?\\d+D)|(?:[-+]?\\d+[.,]\\d+D$))?(?:T(?=[\\d+-])(?:(?:[-+]?\\d+H)|(?:[-+]?\\d+[.,]\\d+H$))?(?:(?:[-+]?\\d+M)|(?:[-+]?\\d+[.,]\\d+M$))?(?:[-+]?\\d+(?:[.,]\\d+)?S)?)??$/;\n// from https://stackoverflow.com/a/46181/1550155\n// old version: too slow, didn't support unicode\n// const emailRegex = /^((([a-z]|\\d|[!#\\$%&'\\*\\+\\-\\/=\\?\\^_`{\\|}~]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])+(\\.([a-z]|\\d|[!#\\$%&'\\*\\+\\-\\/=\\?\\^_`{\\|}~]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])+)*)|((\\x22)((((\\x20|\\x09)*(\\x0d\\x0a))?(\\x20|\\x09)+)?(([\\x01-\\x08\\x0b\\x0c\\x0e-\\x1f\\x7f]|\\x21|[\\x23-\\x5b]|[\\x5d-\\x7e]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])|(\\\\([\\x01-\\x09\\x0b\\x0c\\x0d-\\x7f]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF]))))*(((\\x20|\\x09)*(\\x0d\\x0a))?(\\x20|\\x09)+)?(\\x22)))@((([a-z]|\\d|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])|(([a-z]|\\d|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])([a-z]|\\d|-|\\.|_|~|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])*([a-z]|\\d|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])))\\.)+(([a-z]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])|(([a-z]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])([a-z]|\\d|-|\\.|_|~|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])*([a-z]|[\\u00A0-\\uD7FF\\uF900-\\uFDCF\\uFDF0-\\uFFEF])))$/i;\n//old email regex\n// const emailRegex = /^(([^<>()[\\].,;:\\s@\"]+(\\.[^<>()[\\].,;:\\s@\"]+)*)|(\".+\"))@((?!-)([^<>()[\\].,;:\\s@\"]+\\.)+[^<>()[\\].,;:\\s@\"]{1,})[^-<>()[\\].,;:\\s@\"]$/i;\n// eslint-disable-next-line\n// const emailRegex =\n//   /^(([^<>()[\\]\\\\.,;:\\s@\\\"]+(\\.[^<>()[\\]\\\\.,;:\\s@\\\"]+)*)|(\\\".+\\\"))@((\\[(((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2}))\\.){3}((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2}))\\])|(\\[IPv6:(([a-f0-9]{1,4}:){7}|::([a-f0-9]{1,4}:){0,6}|([a-f0-9]{1,4}:){1}:([a-f0-9]{1,4}:){0,5}|([a-f0-9]{1,4}:){2}:([a-f0-9]{1,4}:){0,4}|([a-f0-9]{1,4}:){3}:([a-f0-9]{1,4}:){0,3}|([a-f0-9]{1,4}:){4}:([a-f0-9]{1,4}:){0,2}|([a-f0-9]{1,4}:){5}:([a-f0-9]{1,4}:){0,1})([a-f0-9]{1,4}|(((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2}))\\.){3}((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2})))\\])|([A-Za-z0-9]([A-Za-z0-9-]*[A-Za-z0-9])*(\\.[A-Za-z]{2,})+))$/;\n// const emailRegex =\n//   /^[a-zA-Z0-9\\.\\!\\#\\$\\%\\&\\'\\*\\+\\/\\=\\?\\^\\_\\`\\{\\|\\}\\~\\-]+@[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?(?:\\.[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?)*$/;\n// const emailRegex =\n//   /^(?:[a-z0-9!#$%&'*+/=?^_`{|}~-]+(?:\\.[a-z0-9!#$%&'*+/=?^_`{|}~-]+)*|\"(?:[\\x01-\\x08\\x0b\\x0c\\x0e-\\x1f\\x21\\x23-\\x5b\\x5d-\\x7f]|\\\\[\\x01-\\x09\\x0b\\x0c\\x0e-\\x7f])*\")@(?:(?:[a-z0-9](?:[a-z0-9-]*[a-z0-9])?\\.)+[a-z0-9](?:[a-z0-9-]*[a-z0-9])?|\\[(?:(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\\.){3}(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?|[a-z0-9-]*[a-z0-9]:(?:[\\x01-\\x08\\x0b\\x0c\\x0e-\\x1f\\x21-\\x5a\\x53-\\x7f]|\\\\[\\x01-\\x09\\x0b\\x0c\\x0e-\\x7f])+)\\])$/i;\nconst emailRegex = /^(?!\\.)(?!.*\\.\\.)([A-Z0-9_'+\\-\\.]*)[A-Z0-9_+-]@([A-Z0-9][A-Z0-9\\-]*\\.)+[A-Z]{2,}$/i;\n// const emailRegex =\n//   /^[a-z0-9.!#$%&\u2019*+/=?^_`{|}~-]+@[a-z0-9-]+(?:\\.[a-z0-9\\-]+)*$/i;\n// from https://thekevinscott.com/emojis-in-javascript/#writing-a-regular-expression\nconst _emojiRegex = `^(\\\\p{Extended_Pictographic}|\\\\p{Emoji_Component})+$`;\nlet emojiRegex;\n// faster, simpler, safer\nconst ipv4Regex = /^(?:(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])$/;\nconst ipv4CidrRegex = /^(?:(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\/(3[0-2]|[12]?[0-9])$/;\n// const ipv6Regex =\n// /^(([a-f0-9]{1,4}:){7}|::([a-f0-9]{1,4}:){0,6}|([a-f0-9]{1,4}:){1}:([a-f0-9]{1,4}:){0,5}|([a-f0-9]{1,4}:){2}:([a-f0-9]{1,4}:){0,4}|([a-f0-9]{1,4}:){3}:([a-f0-9]{1,4}:){0,3}|([a-f0-9]{1,4}:){4}:([a-f0-9]{1,4}:){0,2}|([a-f0-9]{1,4}:){5}:([a-f0-9]{1,4}:){0,1})([a-f0-9]{1,4}|(((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2}))\\.){3}((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2})))$/;\nconst ipv6Regex = /^(([0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,7}:|([0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,5}(:[0-9a-fA-F]{1,4}){1,2}|([0-9a-fA-F]{1,4}:){1,4}(:[0-9a-fA-F]{1,4}){1,3}|([0-9a-fA-F]{1,4}:){1,3}(:[0-9a-fA-F]{1,4}){1,4}|([0-9a-fA-F]{1,4}:){1,2}(:[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:((:[0-9a-fA-F]{1,4}){1,6})|:((:[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(:[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(ffff(:0{1,4}){0,1}:){0,1}((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])|([0-9a-fA-F]{1,4}:){1,4}:((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9]))$/;\nconst ipv6CidrRegex = /^(([0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,7}:|([0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,5}(:[0-9a-fA-F]{1,4}){1,2}|([0-9a-fA-F]{1,4}:){1,4}(:[0-9a-fA-F]{1,4}){1,3}|([0-9a-fA-F]{1,4}:){1,3}(:[0-9a-fA-F]{1,4}){1,4}|([0-9a-fA-F]{1,4}:){1,2}(:[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:((:[0-9a-fA-F]{1,4}){1,6})|:((:[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(:[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(ffff(:0{1,4}){0,1}:){0,1}((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])|([0-9a-fA-F]{1,4}:){1,4}:((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9]))\\/(12[0-8]|1[01][0-9]|[1-9]?[0-9])$/;\n// https://stackoverflow.com/questions/7860392/determine-if-string-is-in-base64-using-javascript\nconst base64Regex = /^([0-9a-zA-Z+/]{4})*(([0-9a-zA-Z+/]{2}==)|([0-9a-zA-Z+/]{3}=))?$/;\n// https://base64.guru/standards/base64url\nconst base64urlRegex = /^([0-9a-zA-Z-_]{4})*(([0-9a-zA-Z-_]{2}(==)?)|([0-9a-zA-Z-_]{3}(=)?))?$/;\n// simple\n// const dateRegexSource = `\\\\d{4}-\\\\d{2}-\\\\d{2}`;\n// no leap year validation\n// const dateRegexSource = `\\\\d{4}-((0[13578]|10|12)-31|(0[13-9]|1[0-2])-30|(0[1-9]|1[0-2])-(0[1-9]|1\\\\d|2\\\\d))`;\n// with leap year validation\nconst dateRegexSource = `((\\\\d\\\\d[2468][048]|\\\\d\\\\d[13579][26]|\\\\d\\\\d0[48]|[02468][048]00|[13579][26]00)-02-29|\\\\d{4}-((0[13578]|1[02])-(0[1-9]|[12]\\\\d|3[01])|(0[469]|11)-(0[1-9]|[12]\\\\d|30)|(02)-(0[1-9]|1\\\\d|2[0-8])))`;\nconst dateRegex = new RegExp(`^${dateRegexSource}$`);\nfunction timeRegexSource(args) {\n    let secondsRegexSource = `[0-5]\\\\d`;\n    if (args.precision) {\n        secondsRegexSource = `${secondsRegexSource}\\\\.\\\\d{${args.precision}}`;\n    }\n    else if (args.precision == null) {\n        secondsRegexSource = `${secondsRegexSource}(\\\\.\\\\d+)?`;\n    }\n    const secondsQuantifier = args.precision ? \"+\" : \"?\"; // require seconds if precision is nonzero\n    return `([01]\\\\d|2[0-3]):[0-5]\\\\d(:${secondsRegexSource})${secondsQuantifier}`;\n}\nfunction timeRegex(args) {\n    return new RegExp(`^${timeRegexSource(args)}$`);\n}\n// Adapted from https://stackoverflow.com/a/3143231\nfunction datetimeRegex(args) {\n    let regex = `${dateRegexSource}T${timeRegexSource(args)}`;\n    const opts = [];\n    opts.push(args.local ? `Z?` : `Z`);\n    if (args.offset)\n        opts.push(`([+-]\\\\d{2}:?\\\\d{2})`);\n    regex = `${regex}(${opts.join(\"|\")})`;\n    return new RegExp(`^${regex}$`);\n}\nfunction isValidIP(ip, version) {\n    if ((version === \"v4\" || !version) && ipv4Regex.test(ip)) {\n        return true;\n    }\n    if ((version === \"v6\" || !version) && ipv6Regex.test(ip)) {\n        return true;\n    }\n    return false;\n}\nfunction isValidJWT(jwt, alg) {\n    if (!jwtRegex.test(jwt))\n        return false;\n    try {\n        const [header] = jwt.split(\".\");\n        // Convert base64url to base64\n        const base64 = header\n            .replace(/-/g, \"+\")\n            .replace(/_/g, \"/\")\n            .padEnd(header.length + ((4 - (header.length % 4)) % 4), \"=\");\n        const decoded = JSON.parse(atob(base64));\n        if (typeof decoded !== \"object\" || decoded === null)\n            return false;\n        if (!decoded.typ || !decoded.alg)\n            return false;\n        if (alg && decoded.alg !== alg)\n            return false;\n        return true;\n    }\n    catch (_a) {\n        return false;\n    }\n}\nfunction isValidCidr(ip, version) {\n    if ((version === \"v4\" || !version) && ipv4CidrRegex.test(ip)) {\n        return true;\n    }\n    if ((version === \"v6\" || !version) && ipv6CidrRegex.test(ip)) {\n        return true;\n    }\n    return false;\n}\nclass ZodString extends ZodType {\n    _parse(input) {\n        if (this._def.coerce) {\n            input.data = String(input.data);\n        }\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.string) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.string,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const status = new ParseStatus();\n        let ctx = undefined;\n        for (const check of this._def.checks) {\n            if (check.kind === \"min\") {\n                if (input.data.length < check.value) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_small,\n                        minimum: check.value,\n                        type: \"string\",\n                        inclusive: true,\n                        exact: false,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"max\") {\n                if (input.data.length > check.value) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_big,\n                        maximum: check.value,\n                        type: \"string\",\n                        inclusive: true,\n                        exact: false,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"length\") {\n                const tooBig = input.data.length > check.value;\n                const tooSmall = input.data.length < check.value;\n                if (tooBig || tooSmall) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    if (tooBig) {\n                        addIssueToContext(ctx, {\n                            code: ZodIssueCode.too_big,\n                            maximum: check.value,\n                            type: \"string\",\n                            inclusive: true,\n                            exact: true,\n                            message: check.message,\n                        });\n                    }\n                    else if (tooSmall) {\n                        addIssueToContext(ctx, {\n                            code: ZodIssueCode.too_small,\n                            minimum: check.value,\n                            type: \"string\",\n                            inclusive: true,\n                            exact: true,\n                            message: check.message,\n                        });\n                    }\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"email\") {\n                if (!emailRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"email\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"emoji\") {\n                if (!emojiRegex) {\n                    emojiRegex = new RegExp(_emojiRegex, \"u\");\n                }\n                if (!emojiRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"emoji\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"uuid\") {\n                if (!uuidRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"uuid\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"nanoid\") {\n                if (!nanoidRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"nanoid\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"cuid\") {\n                if (!cuidRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"cuid\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"cuid2\") {\n                if (!cuid2Regex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"cuid2\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"ulid\") {\n                if (!ulidRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"ulid\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"url\") {\n                try {\n                    new URL(input.data);\n                }\n                catch (_a) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"url\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"regex\") {\n                check.regex.lastIndex = 0;\n                const testResult = check.regex.test(input.data);\n                if (!testResult) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"regex\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"trim\") {\n                input.data = input.data.trim();\n            }\n            else if (check.kind === \"includes\") {\n                if (!input.data.includes(check.value, check.position)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: { includes: check.value, position: check.position },\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"toLowerCase\") {\n                input.data = input.data.toLowerCase();\n            }\n            else if (check.kind === \"toUpperCase\") {\n                input.data = input.data.toUpperCase();\n            }\n            else if (check.kind === \"startsWith\") {\n                if (!input.data.startsWith(check.value)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: { startsWith: check.value },\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"endsWith\") {\n                if (!input.data.endsWith(check.value)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: { endsWith: check.value },\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"datetime\") {\n                const regex = datetimeRegex(check);\n                if (!regex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: \"datetime\",\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"date\") {\n                const regex = dateRegex;\n                if (!regex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: \"date\",\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"time\") {\n                const regex = timeRegex(check);\n                if (!regex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_string,\n                        validation: \"time\",\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"duration\") {\n                if (!durationRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"duration\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"ip\") {\n                if (!isValidIP(input.data, check.version)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"ip\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"jwt\") {\n                if (!isValidJWT(input.data, check.alg)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"jwt\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"cidr\") {\n                if (!isValidCidr(input.data, check.version)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"cidr\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"base64\") {\n                if (!base64Regex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"base64\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"base64url\") {\n                if (!base64urlRegex.test(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        validation: \"base64url\",\n                        code: ZodIssueCode.invalid_string,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else {\n                util.assertNever(check);\n            }\n        }\n        return { status: status.value, value: input.data };\n    }\n    _regex(regex, validation, message) {\n        return this.refinement((data) => regex.test(data), {\n            validation,\n            code: ZodIssueCode.invalid_string,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    _addCheck(check) {\n        return new ZodString({\n            ...this._def,\n            checks: [...this._def.checks, check],\n        });\n    }\n    email(message) {\n        return this._addCheck({ kind: \"email\", ...errorUtil.errToObj(message) });\n    }\n    url(message) {\n        return this._addCheck({ kind: \"url\", ...errorUtil.errToObj(message) });\n    }\n    emoji(message) {\n        return this._addCheck({ kind: \"emoji\", ...errorUtil.errToObj(message) });\n    }\n    uuid(message) {\n        return this._addCheck({ kind: \"uuid\", ...errorUtil.errToObj(message) });\n    }\n    nanoid(message) {\n        return this._addCheck({ kind: \"nanoid\", ...errorUtil.errToObj(message) });\n    }\n    cuid(message) {\n        return this._addCheck({ kind: \"cuid\", ...errorUtil.errToObj(message) });\n    }\n    cuid2(message) {\n        return this._addCheck({ kind: \"cuid2\", ...errorUtil.errToObj(message) });\n    }\n    ulid(message) {\n        return this._addCheck({ kind: \"ulid\", ...errorUtil.errToObj(message) });\n    }\n    base64(message) {\n        return this._addCheck({ kind: \"base64\", ...errorUtil.errToObj(message) });\n    }\n    base64url(message) {\n        // base64url encoding is a modification of base64 that can safely be used in URLs and filenames\n        return this._addCheck({\n            kind: \"base64url\",\n            ...errorUtil.errToObj(message),\n        });\n    }\n    jwt(options) {\n        return this._addCheck({ kind: \"jwt\", ...errorUtil.errToObj(options) });\n    }\n    ip(options) {\n        return this._addCheck({ kind: \"ip\", ...errorUtil.errToObj(options) });\n    }\n    cidr(options) {\n        return this._addCheck({ kind: \"cidr\", ...errorUtil.errToObj(options) });\n    }\n    datetime(options) {\n        var _a, _b;\n        if (typeof options === \"string\") {\n            return this._addCheck({\n                kind: \"datetime\",\n                precision: null,\n                offset: false,\n                local: false,\n                message: options,\n            });\n        }\n        return this._addCheck({\n            kind: \"datetime\",\n            precision: typeof (options === null || options === void 0 ? void 0 : options.precision) === \"undefined\" ? null : options === null || options === void 0 ? void 0 : options.precision,\n            offset: (_a = options === null || options === void 0 ? void 0 : options.offset) !== null && _a !== void 0 ? _a : false,\n            local: (_b = options === null || options === void 0 ? void 0 : options.local) !== null && _b !== void 0 ? _b : false,\n            ...errorUtil.errToObj(options === null || options === void 0 ? void 0 : options.message),\n        });\n    }\n    date(message) {\n        return this._addCheck({ kind: \"date\", message });\n    }\n    time(options) {\n        if (typeof options === \"string\") {\n            return this._addCheck({\n                kind: \"time\",\n                precision: null,\n                message: options,\n            });\n        }\n        return this._addCheck({\n            kind: \"time\",\n            precision: typeof (options === null || options === void 0 ? void 0 : options.precision) === \"undefined\" ? null : options === null || options === void 0 ? void 0 : options.precision,\n            ...errorUtil.errToObj(options === null || options === void 0 ? void 0 : options.message),\n        });\n    }\n    duration(message) {\n        return this._addCheck({ kind: \"duration\", ...errorUtil.errToObj(message) });\n    }\n    regex(regex, message) {\n        return this._addCheck({\n            kind: \"regex\",\n            regex: regex,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    includes(value, options) {\n        return this._addCheck({\n            kind: \"includes\",\n            value: value,\n            position: options === null || options === void 0 ? void 0 : options.position,\n            ...errorUtil.errToObj(options === null || options === void 0 ? void 0 : options.message),\n        });\n    }\n    startsWith(value, message) {\n        return this._addCheck({\n            kind: \"startsWith\",\n            value: value,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    endsWith(value, message) {\n        return this._addCheck({\n            kind: \"endsWith\",\n            value: value,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    min(minLength, message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: minLength,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    max(maxLength, message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: maxLength,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    length(len, message) {\n        return this._addCheck({\n            kind: \"length\",\n            value: len,\n            ...errorUtil.errToObj(message),\n        });\n    }\n    /**\n     * Equivalent to `.min(1)`\n     */\n    nonempty(message) {\n        return this.min(1, errorUtil.errToObj(message));\n    }\n    trim() {\n        return new ZodString({\n            ...this._def,\n            checks: [...this._def.checks, { kind: \"trim\" }],\n        });\n    }\n    toLowerCase() {\n        return new ZodString({\n            ...this._def,\n            checks: [...this._def.checks, { kind: \"toLowerCase\" }],\n        });\n    }\n    toUpperCase() {\n        return new ZodString({\n            ...this._def,\n            checks: [...this._def.checks, { kind: \"toUpperCase\" }],\n        });\n    }\n    get isDatetime() {\n        return !!this._def.checks.find((ch) => ch.kind === \"datetime\");\n    }\n    get isDate() {\n        return !!this._def.checks.find((ch) => ch.kind === \"date\");\n    }\n    get isTime() {\n        return !!this._def.checks.find((ch) => ch.kind === \"time\");\n    }\n    get isDuration() {\n        return !!this._def.checks.find((ch) => ch.kind === \"duration\");\n    }\n    get isEmail() {\n        return !!this._def.checks.find((ch) => ch.kind === \"email\");\n    }\n    get isURL() {\n        return !!this._def.checks.find((ch) => ch.kind === \"url\");\n    }\n    get isEmoji() {\n        return !!this._def.checks.find((ch) => ch.kind === \"emoji\");\n    }\n    get isUUID() {\n        return !!this._def.checks.find((ch) => ch.kind === \"uuid\");\n    }\n    get isNANOID() {\n        return !!this._def.checks.find((ch) => ch.kind === \"nanoid\");\n    }\n    get isCUID() {\n        return !!this._def.checks.find((ch) => ch.kind === \"cuid\");\n    }\n    get isCUID2() {\n        return !!this._def.checks.find((ch) => ch.kind === \"cuid2\");\n    }\n    get isULID() {\n        return !!this._def.checks.find((ch) => ch.kind === \"ulid\");\n    }\n    get isIP() {\n        return !!this._def.checks.find((ch) => ch.kind === \"ip\");\n    }\n    get isCIDR() {\n        return !!this._def.checks.find((ch) => ch.kind === \"cidr\");\n    }\n    get isBase64() {\n        return !!this._def.checks.find((ch) => ch.kind === \"base64\");\n    }\n    get isBase64url() {\n        // base64url encoding is a modification of base64 that can safely be used in URLs and filenames\n        return !!this._def.checks.find((ch) => ch.kind === \"base64url\");\n    }\n    get minLength() {\n        let min = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"min\") {\n                if (min === null || ch.value > min)\n                    min = ch.value;\n            }\n        }\n        return min;\n    }\n    get maxLength() {\n        let max = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"max\") {\n                if (max === null || ch.value < max)\n                    max = ch.value;\n            }\n        }\n        return max;\n    }\n}\nZodString.create = (params) => {\n    var _a;\n    return new ZodString({\n        checks: [],\n        typeName: ZodFirstPartyTypeKind.ZodString,\n        coerce: (_a = params === null || params === void 0 ? void 0 : params.coerce) !== null && _a !== void 0 ? _a : false,\n        ...processCreateParams(params),\n    });\n};\n// https://stackoverflow.com/questions/3966484/why-does-modulus-operator-return-fractional-number-in-javascript/31711034#31711034\nfunction floatSafeRemainder(val, step) {\n    const valDecCount = (val.toString().split(\".\")[1] || \"\").length;\n    const stepDecCount = (step.toString().split(\".\")[1] || \"\").length;\n    const decCount = valDecCount > stepDecCount ? valDecCount : stepDecCount;\n    const valInt = parseInt(val.toFixed(decCount).replace(\".\", \"\"));\n    const stepInt = parseInt(step.toFixed(decCount).replace(\".\", \"\"));\n    return (valInt % stepInt) / Math.pow(10, decCount);\n}\nclass ZodNumber extends ZodType {\n    constructor() {\n        super(...arguments);\n        this.min = this.gte;\n        this.max = this.lte;\n        this.step = this.multipleOf;\n    }\n    _parse(input) {\n        if (this._def.coerce) {\n            input.data = Number(input.data);\n        }\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.number) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.number,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        let ctx = undefined;\n        const status = new ParseStatus();\n        for (const check of this._def.checks) {\n            if (check.kind === \"int\") {\n                if (!util.isInteger(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.invalid_type,\n                        expected: \"integer\",\n                        received: \"float\",\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"min\") {\n                const tooSmall = check.inclusive\n                    ? input.data < check.value\n                    : input.data <= check.value;\n                if (tooSmall) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_small,\n                        minimum: check.value,\n                        type: \"number\",\n                        inclusive: check.inclusive,\n                        exact: false,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"max\") {\n                const tooBig = check.inclusive\n                    ? input.data > check.value\n                    : input.data >= check.value;\n                if (tooBig) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_big,\n                        maximum: check.value,\n                        type: \"number\",\n                        inclusive: check.inclusive,\n                        exact: false,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"multipleOf\") {\n                if (floatSafeRemainder(input.data, check.value) !== 0) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.not_multiple_of,\n                        multipleOf: check.value,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"finite\") {\n                if (!Number.isFinite(input.data)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.not_finite,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else {\n                util.assertNever(check);\n            }\n        }\n        return { status: status.value, value: input.data };\n    }\n    gte(value, message) {\n        return this.setLimit(\"min\", value, true, errorUtil.toString(message));\n    }\n    gt(value, message) {\n        return this.setLimit(\"min\", value, false, errorUtil.toString(message));\n    }\n    lte(value, message) {\n        return this.setLimit(\"max\", value, true, errorUtil.toString(message));\n    }\n    lt(value, message) {\n        return this.setLimit(\"max\", value, false, errorUtil.toString(message));\n    }\n    setLimit(kind, value, inclusive, message) {\n        return new ZodNumber({\n            ...this._def,\n            checks: [\n                ...this._def.checks,\n                {\n                    kind,\n                    value,\n                    inclusive,\n                    message: errorUtil.toString(message),\n                },\n            ],\n        });\n    }\n    _addCheck(check) {\n        return new ZodNumber({\n            ...this._def,\n            checks: [...this._def.checks, check],\n        });\n    }\n    int(message) {\n        return this._addCheck({\n            kind: \"int\",\n            message: errorUtil.toString(message),\n        });\n    }\n    positive(message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: 0,\n            inclusive: false,\n            message: errorUtil.toString(message),\n        });\n    }\n    negative(message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: 0,\n            inclusive: false,\n            message: errorUtil.toString(message),\n        });\n    }\n    nonpositive(message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: 0,\n            inclusive: true,\n            message: errorUtil.toString(message),\n        });\n    }\n    nonnegative(message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: 0,\n            inclusive: true,\n            message: errorUtil.toString(message),\n        });\n    }\n    multipleOf(value, message) {\n        return this._addCheck({\n            kind: \"multipleOf\",\n            value: value,\n            message: errorUtil.toString(message),\n        });\n    }\n    finite(message) {\n        return this._addCheck({\n            kind: \"finite\",\n            message: errorUtil.toString(message),\n        });\n    }\n    safe(message) {\n        return this._addCheck({\n            kind: \"min\",\n            inclusive: true,\n            value: Number.MIN_SAFE_INTEGER,\n            message: errorUtil.toString(message),\n        })._addCheck({\n            kind: \"max\",\n            inclusive: true,\n            value: Number.MAX_SAFE_INTEGER,\n            message: errorUtil.toString(message),\n        });\n    }\n    get minValue() {\n        let min = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"min\") {\n                if (min === null || ch.value > min)\n                    min = ch.value;\n            }\n        }\n        return min;\n    }\n    get maxValue() {\n        let max = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"max\") {\n                if (max === null || ch.value < max)\n                    max = ch.value;\n            }\n        }\n        return max;\n    }\n    get isInt() {\n        return !!this._def.checks.find((ch) => ch.kind === \"int\" ||\n            (ch.kind === \"multipleOf\" && util.isInteger(ch.value)));\n    }\n    get isFinite() {\n        let max = null, min = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"finite\" ||\n                ch.kind === \"int\" ||\n                ch.kind === \"multipleOf\") {\n                return true;\n            }\n            else if (ch.kind === \"min\") {\n                if (min === null || ch.value > min)\n                    min = ch.value;\n            }\n            else if (ch.kind === \"max\") {\n                if (max === null || ch.value < max)\n                    max = ch.value;\n            }\n        }\n        return Number.isFinite(min) && Number.isFinite(max);\n    }\n}\nZodNumber.create = (params) => {\n    return new ZodNumber({\n        checks: [],\n        typeName: ZodFirstPartyTypeKind.ZodNumber,\n        coerce: (params === null || params === void 0 ? void 0 : params.coerce) || false,\n        ...processCreateParams(params),\n    });\n};\nclass ZodBigInt extends ZodType {\n    constructor() {\n        super(...arguments);\n        this.min = this.gte;\n        this.max = this.lte;\n    }\n    _parse(input) {\n        if (this._def.coerce) {\n            try {\n                input.data = BigInt(input.data);\n            }\n            catch (_a) {\n                return this._getInvalidInput(input);\n            }\n        }\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.bigint) {\n            return this._getInvalidInput(input);\n        }\n        let ctx = undefined;\n        const status = new ParseStatus();\n        for (const check of this._def.checks) {\n            if (check.kind === \"min\") {\n                const tooSmall = check.inclusive\n                    ? input.data < check.value\n                    : input.data <= check.value;\n                if (tooSmall) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_small,\n                        type: \"bigint\",\n                        minimum: check.value,\n                        inclusive: check.inclusive,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"max\") {\n                const tooBig = check.inclusive\n                    ? input.data > check.value\n                    : input.data >= check.value;\n                if (tooBig) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_big,\n                        type: \"bigint\",\n                        maximum: check.value,\n                        inclusive: check.inclusive,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"multipleOf\") {\n                if (input.data % check.value !== BigInt(0)) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.not_multiple_of,\n                        multipleOf: check.value,\n                        message: check.message,\n                    });\n                    status.dirty();\n                }\n            }\n            else {\n                util.assertNever(check);\n            }\n        }\n        return { status: status.value, value: input.data };\n    }\n    _getInvalidInput(input) {\n        const ctx = this._getOrReturnCtx(input);\n        addIssueToContext(ctx, {\n            code: ZodIssueCode.invalid_type,\n            expected: ZodParsedType.bigint,\n            received: ctx.parsedType,\n        });\n        return INVALID;\n    }\n    gte(value, message) {\n        return this.setLimit(\"min\", value, true, errorUtil.toString(message));\n    }\n    gt(value, message) {\n        return this.setLimit(\"min\", value, false, errorUtil.toString(message));\n    }\n    lte(value, message) {\n        return this.setLimit(\"max\", value, true, errorUtil.toString(message));\n    }\n    lt(value, message) {\n        return this.setLimit(\"max\", value, false, errorUtil.toString(message));\n    }\n    setLimit(kind, value, inclusive, message) {\n        return new ZodBigInt({\n            ...this._def,\n            checks: [\n                ...this._def.checks,\n                {\n                    kind,\n                    value,\n                    inclusive,\n                    message: errorUtil.toString(message),\n                },\n            ],\n        });\n    }\n    _addCheck(check) {\n        return new ZodBigInt({\n            ...this._def,\n            checks: [...this._def.checks, check],\n        });\n    }\n    positive(message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: BigInt(0),\n            inclusive: false,\n            message: errorUtil.toString(message),\n        });\n    }\n    negative(message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: BigInt(0),\n            inclusive: false,\n            message: errorUtil.toString(message),\n        });\n    }\n    nonpositive(message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: BigInt(0),\n            inclusive: true,\n            message: errorUtil.toString(message),\n        });\n    }\n    nonnegative(message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: BigInt(0),\n            inclusive: true,\n            message: errorUtil.toString(message),\n        });\n    }\n    multipleOf(value, message) {\n        return this._addCheck({\n            kind: \"multipleOf\",\n            value,\n            message: errorUtil.toString(message),\n        });\n    }\n    get minValue() {\n        let min = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"min\") {\n                if (min === null || ch.value > min)\n                    min = ch.value;\n            }\n        }\n        return min;\n    }\n    get maxValue() {\n        let max = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"max\") {\n                if (max === null || ch.value < max)\n                    max = ch.value;\n            }\n        }\n        return max;\n    }\n}\nZodBigInt.create = (params) => {\n    var _a;\n    return new ZodBigInt({\n        checks: [],\n        typeName: ZodFirstPartyTypeKind.ZodBigInt,\n        coerce: (_a = params === null || params === void 0 ? void 0 : params.coerce) !== null && _a !== void 0 ? _a : false,\n        ...processCreateParams(params),\n    });\n};\nclass ZodBoolean extends ZodType {\n    _parse(input) {\n        if (this._def.coerce) {\n            input.data = Boolean(input.data);\n        }\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.boolean) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.boolean,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n}\nZodBoolean.create = (params) => {\n    return new ZodBoolean({\n        typeName: ZodFirstPartyTypeKind.ZodBoolean,\n        coerce: (params === null || params === void 0 ? void 0 : params.coerce) || false,\n        ...processCreateParams(params),\n    });\n};\nclass ZodDate extends ZodType {\n    _parse(input) {\n        if (this._def.coerce) {\n            input.data = new Date(input.data);\n        }\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.date) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.date,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        if (isNaN(input.data.getTime())) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_date,\n            });\n            return INVALID;\n        }\n        const status = new ParseStatus();\n        let ctx = undefined;\n        for (const check of this._def.checks) {\n            if (check.kind === \"min\") {\n                if (input.data.getTime() < check.value) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_small,\n                        message: check.message,\n                        inclusive: true,\n                        exact: false,\n                        minimum: check.value,\n                        type: \"date\",\n                    });\n                    status.dirty();\n                }\n            }\n            else if (check.kind === \"max\") {\n                if (input.data.getTime() > check.value) {\n                    ctx = this._getOrReturnCtx(input, ctx);\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.too_big,\n                        message: check.message,\n                        inclusive: true,\n                        exact: false,\n                        maximum: check.value,\n                        type: \"date\",\n                    });\n                    status.dirty();\n                }\n            }\n            else {\n                util.assertNever(check);\n            }\n        }\n        return {\n            status: status.value,\n            value: new Date(input.data.getTime()),\n        };\n    }\n    _addCheck(check) {\n        return new ZodDate({\n            ...this._def,\n            checks: [...this._def.checks, check],\n        });\n    }\n    min(minDate, message) {\n        return this._addCheck({\n            kind: \"min\",\n            value: minDate.getTime(),\n            message: errorUtil.toString(message),\n        });\n    }\n    max(maxDate, message) {\n        return this._addCheck({\n            kind: \"max\",\n            value: maxDate.getTime(),\n            message: errorUtil.toString(message),\n        });\n    }\n    get minDate() {\n        let min = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"min\") {\n                if (min === null || ch.value > min)\n                    min = ch.value;\n            }\n        }\n        return min != null ? new Date(min) : null;\n    }\n    get maxDate() {\n        let max = null;\n        for (const ch of this._def.checks) {\n            if (ch.kind === \"max\") {\n                if (max === null || ch.value < max)\n                    max = ch.value;\n            }\n        }\n        return max != null ? new Date(max) : null;\n    }\n}\nZodDate.create = (params) => {\n    return new ZodDate({\n        checks: [],\n        coerce: (params === null || params === void 0 ? void 0 : params.coerce) || false,\n        typeName: ZodFirstPartyTypeKind.ZodDate,\n        ...processCreateParams(params),\n    });\n};\nclass ZodSymbol extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.symbol) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.symbol,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n}\nZodSymbol.create = (params) => {\n    return new ZodSymbol({\n        typeName: ZodFirstPartyTypeKind.ZodSymbol,\n        ...processCreateParams(params),\n    });\n};\nclass ZodUndefined extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.undefined) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.undefined,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n}\nZodUndefined.create = (params) => {\n    return new ZodUndefined({\n        typeName: ZodFirstPartyTypeKind.ZodUndefined,\n        ...processCreateParams(params),\n    });\n};\nclass ZodNull extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.null) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.null,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n}\nZodNull.create = (params) => {\n    return new ZodNull({\n        typeName: ZodFirstPartyTypeKind.ZodNull,\n        ...processCreateParams(params),\n    });\n};\nclass ZodAny extends ZodType {\n    constructor() {\n        super(...arguments);\n        // to prevent instances of other classes from extending ZodAny. this causes issues with catchall in ZodObject.\n        this._any = true;\n    }\n    _parse(input) {\n        return OK(input.data);\n    }\n}\nZodAny.create = (params) => {\n    return new ZodAny({\n        typeName: ZodFirstPartyTypeKind.ZodAny,\n        ...processCreateParams(params),\n    });\n};\nclass ZodUnknown extends ZodType {\n    constructor() {\n        super(...arguments);\n        // required\n        this._unknown = true;\n    }\n    _parse(input) {\n        return OK(input.data);\n    }\n}\nZodUnknown.create = (params) => {\n    return new ZodUnknown({\n        typeName: ZodFirstPartyTypeKind.ZodUnknown,\n        ...processCreateParams(params),\n    });\n};\nclass ZodNever extends ZodType {\n    _parse(input) {\n        const ctx = this._getOrReturnCtx(input);\n        addIssueToContext(ctx, {\n            code: ZodIssueCode.invalid_type,\n            expected: ZodParsedType.never,\n            received: ctx.parsedType,\n        });\n        return INVALID;\n    }\n}\nZodNever.create = (params) => {\n    return new ZodNever({\n        typeName: ZodFirstPartyTypeKind.ZodNever,\n        ...processCreateParams(params),\n    });\n};\nclass ZodVoid extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.undefined) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.void,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n}\nZodVoid.create = (params) => {\n    return new ZodVoid({\n        typeName: ZodFirstPartyTypeKind.ZodVoid,\n        ...processCreateParams(params),\n    });\n};\nclass ZodArray extends ZodType {\n    _parse(input) {\n        const { ctx, status } = this._processInputParams(input);\n        const def = this._def;\n        if (ctx.parsedType !== ZodParsedType.array) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.array,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        if (def.exactLength !== null) {\n            const tooBig = ctx.data.length > def.exactLength.value;\n            const tooSmall = ctx.data.length < def.exactLength.value;\n            if (tooBig || tooSmall) {\n                addIssueToContext(ctx, {\n                    code: tooBig ? ZodIssueCode.too_big : ZodIssueCode.too_small,\n                    minimum: (tooSmall ? def.exactLength.value : undefined),\n                    maximum: (tooBig ? def.exactLength.value : undefined),\n                    type: \"array\",\n                    inclusive: true,\n                    exact: true,\n                    message: def.exactLength.message,\n                });\n                status.dirty();\n            }\n        }\n        if (def.minLength !== null) {\n            if (ctx.data.length < def.minLength.value) {\n                addIssueToContext(ctx, {\n                    code: ZodIssueCode.too_small,\n                    minimum: def.minLength.value,\n                    type: \"array\",\n                    inclusive: true,\n                    exact: false,\n                    message: def.minLength.message,\n                });\n                status.dirty();\n            }\n        }\n        if (def.maxLength !== null) {\n            if (ctx.data.length > def.maxLength.value) {\n                addIssueToContext(ctx, {\n                    code: ZodIssueCode.too_big,\n                    maximum: def.maxLength.value,\n                    type: \"array\",\n                    inclusive: true,\n                    exact: false,\n                    message: def.maxLength.message,\n                });\n                status.dirty();\n            }\n        }\n        if (ctx.common.async) {\n            return Promise.all([...ctx.data].map((item, i) => {\n                return def.type._parseAsync(new ParseInputLazyPath(ctx, item, ctx.path, i));\n            })).then((result) => {\n                return ParseStatus.mergeArray(status, result);\n            });\n        }\n        const result = [...ctx.data].map((item, i) => {\n            return def.type._parseSync(new ParseInputLazyPath(ctx, item, ctx.path, i));\n        });\n        return ParseStatus.mergeArray(status, result);\n    }\n    get element() {\n        return this._def.type;\n    }\n    min(minLength, message) {\n        return new ZodArray({\n            ...this._def,\n            minLength: { value: minLength, message: errorUtil.toString(message) },\n        });\n    }\n    max(maxLength, message) {\n        return new ZodArray({\n            ...this._def,\n            maxLength: { value: maxLength, message: errorUtil.toString(message) },\n        });\n    }\n    length(len, message) {\n        return new ZodArray({\n            ...this._def,\n            exactLength: { value: len, message: errorUtil.toString(message) },\n        });\n    }\n    nonempty(message) {\n        return this.min(1, message);\n    }\n}\nZodArray.create = (schema, params) => {\n    return new ZodArray({\n        type: schema,\n        minLength: null,\n        maxLength: null,\n        exactLength: null,\n        typeName: ZodFirstPartyTypeKind.ZodArray,\n        ...processCreateParams(params),\n    });\n};\nfunction deepPartialify(schema) {\n    if (schema instanceof ZodObject) {\n        const newShape = {};\n        for (const key in schema.shape) {\n            const fieldSchema = schema.shape[key];\n            newShape[key] = ZodOptional.create(deepPartialify(fieldSchema));\n        }\n        return new ZodObject({\n            ...schema._def,\n            shape: () => newShape,\n        });\n    }\n    else if (schema instanceof ZodArray) {\n        return new ZodArray({\n            ...schema._def,\n            type: deepPartialify(schema.element),\n        });\n    }\n    else if (schema instanceof ZodOptional) {\n        return ZodOptional.create(deepPartialify(schema.unwrap()));\n    }\n    else if (schema instanceof ZodNullable) {\n        return ZodNullable.create(deepPartialify(schema.unwrap()));\n    }\n    else if (schema instanceof ZodTuple) {\n        return ZodTuple.create(schema.items.map((item) => deepPartialify(item)));\n    }\n    else {\n        return schema;\n    }\n}\nclass ZodObject extends ZodType {\n    constructor() {\n        super(...arguments);\n        this._cached = null;\n        /**\n         * @deprecated In most cases, this is no longer needed - unknown properties are now silently stripped.\n         * If you want to pass through unknown properties, use `.passthrough()` instead.\n         */\n        this.nonstrict = this.passthrough;\n        // extend<\n        //   Augmentation extends ZodRawShape,\n        //   NewOutput extends util.flatten<{\n        //     [k in keyof Augmentation | keyof Output]: k extends keyof Augmentation\n        //       ? Augmentation[k][\"_output\"]\n        //       : k extends keyof Output\n        //       ? Output[k]\n        //       : never;\n        //   }>,\n        //   NewInput extends util.flatten<{\n        //     [k in keyof Augmentation | keyof Input]: k extends keyof Augmentation\n        //       ? Augmentation[k][\"_input\"]\n        //       : k extends keyof Input\n        //       ? Input[k]\n        //       : never;\n        //   }>\n        // >(\n        //   augmentation: Augmentation\n        // ): ZodObject<\n        //   extendShape<T, Augmentation>,\n        //   UnknownKeys,\n        //   Catchall,\n        //   NewOutput,\n        //   NewInput\n        // > {\n        //   return new ZodObject({\n        //     ...this._def,\n        //     shape: () => ({\n        //       ...this._def.shape(),\n        //       ...augmentation,\n        //     }),\n        //   }) as any;\n        // }\n        /**\n         * @deprecated Use `.extend` instead\n         *  */\n        this.augment = this.extend;\n    }\n    _getCached() {\n        if (this._cached !== null)\n            return this._cached;\n        const shape = this._def.shape();\n        const keys = util.objectKeys(shape);\n        return (this._cached = { shape, keys });\n    }\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.object) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.object,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const { status, ctx } = this._processInputParams(input);\n        const { shape, keys: shapeKeys } = this._getCached();\n        const extraKeys = [];\n        if (!(this._def.catchall instanceof ZodNever &&\n            this._def.unknownKeys === \"strip\")) {\n            for (const key in ctx.data) {\n                if (!shapeKeys.includes(key)) {\n                    extraKeys.push(key);\n                }\n            }\n        }\n        const pairs = [];\n        for (const key of shapeKeys) {\n            const keyValidator = shape[key];\n            const value = ctx.data[key];\n            pairs.push({\n                key: { status: \"valid\", value: key },\n                value: keyValidator._parse(new ParseInputLazyPath(ctx, value, ctx.path, key)),\n                alwaysSet: key in ctx.data,\n            });\n        }\n        if (this._def.catchall instanceof ZodNever) {\n            const unknownKeys = this._def.unknownKeys;\n            if (unknownKeys === \"passthrough\") {\n                for (const key of extraKeys) {\n                    pairs.push({\n                        key: { status: \"valid\", value: key },\n                        value: { status: \"valid\", value: ctx.data[key] },\n                    });\n                }\n            }\n            else if (unknownKeys === \"strict\") {\n                if (extraKeys.length > 0) {\n                    addIssueToContext(ctx, {\n                        code: ZodIssueCode.unrecognized_keys,\n                        keys: extraKeys,\n                    });\n                    status.dirty();\n                }\n            }\n            else if (unknownKeys === \"strip\") ;\n            else {\n                throw new Error(`Internal ZodObject error: invalid unknownKeys value.`);\n            }\n        }\n        else {\n            // run catchall validation\n            const catchall = this._def.catchall;\n            for (const key of extraKeys) {\n                const value = ctx.data[key];\n                pairs.push({\n                    key: { status: \"valid\", value: key },\n                    value: catchall._parse(new ParseInputLazyPath(ctx, value, ctx.path, key) //, ctx.child(key), value, getParsedType(value)\n                    ),\n                    alwaysSet: key in ctx.data,\n                });\n            }\n        }\n        if (ctx.common.async) {\n            return Promise.resolve()\n                .then(async () => {\n                const syncPairs = [];\n                for (const pair of pairs) {\n                    const key = await pair.key;\n                    const value = await pair.value;\n                    syncPairs.push({\n                        key,\n                        value,\n                        alwaysSet: pair.alwaysSet,\n                    });\n                }\n                return syncPairs;\n            })\n                .then((syncPairs) => {\n                return ParseStatus.mergeObjectSync(status, syncPairs);\n            });\n        }\n        else {\n            return ParseStatus.mergeObjectSync(status, pairs);\n        }\n    }\n    get shape() {\n        return this._def.shape();\n    }\n    strict(message) {\n        errorUtil.errToObj;\n        return new ZodObject({\n            ...this._def,\n            unknownKeys: \"strict\",\n            ...(message !== undefined\n                ? {\n                    errorMap: (issue, ctx) => {\n                        var _a, _b, _c, _d;\n                        const defaultError = (_c = (_b = (_a = this._def).errorMap) === null || _b === void 0 ? void 0 : _b.call(_a, issue, ctx).message) !== null && _c !== void 0 ? _c : ctx.defaultError;\n                        if (issue.code === \"unrecognized_keys\")\n                            return {\n                                message: (_d = errorUtil.errToObj(message).message) !== null && _d !== void 0 ? _d : defaultError,\n                            };\n                        return {\n                            message: defaultError,\n                        };\n                    },\n                }\n                : {}),\n        });\n    }\n    strip() {\n        return new ZodObject({\n            ...this._def,\n            unknownKeys: \"strip\",\n        });\n    }\n    passthrough() {\n        return new ZodObject({\n            ...this._def,\n            unknownKeys: \"passthrough\",\n        });\n    }\n    // const AugmentFactory =\n    //   <Def extends ZodObjectDef>(def: Def) =>\n    //   <Augmentation extends ZodRawShape>(\n    //     augmentation: Augmentation\n    //   ): ZodObject<\n    //     extendShape<ReturnType<Def[\"shape\"]>, Augmentation>,\n    //     Def[\"unknownKeys\"],\n    //     Def[\"catchall\"]\n    //   > => {\n    //     return new ZodObject({\n    //       ...def,\n    //       shape: () => ({\n    //         ...def.shape(),\n    //         ...augmentation,\n    //       }),\n    //     }) as any;\n    //   };\n    extend(augmentation) {\n        return new ZodObject({\n            ...this._def,\n            shape: () => ({\n                ...this._def.shape(),\n                ...augmentation,\n            }),\n        });\n    }\n    /**\n     * Prior to zod@1.0.12 there was a bug in the\n     * inferred type of merged objects. Please\n     * upgrade if you are experiencing issues.\n     */\n    merge(merging) {\n        const merged = new ZodObject({\n            unknownKeys: merging._def.unknownKeys,\n            catchall: merging._def.catchall,\n            shape: () => ({\n                ...this._def.shape(),\n                ...merging._def.shape(),\n            }),\n            typeName: ZodFirstPartyTypeKind.ZodObject,\n        });\n        return merged;\n    }\n    // merge<\n    //   Incoming extends AnyZodObject,\n    //   Augmentation extends Incoming[\"shape\"],\n    //   NewOutput extends {\n    //     [k in keyof Augmentation | keyof Output]: k extends keyof Augmentation\n    //       ? Augmentation[k][\"_output\"]\n    //       : k extends keyof Output\n    //       ? Output[k]\n    //       : never;\n    //   },\n    //   NewInput extends {\n    //     [k in keyof Augmentation | keyof Input]: k extends keyof Augmentation\n    //       ? Augmentation[k][\"_input\"]\n    //       : k extends keyof Input\n    //       ? Input[k]\n    //       : never;\n    //   }\n    // >(\n    //   merging: Incoming\n    // ): ZodObject<\n    //   extendShape<T, ReturnType<Incoming[\"_def\"][\"shape\"]>>,\n    //   Incoming[\"_def\"][\"unknownKeys\"],\n    //   Incoming[\"_def\"][\"catchall\"],\n    //   NewOutput,\n    //   NewInput\n    // > {\n    //   const merged: any = new ZodObject({\n    //     unknownKeys: merging._def.unknownKeys,\n    //     catchall: merging._def.catchall,\n    //     shape: () =>\n    //       objectUtil.mergeShapes(this._def.shape(), merging._def.shape()),\n    //     typeName: ZodFirstPartyTypeKind.ZodObject,\n    //   }) as any;\n    //   return merged;\n    // }\n    setKey(key, schema) {\n        return this.augment({ [key]: schema });\n    }\n    // merge<Incoming extends AnyZodObject>(\n    //   merging: Incoming\n    // ): //ZodObject<T & Incoming[\"_shape\"], UnknownKeys, Catchall> = (merging) => {\n    // ZodObject<\n    //   extendShape<T, ReturnType<Incoming[\"_def\"][\"shape\"]>>,\n    //   Incoming[\"_def\"][\"unknownKeys\"],\n    //   Incoming[\"_def\"][\"catchall\"]\n    // > {\n    //   // const mergedShape = objectUtil.mergeShapes(\n    //   //   this._def.shape(),\n    //   //   merging._def.shape()\n    //   // );\n    //   const merged: any = new ZodObject({\n    //     unknownKeys: merging._def.unknownKeys,\n    //     catchall: merging._def.catchall,\n    //     shape: () =>\n    //       objectUtil.mergeShapes(this._def.shape(), merging._def.shape()),\n    //     typeName: ZodFirstPartyTypeKind.ZodObject,\n    //   }) as any;\n    //   return merged;\n    // }\n    catchall(index) {\n        return new ZodObject({\n            ...this._def,\n            catchall: index,\n        });\n    }\n    pick(mask) {\n        const shape = {};\n        util.objectKeys(mask).forEach((key) => {\n            if (mask[key] && this.shape[key]) {\n                shape[key] = this.shape[key];\n            }\n        });\n        return new ZodObject({\n            ...this._def,\n            shape: () => shape,\n        });\n    }\n    omit(mask) {\n        const shape = {};\n        util.objectKeys(this.shape).forEach((key) => {\n            if (!mask[key]) {\n                shape[key] = this.shape[key];\n            }\n        });\n        return new ZodObject({\n            ...this._def,\n            shape: () => shape,\n        });\n    }\n    /**\n     * @deprecated\n     */\n    deepPartial() {\n        return deepPartialify(this);\n    }\n    partial(mask) {\n        const newShape = {};\n        util.objectKeys(this.shape).forEach((key) => {\n            const fieldSchema = this.shape[key];\n            if (mask && !mask[key]) {\n                newShape[key] = fieldSchema;\n            }\n            else {\n                newShape[key] = fieldSchema.optional();\n            }\n        });\n        return new ZodObject({\n            ...this._def,\n            shape: () => newShape,\n        });\n    }\n    required(mask) {\n        const newShape = {};\n        util.objectKeys(this.shape).forEach((key) => {\n            if (mask && !mask[key]) {\n                newShape[key] = this.shape[key];\n            }\n            else {\n                const fieldSchema = this.shape[key];\n                let newField = fieldSchema;\n                while (newField instanceof ZodOptional) {\n                    newField = newField._def.innerType;\n                }\n                newShape[key] = newField;\n            }\n        });\n        return new ZodObject({\n            ...this._def,\n            shape: () => newShape,\n        });\n    }\n    keyof() {\n        return createZodEnum(util.objectKeys(this.shape));\n    }\n}\nZodObject.create = (shape, params) => {\n    return new ZodObject({\n        shape: () => shape,\n        unknownKeys: \"strip\",\n        catchall: ZodNever.create(),\n        typeName: ZodFirstPartyTypeKind.ZodObject,\n        ...processCreateParams(params),\n    });\n};\nZodObject.strictCreate = (shape, params) => {\n    return new ZodObject({\n        shape: () => shape,\n        unknownKeys: \"strict\",\n        catchall: ZodNever.create(),\n        typeName: ZodFirstPartyTypeKind.ZodObject,\n        ...processCreateParams(params),\n    });\n};\nZodObject.lazycreate = (shape, params) => {\n    return new ZodObject({\n        shape,\n        unknownKeys: \"strip\",\n        catchall: ZodNever.create(),\n        typeName: ZodFirstPartyTypeKind.ZodObject,\n        ...processCreateParams(params),\n    });\n};\nclass ZodUnion extends ZodType {\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        const options = this._def.options;\n        function handleResults(results) {\n            // return first issue-free validation if it exists\n            for (const result of results) {\n                if (result.result.status === \"valid\") {\n                    return result.result;\n                }\n            }\n            for (const result of results) {\n                if (result.result.status === \"dirty\") {\n                    // add issues from dirty option\n                    ctx.common.issues.push(...result.ctx.common.issues);\n                    return result.result;\n                }\n            }\n            // return invalid\n            const unionErrors = results.map((result) => new ZodError(result.ctx.common.issues));\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_union,\n                unionErrors,\n            });\n            return INVALID;\n        }\n        if (ctx.common.async) {\n            return Promise.all(options.map(async (option) => {\n                const childCtx = {\n                    ...ctx,\n                    common: {\n                        ...ctx.common,\n                        issues: [],\n                    },\n                    parent: null,\n                };\n                return {\n                    result: await option._parseAsync({\n                        data: ctx.data,\n                        path: ctx.path,\n                        parent: childCtx,\n                    }),\n                    ctx: childCtx,\n                };\n            })).then(handleResults);\n        }\n        else {\n            let dirty = undefined;\n            const issues = [];\n            for (const option of options) {\n                const childCtx = {\n                    ...ctx,\n                    common: {\n                        ...ctx.common,\n                        issues: [],\n                    },\n                    parent: null,\n                };\n                const result = option._parseSync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: childCtx,\n                });\n                if (result.status === \"valid\") {\n                    return result;\n                }\n                else if (result.status === \"dirty\" && !dirty) {\n                    dirty = { result, ctx: childCtx };\n                }\n                if (childCtx.common.issues.length) {\n                    issues.push(childCtx.common.issues);\n                }\n            }\n            if (dirty) {\n                ctx.common.issues.push(...dirty.ctx.common.issues);\n                return dirty.result;\n            }\n            const unionErrors = issues.map((issues) => new ZodError(issues));\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_union,\n                unionErrors,\n            });\n            return INVALID;\n        }\n    }\n    get options() {\n        return this._def.options;\n    }\n}\nZodUnion.create = (types, params) => {\n    return new ZodUnion({\n        options: types,\n        typeName: ZodFirstPartyTypeKind.ZodUnion,\n        ...processCreateParams(params),\n    });\n};\n/////////////////////////////////////////////////////\n/////////////////////////////////////////////////////\n//////////                                 //////////\n//////////      ZodDiscriminatedUnion      //////////\n//////////                                 //////////\n/////////////////////////////////////////////////////\n/////////////////////////////////////////////////////\nconst getDiscriminator = (type) => {\n    if (type instanceof ZodLazy) {\n        return getDiscriminator(type.schema);\n    }\n    else if (type instanceof ZodEffects) {\n        return getDiscriminator(type.innerType());\n    }\n    else if (type instanceof ZodLiteral) {\n        return [type.value];\n    }\n    else if (type instanceof ZodEnum) {\n        return type.options;\n    }\n    else if (type instanceof ZodNativeEnum) {\n        // eslint-disable-next-line ban/ban\n        return util.objectValues(type.enum);\n    }\n    else if (type instanceof ZodDefault) {\n        return getDiscriminator(type._def.innerType);\n    }\n    else if (type instanceof ZodUndefined) {\n        return [undefined];\n    }\n    else if (type instanceof ZodNull) {\n        return [null];\n    }\n    else if (type instanceof ZodOptional) {\n        return [undefined, ...getDiscriminator(type.unwrap())];\n    }\n    else if (type instanceof ZodNullable) {\n        return [null, ...getDiscriminator(type.unwrap())];\n    }\n    else if (type instanceof ZodBranded) {\n        return getDiscriminator(type.unwrap());\n    }\n    else if (type instanceof ZodReadonly) {\n        return getDiscriminator(type.unwrap());\n    }\n    else if (type instanceof ZodCatch) {\n        return getDiscriminator(type._def.innerType);\n    }\n    else {\n        return [];\n    }\n};\nclass ZodDiscriminatedUnion extends ZodType {\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.object) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.object,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const discriminator = this.discriminator;\n        const discriminatorValue = ctx.data[discriminator];\n        const option = this.optionsMap.get(discriminatorValue);\n        if (!option) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_union_discriminator,\n                options: Array.from(this.optionsMap.keys()),\n                path: [discriminator],\n            });\n            return INVALID;\n        }\n        if (ctx.common.async) {\n            return option._parseAsync({\n                data: ctx.data,\n                path: ctx.path,\n                parent: ctx,\n            });\n        }\n        else {\n            return option._parseSync({\n                data: ctx.data,\n                path: ctx.path,\n                parent: ctx,\n            });\n        }\n    }\n    get discriminator() {\n        return this._def.discriminator;\n    }\n    get options() {\n        return this._def.options;\n    }\n    get optionsMap() {\n        return this._def.optionsMap;\n    }\n    /**\n     * The constructor of the discriminated union schema. Its behaviour is very similar to that of the normal z.union() constructor.\n     * However, it only allows a union of objects, all of which need to share a discriminator property. This property must\n     * have a different value for each object in the union.\n     * @param discriminator the name of the discriminator property\n     * @param types an array of object schemas\n     * @param params\n     */\n    static create(discriminator, options, params) {\n        // Get all the valid discriminator values\n        const optionsMap = new Map();\n        // try {\n        for (const type of options) {\n            const discriminatorValues = getDiscriminator(type.shape[discriminator]);\n            if (!discriminatorValues.length) {\n                throw new Error(`A discriminator value for key \\`${discriminator}\\` could not be extracted from all schema options`);\n            }\n            for (const value of discriminatorValues) {\n                if (optionsMap.has(value)) {\n                    throw new Error(`Discriminator property ${String(discriminator)} has duplicate value ${String(value)}`);\n                }\n                optionsMap.set(value, type);\n            }\n        }\n        return new ZodDiscriminatedUnion({\n            typeName: ZodFirstPartyTypeKind.ZodDiscriminatedUnion,\n            discriminator,\n            options,\n            optionsMap,\n            ...processCreateParams(params),\n        });\n    }\n}\nfunction mergeValues(a, b) {\n    const aType = getParsedType(a);\n    const bType = getParsedType(b);\n    if (a === b) {\n        return { valid: true, data: a };\n    }\n    else if (aType === ZodParsedType.object && bType === ZodParsedType.object) {\n        const bKeys = util.objectKeys(b);\n        const sharedKeys = util\n            .objectKeys(a)\n            .filter((key) => bKeys.indexOf(key) !== -1);\n        const newObj = { ...a, ...b };\n        for (const key of sharedKeys) {\n            const sharedValue = mergeValues(a[key], b[key]);\n            if (!sharedValue.valid) {\n                return { valid: false };\n            }\n            newObj[key] = sharedValue.data;\n        }\n        return { valid: true, data: newObj };\n    }\n    else if (aType === ZodParsedType.array && bType === ZodParsedType.array) {\n        if (a.length !== b.length) {\n            return { valid: false };\n        }\n        const newArray = [];\n        for (let index = 0; index < a.length; index++) {\n            const itemA = a[index];\n            const itemB = b[index];\n            const sharedValue = mergeValues(itemA, itemB);\n            if (!sharedValue.valid) {\n                return { valid: false };\n            }\n            newArray.push(sharedValue.data);\n        }\n        return { valid: true, data: newArray };\n    }\n    else if (aType === ZodParsedType.date &&\n        bType === ZodParsedType.date &&\n        +a === +b) {\n        return { valid: true, data: a };\n    }\n    else {\n        return { valid: false };\n    }\n}\nclass ZodIntersection extends ZodType {\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        const handleParsed = (parsedLeft, parsedRight) => {\n            if (isAborted(parsedLeft) || isAborted(parsedRight)) {\n                return INVALID;\n            }\n            const merged = mergeValues(parsedLeft.value, parsedRight.value);\n            if (!merged.valid) {\n                addIssueToContext(ctx, {\n                    code: ZodIssueCode.invalid_intersection_types,\n                });\n                return INVALID;\n            }\n            if (isDirty(parsedLeft) || isDirty(parsedRight)) {\n                status.dirty();\n            }\n            return { status: status.value, value: merged.data };\n        };\n        if (ctx.common.async) {\n            return Promise.all([\n                this._def.left._parseAsync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: ctx,\n                }),\n                this._def.right._parseAsync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: ctx,\n                }),\n            ]).then(([left, right]) => handleParsed(left, right));\n        }\n        else {\n            return handleParsed(this._def.left._parseSync({\n                data: ctx.data,\n                path: ctx.path,\n                parent: ctx,\n            }), this._def.right._parseSync({\n                data: ctx.data,\n                path: ctx.path,\n                parent: ctx,\n            }));\n        }\n    }\n}\nZodIntersection.create = (left, right, params) => {\n    return new ZodIntersection({\n        left: left,\n        right: right,\n        typeName: ZodFirstPartyTypeKind.ZodIntersection,\n        ...processCreateParams(params),\n    });\n};\nclass ZodTuple extends ZodType {\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.array) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.array,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        if (ctx.data.length < this._def.items.length) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.too_small,\n                minimum: this._def.items.length,\n                inclusive: true,\n                exact: false,\n                type: \"array\",\n            });\n            return INVALID;\n        }\n        const rest = this._def.rest;\n        if (!rest && ctx.data.length > this._def.items.length) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.too_big,\n                maximum: this._def.items.length,\n                inclusive: true,\n                exact: false,\n                type: \"array\",\n            });\n            status.dirty();\n        }\n        const items = [...ctx.data]\n            .map((item, itemIndex) => {\n            const schema = this._def.items[itemIndex] || this._def.rest;\n            if (!schema)\n                return null;\n            return schema._parse(new ParseInputLazyPath(ctx, item, ctx.path, itemIndex));\n        })\n            .filter((x) => !!x); // filter nulls\n        if (ctx.common.async) {\n            return Promise.all(items).then((results) => {\n                return ParseStatus.mergeArray(status, results);\n            });\n        }\n        else {\n            return ParseStatus.mergeArray(status, items);\n        }\n    }\n    get items() {\n        return this._def.items;\n    }\n    rest(rest) {\n        return new ZodTuple({\n            ...this._def,\n            rest,\n        });\n    }\n}\nZodTuple.create = (schemas, params) => {\n    if (!Array.isArray(schemas)) {\n        throw new Error(\"You must pass an array of schemas to z.tuple([ ... ])\");\n    }\n    return new ZodTuple({\n        items: schemas,\n        typeName: ZodFirstPartyTypeKind.ZodTuple,\n        rest: null,\n        ...processCreateParams(params),\n    });\n};\nclass ZodRecord extends ZodType {\n    get keySchema() {\n        return this._def.keyType;\n    }\n    get valueSchema() {\n        return this._def.valueType;\n    }\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.object) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.object,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const pairs = [];\n        const keyType = this._def.keyType;\n        const valueType = this._def.valueType;\n        for (const key in ctx.data) {\n            pairs.push({\n                key: keyType._parse(new ParseInputLazyPath(ctx, key, ctx.path, key)),\n                value: valueType._parse(new ParseInputLazyPath(ctx, ctx.data[key], ctx.path, key)),\n                alwaysSet: key in ctx.data,\n            });\n        }\n        if (ctx.common.async) {\n            return ParseStatus.mergeObjectAsync(status, pairs);\n        }\n        else {\n            return ParseStatus.mergeObjectSync(status, pairs);\n        }\n    }\n    get element() {\n        return this._def.valueType;\n    }\n    static create(first, second, third) {\n        if (second instanceof ZodType) {\n            return new ZodRecord({\n                keyType: first,\n                valueType: second,\n                typeName: ZodFirstPartyTypeKind.ZodRecord,\n                ...processCreateParams(third),\n            });\n        }\n        return new ZodRecord({\n            keyType: ZodString.create(),\n            valueType: first,\n            typeName: ZodFirstPartyTypeKind.ZodRecord,\n            ...processCreateParams(second),\n        });\n    }\n}\nclass ZodMap extends ZodType {\n    get keySchema() {\n        return this._def.keyType;\n    }\n    get valueSchema() {\n        return this._def.valueType;\n    }\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.map) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.map,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const keyType = this._def.keyType;\n        const valueType = this._def.valueType;\n        const pairs = [...ctx.data.entries()].map(([key, value], index) => {\n            return {\n                key: keyType._parse(new ParseInputLazyPath(ctx, key, ctx.path, [index, \"key\"])),\n                value: valueType._parse(new ParseInputLazyPath(ctx, value, ctx.path, [index, \"value\"])),\n            };\n        });\n        if (ctx.common.async) {\n            const finalMap = new Map();\n            return Promise.resolve().then(async () => {\n                for (const pair of pairs) {\n                    const key = await pair.key;\n                    const value = await pair.value;\n                    if (key.status === \"aborted\" || value.status === \"aborted\") {\n                        return INVALID;\n                    }\n                    if (key.status === \"dirty\" || value.status === \"dirty\") {\n                        status.dirty();\n                    }\n                    finalMap.set(key.value, value.value);\n                }\n                return { status: status.value, value: finalMap };\n            });\n        }\n        else {\n            const finalMap = new Map();\n            for (const pair of pairs) {\n                const key = pair.key;\n                const value = pair.value;\n                if (key.status === \"aborted\" || value.status === \"aborted\") {\n                    return INVALID;\n                }\n                if (key.status === \"dirty\" || value.status === \"dirty\") {\n                    status.dirty();\n                }\n                finalMap.set(key.value, value.value);\n            }\n            return { status: status.value, value: finalMap };\n        }\n    }\n}\nZodMap.create = (keyType, valueType, params) => {\n    return new ZodMap({\n        valueType,\n        keyType,\n        typeName: ZodFirstPartyTypeKind.ZodMap,\n        ...processCreateParams(params),\n    });\n};\nclass ZodSet extends ZodType {\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.set) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.set,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const def = this._def;\n        if (def.minSize !== null) {\n            if (ctx.data.size < def.minSize.value) {\n                addIssueToContext(ctx, {\n                    code: ZodIssueCode.too_small,\n                    minimum: def.minSize.value,\n                    type: \"set\",\n                    inclusive: true,\n                    exact: false,\n                    message: def.minSize.message,\n                });\n                status.dirty();\n            }\n        }\n        if (def.maxSize !== null) {\n            if (ctx.data.size > def.maxSize.value) {\n                addIssueToContext(ctx, {\n                    code: ZodIssueCode.too_big,\n                    maximum: def.maxSize.value,\n                    type: \"set\",\n                    inclusive: true,\n                    exact: false,\n                    message: def.maxSize.message,\n                });\n                status.dirty();\n            }\n        }\n        const valueType = this._def.valueType;\n        function finalizeSet(elements) {\n            const parsedSet = new Set();\n            for (const element of elements) {\n                if (element.status === \"aborted\")\n                    return INVALID;\n                if (element.status === \"dirty\")\n                    status.dirty();\n                parsedSet.add(element.value);\n            }\n            return { status: status.value, value: parsedSet };\n        }\n        const elements = [...ctx.data.values()].map((item, i) => valueType._parse(new ParseInputLazyPath(ctx, item, ctx.path, i)));\n        if (ctx.common.async) {\n            return Promise.all(elements).then((elements) => finalizeSet(elements));\n        }\n        else {\n            return finalizeSet(elements);\n        }\n    }\n    min(minSize, message) {\n        return new ZodSet({\n            ...this._def,\n            minSize: { value: minSize, message: errorUtil.toString(message) },\n        });\n    }\n    max(maxSize, message) {\n        return new ZodSet({\n            ...this._def,\n            maxSize: { value: maxSize, message: errorUtil.toString(message) },\n        });\n    }\n    size(size, message) {\n        return this.min(size, message).max(size, message);\n    }\n    nonempty(message) {\n        return this.min(1, message);\n    }\n}\nZodSet.create = (valueType, params) => {\n    return new ZodSet({\n        valueType,\n        minSize: null,\n        maxSize: null,\n        typeName: ZodFirstPartyTypeKind.ZodSet,\n        ...processCreateParams(params),\n    });\n};\nclass ZodFunction extends ZodType {\n    constructor() {\n        super(...arguments);\n        this.validate = this.implement;\n    }\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.function) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.function,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        function makeArgsIssue(args, error) {\n            return makeIssue({\n                data: args,\n                path: ctx.path,\n                errorMaps: [\n                    ctx.common.contextualErrorMap,\n                    ctx.schemaErrorMap,\n                    getErrorMap(),\n                    errorMap,\n                ].filter((x) => !!x),\n                issueData: {\n                    code: ZodIssueCode.invalid_arguments,\n                    argumentsError: error,\n                },\n            });\n        }\n        function makeReturnsIssue(returns, error) {\n            return makeIssue({\n                data: returns,\n                path: ctx.path,\n                errorMaps: [\n                    ctx.common.contextualErrorMap,\n                    ctx.schemaErrorMap,\n                    getErrorMap(),\n                    errorMap,\n                ].filter((x) => !!x),\n                issueData: {\n                    code: ZodIssueCode.invalid_return_type,\n                    returnTypeError: error,\n                },\n            });\n        }\n        const params = { errorMap: ctx.common.contextualErrorMap };\n        const fn = ctx.data;\n        if (this._def.returns instanceof ZodPromise) {\n            // Would love a way to avoid disabling this rule, but we need\n            // an alias (using an arrow function was what caused 2651).\n            // eslint-disable-next-line @typescript-eslint/no-this-alias\n            const me = this;\n            return OK(async function (...args) {\n                const error = new ZodError([]);\n                const parsedArgs = await me._def.args\n                    .parseAsync(args, params)\n                    .catch((e) => {\n                    error.addIssue(makeArgsIssue(args, e));\n                    throw error;\n                });\n                const result = await Reflect.apply(fn, this, parsedArgs);\n                const parsedReturns = await me._def.returns._def.type\n                    .parseAsync(result, params)\n                    .catch((e) => {\n                    error.addIssue(makeReturnsIssue(result, e));\n                    throw error;\n                });\n                return parsedReturns;\n            });\n        }\n        else {\n            // Would love a way to avoid disabling this rule, but we need\n            // an alias (using an arrow function was what caused 2651).\n            // eslint-disable-next-line @typescript-eslint/no-this-alias\n            const me = this;\n            return OK(function (...args) {\n                const parsedArgs = me._def.args.safeParse(args, params);\n                if (!parsedArgs.success) {\n                    throw new ZodError([makeArgsIssue(args, parsedArgs.error)]);\n                }\n                const result = Reflect.apply(fn, this, parsedArgs.data);\n                const parsedReturns = me._def.returns.safeParse(result, params);\n                if (!parsedReturns.success) {\n                    throw new ZodError([makeReturnsIssue(result, parsedReturns.error)]);\n                }\n                return parsedReturns.data;\n            });\n        }\n    }\n    parameters() {\n        return this._def.args;\n    }\n    returnType() {\n        return this._def.returns;\n    }\n    args(...items) {\n        return new ZodFunction({\n            ...this._def,\n            args: ZodTuple.create(items).rest(ZodUnknown.create()),\n        });\n    }\n    returns(returnType) {\n        return new ZodFunction({\n            ...this._def,\n            returns: returnType,\n        });\n    }\n    implement(func) {\n        const validatedFunc = this.parse(func);\n        return validatedFunc;\n    }\n    strictImplement(func) {\n        const validatedFunc = this.parse(func);\n        return validatedFunc;\n    }\n    static create(args, returns, params) {\n        return new ZodFunction({\n            args: (args\n                ? args\n                : ZodTuple.create([]).rest(ZodUnknown.create())),\n            returns: returns || ZodUnknown.create(),\n            typeName: ZodFirstPartyTypeKind.ZodFunction,\n            ...processCreateParams(params),\n        });\n    }\n}\nclass ZodLazy extends ZodType {\n    get schema() {\n        return this._def.getter();\n    }\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        const lazySchema = this._def.getter();\n        return lazySchema._parse({ data: ctx.data, path: ctx.path, parent: ctx });\n    }\n}\nZodLazy.create = (getter, params) => {\n    return new ZodLazy({\n        getter: getter,\n        typeName: ZodFirstPartyTypeKind.ZodLazy,\n        ...processCreateParams(params),\n    });\n};\nclass ZodLiteral extends ZodType {\n    _parse(input) {\n        if (input.data !== this._def.value) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                received: ctx.data,\n                code: ZodIssueCode.invalid_literal,\n                expected: this._def.value,\n            });\n            return INVALID;\n        }\n        return { status: \"valid\", value: input.data };\n    }\n    get value() {\n        return this._def.value;\n    }\n}\nZodLiteral.create = (value, params) => {\n    return new ZodLiteral({\n        value: value,\n        typeName: ZodFirstPartyTypeKind.ZodLiteral,\n        ...processCreateParams(params),\n    });\n};\nfunction createZodEnum(values, params) {\n    return new ZodEnum({\n        values,\n        typeName: ZodFirstPartyTypeKind.ZodEnum,\n        ...processCreateParams(params),\n    });\n}\nclass ZodEnum extends ZodType {\n    constructor() {\n        super(...arguments);\n        _ZodEnum_cache.set(this, void 0);\n    }\n    _parse(input) {\n        if (typeof input.data !== \"string\") {\n            const ctx = this._getOrReturnCtx(input);\n            const expectedValues = this._def.values;\n            addIssueToContext(ctx, {\n                expected: util.joinValues(expectedValues),\n                received: ctx.parsedType,\n                code: ZodIssueCode.invalid_type,\n            });\n            return INVALID;\n        }\n        if (!__classPrivateFieldGet(this, _ZodEnum_cache, \"f\")) {\n            __classPrivateFieldSet(this, _ZodEnum_cache, new Set(this._def.values), \"f\");\n        }\n        if (!__classPrivateFieldGet(this, _ZodEnum_cache, \"f\").has(input.data)) {\n            const ctx = this._getOrReturnCtx(input);\n            const expectedValues = this._def.values;\n            addIssueToContext(ctx, {\n                received: ctx.data,\n                code: ZodIssueCode.invalid_enum_value,\n                options: expectedValues,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n    get options() {\n        return this._def.values;\n    }\n    get enum() {\n        const enumValues = {};\n        for (const val of this._def.values) {\n            enumValues[val] = val;\n        }\n        return enumValues;\n    }\n    get Values() {\n        const enumValues = {};\n        for (const val of this._def.values) {\n            enumValues[val] = val;\n        }\n        return enumValues;\n    }\n    get Enum() {\n        const enumValues = {};\n        for (const val of this._def.values) {\n            enumValues[val] = val;\n        }\n        return enumValues;\n    }\n    extract(values, newDef = this._def) {\n        return ZodEnum.create(values, {\n            ...this._def,\n            ...newDef,\n        });\n    }\n    exclude(values, newDef = this._def) {\n        return ZodEnum.create(this.options.filter((opt) => !values.includes(opt)), {\n            ...this._def,\n            ...newDef,\n        });\n    }\n}\n_ZodEnum_cache = new WeakMap();\nZodEnum.create = createZodEnum;\nclass ZodNativeEnum extends ZodType {\n    constructor() {\n        super(...arguments);\n        _ZodNativeEnum_cache.set(this, void 0);\n    }\n    _parse(input) {\n        const nativeEnumValues = util.getValidEnumValues(this._def.values);\n        const ctx = this._getOrReturnCtx(input);\n        if (ctx.parsedType !== ZodParsedType.string &&\n            ctx.parsedType !== ZodParsedType.number) {\n            const expectedValues = util.objectValues(nativeEnumValues);\n            addIssueToContext(ctx, {\n                expected: util.joinValues(expectedValues),\n                received: ctx.parsedType,\n                code: ZodIssueCode.invalid_type,\n            });\n            return INVALID;\n        }\n        if (!__classPrivateFieldGet(this, _ZodNativeEnum_cache, \"f\")) {\n            __classPrivateFieldSet(this, _ZodNativeEnum_cache, new Set(util.getValidEnumValues(this._def.values)), \"f\");\n        }\n        if (!__classPrivateFieldGet(this, _ZodNativeEnum_cache, \"f\").has(input.data)) {\n            const expectedValues = util.objectValues(nativeEnumValues);\n            addIssueToContext(ctx, {\n                received: ctx.data,\n                code: ZodIssueCode.invalid_enum_value,\n                options: expectedValues,\n            });\n            return INVALID;\n        }\n        return OK(input.data);\n    }\n    get enum() {\n        return this._def.values;\n    }\n}\n_ZodNativeEnum_cache = new WeakMap();\nZodNativeEnum.create = (values, params) => {\n    return new ZodNativeEnum({\n        values: values,\n        typeName: ZodFirstPartyTypeKind.ZodNativeEnum,\n        ...processCreateParams(params),\n    });\n};\nclass ZodPromise extends ZodType {\n    unwrap() {\n        return this._def.type;\n    }\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        if (ctx.parsedType !== ZodParsedType.promise &&\n            ctx.common.async === false) {\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.promise,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        const promisified = ctx.parsedType === ZodParsedType.promise\n            ? ctx.data\n            : Promise.resolve(ctx.data);\n        return OK(promisified.then((data) => {\n            return this._def.type.parseAsync(data, {\n                path: ctx.path,\n                errorMap: ctx.common.contextualErrorMap,\n            });\n        }));\n    }\n}\nZodPromise.create = (schema, params) => {\n    return new ZodPromise({\n        type: schema,\n        typeName: ZodFirstPartyTypeKind.ZodPromise,\n        ...processCreateParams(params),\n    });\n};\nclass ZodEffects extends ZodType {\n    innerType() {\n        return this._def.schema;\n    }\n    sourceType() {\n        return this._def.schema._def.typeName === ZodFirstPartyTypeKind.ZodEffects\n            ? this._def.schema.sourceType()\n            : this._def.schema;\n    }\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        const effect = this._def.effect || null;\n        const checkCtx = {\n            addIssue: (arg) => {\n                addIssueToContext(ctx, arg);\n                if (arg.fatal) {\n                    status.abort();\n                }\n                else {\n                    status.dirty();\n                }\n            },\n            get path() {\n                return ctx.path;\n            },\n        };\n        checkCtx.addIssue = checkCtx.addIssue.bind(checkCtx);\n        if (effect.type === \"preprocess\") {\n            const processed = effect.transform(ctx.data, checkCtx);\n            if (ctx.common.async) {\n                return Promise.resolve(processed).then(async (processed) => {\n                    if (status.value === \"aborted\")\n                        return INVALID;\n                    const result = await this._def.schema._parseAsync({\n                        data: processed,\n                        path: ctx.path,\n                        parent: ctx,\n                    });\n                    if (result.status === \"aborted\")\n                        return INVALID;\n                    if (result.status === \"dirty\")\n                        return DIRTY(result.value);\n                    if (status.value === \"dirty\")\n                        return DIRTY(result.value);\n                    return result;\n                });\n            }\n            else {\n                if (status.value === \"aborted\")\n                    return INVALID;\n                const result = this._def.schema._parseSync({\n                    data: processed,\n                    path: ctx.path,\n                    parent: ctx,\n                });\n                if (result.status === \"aborted\")\n                    return INVALID;\n                if (result.status === \"dirty\")\n                    return DIRTY(result.value);\n                if (status.value === \"dirty\")\n                    return DIRTY(result.value);\n                return result;\n            }\n        }\n        if (effect.type === \"refinement\") {\n            const executeRefinement = (acc) => {\n                const result = effect.refinement(acc, checkCtx);\n                if (ctx.common.async) {\n                    return Promise.resolve(result);\n                }\n                if (result instanceof Promise) {\n                    throw new Error(\"Async refinement encountered during synchronous parse operation. Use .parseAsync instead.\");\n                }\n                return acc;\n            };\n            if (ctx.common.async === false) {\n                const inner = this._def.schema._parseSync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: ctx,\n                });\n                if (inner.status === \"aborted\")\n                    return INVALID;\n                if (inner.status === \"dirty\")\n                    status.dirty();\n                // return value is ignored\n                executeRefinement(inner.value);\n                return { status: status.value, value: inner.value };\n            }\n            else {\n                return this._def.schema\n                    ._parseAsync({ data: ctx.data, path: ctx.path, parent: ctx })\n                    .then((inner) => {\n                    if (inner.status === \"aborted\")\n                        return INVALID;\n                    if (inner.status === \"dirty\")\n                        status.dirty();\n                    return executeRefinement(inner.value).then(() => {\n                        return { status: status.value, value: inner.value };\n                    });\n                });\n            }\n        }\n        if (effect.type === \"transform\") {\n            if (ctx.common.async === false) {\n                const base = this._def.schema._parseSync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: ctx,\n                });\n                if (!isValid(base))\n                    return base;\n                const result = effect.transform(base.value, checkCtx);\n                if (result instanceof Promise) {\n                    throw new Error(`Asynchronous transform encountered during synchronous parse operation. Use .parseAsync instead.`);\n                }\n                return { status: status.value, value: result };\n            }\n            else {\n                return this._def.schema\n                    ._parseAsync({ data: ctx.data, path: ctx.path, parent: ctx })\n                    .then((base) => {\n                    if (!isValid(base))\n                        return base;\n                    return Promise.resolve(effect.transform(base.value, checkCtx)).then((result) => ({ status: status.value, value: result }));\n                });\n            }\n        }\n        util.assertNever(effect);\n    }\n}\nZodEffects.create = (schema, effect, params) => {\n    return new ZodEffects({\n        schema,\n        typeName: ZodFirstPartyTypeKind.ZodEffects,\n        effect,\n        ...processCreateParams(params),\n    });\n};\nZodEffects.createWithPreprocess = (preprocess, schema, params) => {\n    return new ZodEffects({\n        schema,\n        effect: { type: \"preprocess\", transform: preprocess },\n        typeName: ZodFirstPartyTypeKind.ZodEffects,\n        ...processCreateParams(params),\n    });\n};\nclass ZodOptional extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType === ZodParsedType.undefined) {\n            return OK(undefined);\n        }\n        return this._def.innerType._parse(input);\n    }\n    unwrap() {\n        return this._def.innerType;\n    }\n}\nZodOptional.create = (type, params) => {\n    return new ZodOptional({\n        innerType: type,\n        typeName: ZodFirstPartyTypeKind.ZodOptional,\n        ...processCreateParams(params),\n    });\n};\nclass ZodNullable extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType === ZodParsedType.null) {\n            return OK(null);\n        }\n        return this._def.innerType._parse(input);\n    }\n    unwrap() {\n        return this._def.innerType;\n    }\n}\nZodNullable.create = (type, params) => {\n    return new ZodNullable({\n        innerType: type,\n        typeName: ZodFirstPartyTypeKind.ZodNullable,\n        ...processCreateParams(params),\n    });\n};\nclass ZodDefault extends ZodType {\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        let data = ctx.data;\n        if (ctx.parsedType === ZodParsedType.undefined) {\n            data = this._def.defaultValue();\n        }\n        return this._def.innerType._parse({\n            data,\n            path: ctx.path,\n            parent: ctx,\n        });\n    }\n    removeDefault() {\n        return this._def.innerType;\n    }\n}\nZodDefault.create = (type, params) => {\n    return new ZodDefault({\n        innerType: type,\n        typeName: ZodFirstPartyTypeKind.ZodDefault,\n        defaultValue: typeof params.default === \"function\"\n            ? params.default\n            : () => params.default,\n        ...processCreateParams(params),\n    });\n};\nclass ZodCatch extends ZodType {\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        // newCtx is used to not collect issues from inner types in ctx\n        const newCtx = {\n            ...ctx,\n            common: {\n                ...ctx.common,\n                issues: [],\n            },\n        };\n        const result = this._def.innerType._parse({\n            data: newCtx.data,\n            path: newCtx.path,\n            parent: {\n                ...newCtx,\n            },\n        });\n        if (isAsync(result)) {\n            return result.then((result) => {\n                return {\n                    status: \"valid\",\n                    value: result.status === \"valid\"\n                        ? result.value\n                        : this._def.catchValue({\n                            get error() {\n                                return new ZodError(newCtx.common.issues);\n                            },\n                            input: newCtx.data,\n                        }),\n                };\n            });\n        }\n        else {\n            return {\n                status: \"valid\",\n                value: result.status === \"valid\"\n                    ? result.value\n                    : this._def.catchValue({\n                        get error() {\n                            return new ZodError(newCtx.common.issues);\n                        },\n                        input: newCtx.data,\n                    }),\n            };\n        }\n    }\n    removeCatch() {\n        return this._def.innerType;\n    }\n}\nZodCatch.create = (type, params) => {\n    return new ZodCatch({\n        innerType: type,\n        typeName: ZodFirstPartyTypeKind.ZodCatch,\n        catchValue: typeof params.catch === \"function\" ? params.catch : () => params.catch,\n        ...processCreateParams(params),\n    });\n};\nclass ZodNaN extends ZodType {\n    _parse(input) {\n        const parsedType = this._getType(input);\n        if (parsedType !== ZodParsedType.nan) {\n            const ctx = this._getOrReturnCtx(input);\n            addIssueToContext(ctx, {\n                code: ZodIssueCode.invalid_type,\n                expected: ZodParsedType.nan,\n                received: ctx.parsedType,\n            });\n            return INVALID;\n        }\n        return { status: \"valid\", value: input.data };\n    }\n}\nZodNaN.create = (params) => {\n    return new ZodNaN({\n        typeName: ZodFirstPartyTypeKind.ZodNaN,\n        ...processCreateParams(params),\n    });\n};\nconst BRAND = Symbol(\"zod_brand\");\nclass ZodBranded extends ZodType {\n    _parse(input) {\n        const { ctx } = this._processInputParams(input);\n        const data = ctx.data;\n        return this._def.type._parse({\n            data,\n            path: ctx.path,\n            parent: ctx,\n        });\n    }\n    unwrap() {\n        return this._def.type;\n    }\n}\nclass ZodPipeline extends ZodType {\n    _parse(input) {\n        const { status, ctx } = this._processInputParams(input);\n        if (ctx.common.async) {\n            const handleAsync = async () => {\n                const inResult = await this._def.in._parseAsync({\n                    data: ctx.data,\n                    path: ctx.path,\n                    parent: ctx,\n                });\n                if (inResult.status === \"aborted\")\n                    return INVALID;\n                if (inResult.status === \"dirty\") {\n                    status.dirty();\n                    return DIRTY(inResult.value);\n                }\n                else {\n                    return this._def.out._parseAsync({\n                        data: inResult.value,\n                        path: ctx.path,\n                        parent: ctx,\n                    });\n                }\n            };\n            return handleAsync();\n        }\n        else {\n            const inResult = this._def.in._parseSync({\n                data: ctx.data,\n                path: ctx.path,\n                parent: ctx,\n            });\n            if (inResult.status === \"aborted\")\n                return INVALID;\n            if (inResult.status === \"dirty\") {\n                status.dirty();\n                return {\n                    status: \"dirty\",\n                    value: inResult.value,\n                };\n            }\n            else {\n                return this._def.out._parseSync({\n                    data: inResult.value,\n                    path: ctx.path,\n                    parent: ctx,\n                });\n            }\n        }\n    }\n    static create(a, b) {\n        return new ZodPipeline({\n            in: a,\n            out: b,\n            typeName: ZodFirstPartyTypeKind.ZodPipeline,\n        });\n    }\n}\nclass ZodReadonly extends ZodType {\n    _parse(input) {\n        const result = this._def.innerType._parse(input);\n        const freeze = (data) => {\n            if (isValid(data)) {\n                data.value = Object.freeze(data.value);\n            }\n            return data;\n        };\n        return isAsync(result)\n            ? result.then((data) => freeze(data))\n            : freeze(result);\n    }\n    unwrap() {\n        return this._def.innerType;\n    }\n}\nZodReadonly.create = (type, params) => {\n    return new ZodReadonly({\n        innerType: type,\n        typeName: ZodFirstPartyTypeKind.ZodReadonly,\n        ...processCreateParams(params),\n    });\n};\n////////////////////////////////////////\n////////////////////////////////////////\n//////////                    //////////\n//////////      z.custom      //////////\n//////////                    //////////\n////////////////////////////////////////\n////////////////////////////////////////\nfunction cleanParams(params, data) {\n    const p = typeof params === \"function\"\n        ? params(data)\n        : typeof params === \"string\"\n            ? { message: params }\n            : params;\n    const p2 = typeof p === \"string\" ? { message: p } : p;\n    return p2;\n}\nfunction custom(check, _params = {}, \n/**\n * @deprecated\n *\n * Pass `fatal` into the params object instead:\n *\n * ```ts\n * z.string().custom((val) => val.length > 5, { fatal: false })\n * ```\n *\n */\nfatal) {\n    if (check)\n        return ZodAny.create().superRefine((data, ctx) => {\n            var _a, _b;\n            const r = check(data);\n            if (r instanceof Promise) {\n                return r.then((r) => {\n                    var _a, _b;\n                    if (!r) {\n                        const params = cleanParams(_params, data);\n                        const _fatal = (_b = (_a = params.fatal) !== null && _a !== void 0 ? _a : fatal) !== null && _b !== void 0 ? _b : true;\n                        ctx.addIssue({ code: \"custom\", ...params, fatal: _fatal });\n                    }\n                });\n            }\n            if (!r) {\n                const params = cleanParams(_params, data);\n                const _fatal = (_b = (_a = params.fatal) !== null && _a !== void 0 ? _a : fatal) !== null && _b !== void 0 ? _b : true;\n                ctx.addIssue({ code: \"custom\", ...params, fatal: _fatal });\n            }\n            return;\n        });\n    return ZodAny.create();\n}\nconst late = {\n    object: ZodObject.lazycreate,\n};\nvar ZodFirstPartyTypeKind;\n(function (ZodFirstPartyTypeKind) {\n    ZodFirstPartyTypeKind[\"ZodString\"] = \"ZodString\";\n    ZodFirstPartyTypeKind[\"ZodNumber\"] = \"ZodNumber\";\n    ZodFirstPartyTypeKind[\"ZodNaN\"] = \"ZodNaN\";\n    ZodFirstPartyTypeKind[\"ZodBigInt\"] = \"ZodBigInt\";\n    ZodFirstPartyTypeKind[\"ZodBoolean\"] = \"ZodBoolean\";\n    ZodFirstPartyTypeKind[\"ZodDate\"] = \"ZodDate\";\n    ZodFirstPartyTypeKind[\"ZodSymbol\"] = \"ZodSymbol\";\n    ZodFirstPartyTypeKind[\"ZodUndefined\"] = \"ZodUndefined\";\n    ZodFirstPartyTypeKind[\"ZodNull\"] = \"ZodNull\";\n    ZodFirstPartyTypeKind[\"ZodAny\"] = \"ZodAny\";\n    ZodFirstPartyTypeKind[\"ZodUnknown\"] = \"ZodUnknown\";\n    ZodFirstPartyTypeKind[\"ZodNever\"] = \"ZodNever\";\n    ZodFirstPartyTypeKind[\"ZodVoid\"] = \"ZodVoid\";\n    ZodFirstPartyTypeKind[\"ZodArray\"] = \"ZodArray\";\n    ZodFirstPartyTypeKind[\"ZodObject\"] = \"ZodObject\";\n    ZodFirstPartyTypeKind[\"ZodUnion\"] = \"ZodUnion\";\n    ZodFirstPartyTypeKind[\"ZodDiscriminatedUnion\"] = \"ZodDiscriminatedUnion\";\n    ZodFirstPartyTypeKind[\"ZodIntersection\"] = \"ZodIntersection\";\n    ZodFirstPartyTypeKind[\"ZodTuple\"] = \"ZodTuple\";\n    ZodFirstPartyTypeKind[\"ZodRecord\"] = \"ZodRecord\";\n    ZodFirstPartyTypeKind[\"ZodMap\"] = \"ZodMap\";\n    ZodFirstPartyTypeKind[\"ZodSet\"] = \"ZodSet\";\n    ZodFirstPartyTypeKind[\"ZodFunction\"] = \"ZodFunction\";\n    ZodFirstPartyTypeKind[\"ZodLazy\"] = \"ZodLazy\";\n    ZodFirstPartyTypeKind[\"ZodLiteral\"] = \"ZodLiteral\";\n    ZodFirstPartyTypeKind[\"ZodEnum\"] = \"ZodEnum\";\n    ZodFirstPartyTypeKind[\"ZodEffects\"] = \"ZodEffects\";\n    ZodFirstPartyTypeKind[\"ZodNativeEnum\"] = \"ZodNativeEnum\";\n    ZodFirstPartyTypeKind[\"ZodOptional\"] = \"ZodOptional\";\n    ZodFirstPartyTypeKind[\"ZodNullable\"] = \"ZodNullable\";\n    ZodFirstPartyTypeKind[\"ZodDefault\"] = \"ZodDefault\";\n    ZodFirstPartyTypeKind[\"ZodCatch\"] = \"ZodCatch\";\n    ZodFirstPartyTypeKind[\"ZodPromise\"] = \"ZodPromise\";\n    ZodFirstPartyTypeKind[\"ZodBranded\"] = \"ZodBranded\";\n    ZodFirstPartyTypeKind[\"ZodPipeline\"] = \"ZodPipeline\";\n    ZodFirstPartyTypeKind[\"ZodReadonly\"] = \"ZodReadonly\";\n})(ZodFirstPartyTypeKind || (ZodFirstPartyTypeKind = {}));\nconst instanceOfType = (\n// const instanceOfType = <T extends new (...args: any[]) => any>(\ncls, params = {\n    message: `Input not instance of ${cls.name}`,\n}) => custom((data) => data instanceof cls, params);\nconst stringType = ZodString.create;\nconst numberType = ZodNumber.create;\nconst nanType = ZodNaN.create;\nconst bigIntType = ZodBigInt.create;\nconst booleanType = ZodBoolean.create;\nconst dateType = ZodDate.create;\nconst symbolType = ZodSymbol.create;\nconst undefinedType = ZodUndefined.create;\nconst nullType = ZodNull.create;\nconst anyType = ZodAny.create;\nconst unknownType = ZodUnknown.create;\nconst neverType = ZodNever.create;\nconst voidType = ZodVoid.create;\nconst arrayType = ZodArray.create;\nconst objectType = ZodObject.create;\nconst strictObjectType = ZodObject.strictCreate;\nconst unionType = ZodUnion.create;\nconst discriminatedUnionType = ZodDiscriminatedUnion.create;\nconst intersectionType = ZodIntersection.create;\nconst tupleType = ZodTuple.create;\nconst recordType = ZodRecord.create;\nconst mapType = ZodMap.create;\nconst setType = ZodSet.create;\nconst functionType = ZodFunction.create;\nconst lazyType = ZodLazy.create;\nconst literalType = ZodLiteral.create;\nconst enumType = ZodEnum.create;\nconst nativeEnumType = ZodNativeEnum.create;\nconst promiseType = ZodPromise.create;\nconst effectsType = ZodEffects.create;\nconst optionalType = ZodOptional.create;\nconst nullableType = ZodNullable.create;\nconst preprocessType = ZodEffects.createWithPreprocess;\nconst pipelineType = ZodPipeline.create;\nconst ostring = () => stringType().optional();\nconst onumber = () => numberType().optional();\nconst oboolean = () => booleanType().optional();\nconst coerce = {\n    string: ((arg) => ZodString.create({ ...arg, coerce: true })),\n    number: ((arg) => ZodNumber.create({ ...arg, coerce: true })),\n    boolean: ((arg) => ZodBoolean.create({\n        ...arg,\n        coerce: true,\n    })),\n    bigint: ((arg) => ZodBigInt.create({ ...arg, coerce: true })),\n    date: ((arg) => ZodDate.create({ ...arg, coerce: true })),\n};\nconst NEVER = INVALID;\n\nvar z = /*#__PURE__*/Object.freeze({\n    __proto__: null,\n    defaultErrorMap: errorMap,\n    setErrorMap: setErrorMap,\n    getErrorMap: getErrorMap,\n    makeIssue: makeIssue,\n    EMPTY_PATH: EMPTY_PATH,\n    addIssueToContext: addIssueToContext,\n    ParseStatus: ParseStatus,\n    INVALID: INVALID,\n    DIRTY: DIRTY,\n    OK: OK,\n    isAborted: isAborted,\n    isDirty: isDirty,\n    isValid: isValid,\n    isAsync: isAsync,\n    get util () { return util; },\n    get objectUtil () { return objectUtil; },\n    ZodParsedType: ZodParsedType,\n    getParsedType: getParsedType,\n    ZodType: ZodType,\n    datetimeRegex: datetimeRegex,\n    ZodString: ZodString,\n    ZodNumber: ZodNumber,\n    ZodBigInt: ZodBigInt,\n    ZodBoolean: ZodBoolean,\n    ZodDate: ZodDate,\n    ZodSymbol: ZodSymbol,\n    ZodUndefined: ZodUndefined,\n    ZodNull: ZodNull,\n    ZodAny: ZodAny,\n    ZodUnknown: ZodUnknown,\n    ZodNever: ZodNever,\n    ZodVoid: ZodVoid,\n    ZodArray: ZodArray,\n    ZodObject: ZodObject,\n    ZodUnion: ZodUnion,\n    ZodDiscriminatedUnion: ZodDiscriminatedUnion,\n    ZodIntersection: ZodIntersection,\n    ZodTuple: ZodTuple,\n    ZodRecord: ZodRecord,\n    ZodMap: ZodMap,\n    ZodSet: ZodSet,\n    ZodFunction: ZodFunction,\n    ZodLazy: ZodLazy,\n    ZodLiteral: ZodLiteral,\n    ZodEnum: ZodEnum,\n    ZodNativeEnum: ZodNativeEnum,\n    ZodPromise: ZodPromise,\n    ZodEffects: ZodEffects,\n    ZodTransformer: ZodEffects,\n    ZodOptional: ZodOptional,\n    ZodNullable: ZodNullable,\n    ZodDefault: ZodDefault,\n    ZodCatch: ZodCatch,\n    ZodNaN: ZodNaN,\n    BRAND: BRAND,\n    ZodBranded: ZodBranded,\n    ZodPipeline: ZodPipeline,\n    ZodReadonly: ZodReadonly,\n    custom: custom,\n    Schema: ZodType,\n    ZodSchema: ZodType,\n    late: late,\n    get ZodFirstPartyTypeKind () { return ZodFirstPartyTypeKind; },\n    coerce: coerce,\n    any: anyType,\n    array: arrayType,\n    bigint: bigIntType,\n    boolean: booleanType,\n    date: dateType,\n    discriminatedUnion: discriminatedUnionType,\n    effect: effectsType,\n    'enum': enumType,\n    'function': functionType,\n    'instanceof': instanceOfType,\n    intersection: intersectionType,\n    lazy: lazyType,\n    literal: literalType,\n    map: mapType,\n    nan: nanType,\n    nativeEnum: nativeEnumType,\n    never: neverType,\n    'null': nullType,\n    nullable: nullableType,\n    number: numberType,\n    object: objectType,\n    oboolean: oboolean,\n    onumber: onumber,\n    optional: optionalType,\n    ostring: ostring,\n    pipeline: pipelineType,\n    preprocess: preprocessType,\n    promise: promiseType,\n    record: recordType,\n    set: setType,\n    strictObject: strictObjectType,\n    string: stringType,\n    symbol: symbolType,\n    transformer: effectsType,\n    tuple: tupleType,\n    'undefined': undefinedType,\n    union: unionType,\n    unknown: unknownType,\n    'void': voidType,\n    NEVER: NEVER,\n    ZodIssueCode: ZodIssueCode,\n    quotelessJson: quotelessJson,\n    ZodError: ZodError\n});\n\nexport { BRAND, DIRTY, EMPTY_PATH, INVALID, NEVER, OK, ParseStatus, ZodType as Schema, ZodAny, ZodArray, ZodBigInt, ZodBoolean, ZodBranded, ZodCatch, ZodDate, ZodDefault, ZodDiscriminatedUnion, ZodEffects, ZodEnum, ZodError, ZodFirstPartyTypeKind, ZodFunction, ZodIntersection, ZodIssueCode, ZodLazy, ZodLiteral, ZodMap, ZodNaN, ZodNativeEnum, ZodNever, ZodNull, ZodNullable, ZodNumber, ZodObject, ZodOptional, ZodParsedType, ZodPipeline, ZodPromise, ZodReadonly, ZodRecord, ZodType as ZodSchema, ZodSet, ZodString, ZodSymbol, ZodEffects as ZodTransformer, ZodTuple, ZodType, ZodUndefined, ZodUnion, ZodUnknown, ZodVoid, addIssueToContext, anyType as any, arrayType as array, bigIntType as bigint, booleanType as boolean, coerce, custom, dateType as date, datetimeRegex, z as default, errorMap as defaultErrorMap, discriminatedUnionType as discriminatedUnion, effectsType as effect, enumType as enum, functionType as function, getErrorMap, getParsedType, instanceOfType as instanceof, intersectionType as intersection, isAborted, isAsync, isDirty, isValid, late, lazyType as lazy, literalType as literal, makeIssue, mapType as map, nanType as nan, nativeEnumType as nativeEnum, neverType as never, nullType as null, nullableType as nullable, numberType as number, objectType as object, objectUtil, oboolean, onumber, optionalType as optional, ostring, pipelineType as pipeline, preprocessType as preprocess, promiseType as promise, quotelessJson, recordType as record, setType as set, setErrorMap, strictObjectType as strictObject, stringType as string, symbolType as symbol, effectsType as transformer, tupleType as tuple, undefinedType as undefined, unionType as union, unknownType as unknown, util, voidType as void, z };\n", "/**\n * Internal webcrypto alias.\n * We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.\n * See utils.ts for details.\n * @module\n */\ndeclare const globalThis: Record<string, any> | undefined;\nexport const crypto: any =\n  typeof globalThis === 'object' && 'crypto' in globalThis ? globalThis.crypto : undefined;\n", "/**\n * Utilities for hex, bytes, CSPRNG.\n * @module\n */\n/*! noble-hashes - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\n// We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.\n// node.js versions earlier than v19 don't declare it in global scope.\n// For node.js, package.json#exports field mapping rewrites import\n// from `crypto` to `cryptoNode`, which imports native module.\n// Makes the utils un-importable in browsers without a bundler.\n// Once node.js 18 is deprecated (2025-04-30), we can just drop the import.\nimport { crypto } from '@noble/hashes/crypto';\n\n/** Checks if something is Uint8Array. Be careful: nodejs Buffer will return true. */\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\n/** Asserts something is positive integer. */\nexport function anumber(n: number): void {\n  if (!Number.isSafeInteger(n) || n < 0) throw new Error('positive integer expected, got ' + n);\n}\n\n/** Asserts something is Uint8Array. */\nexport function abytes(b: Uint8Array | undefined, ...lengths: number[]): void {\n  if (!isBytes(b)) throw new Error('Uint8Array expected');\n  if (lengths.length > 0 && !lengths.includes(b.length))\n    throw new Error('Uint8Array expected of length ' + lengths + ', got length=' + b.length);\n}\n\n/** Asserts something is hash */\nexport function ahash(h: IHash): void {\n  if (typeof h !== 'function' || typeof h.create !== 'function')\n    throw new Error('Hash should be wrapped by utils.createHasher');\n  anumber(h.outputLen);\n  anumber(h.blockLen);\n}\n\n/** Asserts a hash instance has not been destroyed / finished */\nexport function aexists(instance: any, checkFinished = true): void {\n  if (instance.destroyed) throw new Error('Hash instance has been destroyed');\n  if (checkFinished && instance.finished) throw new Error('Hash#digest() has already been called');\n}\n\n/** Asserts output is properly-sized byte array */\nexport function aoutput(out: any, instance: any): void {\n  abytes(out);\n  const min = instance.outputLen;\n  if (out.length < min) {\n    throw new Error('digestInto() expects output buffer of length at least ' + min);\n  }\n}\n\n/** Generic type encompassing 8/16/32-byte arrays - but not 64-byte. */\n// prettier-ignore\nexport type TypedArray = Int8Array | Uint8ClampedArray | Uint8Array |\n  Uint16Array | Int16Array | Uint32Array | Int32Array;\n\n/** Cast u8 / u16 / u32 to u8. */\nexport function u8(arr: TypedArray): Uint8Array {\n  return new Uint8Array(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** Cast u8 / u16 / u32 to u32. */\nexport function u32(arr: TypedArray): Uint32Array {\n  return new Uint32Array(arr.buffer, arr.byteOffset, Math.floor(arr.byteLength / 4));\n}\n\n/** Zeroize a byte array. Warning: JS provides no guarantees. */\nexport function clean(...arrays: TypedArray[]): void {\n  for (let i = 0; i < arrays.length; i++) {\n    arrays[i].fill(0);\n  }\n}\n\n/** Create DataView of an array for easy byte-level manipulation. */\nexport function createView(arr: TypedArray): DataView {\n  return new DataView(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** The rotate right (circular right shift) operation for uint32 */\nexport function rotr(word: number, shift: number): number {\n  return (word << (32 - shift)) | (word >>> shift);\n}\n\n/** The rotate left (circular left shift) operation for uint32 */\nexport function rotl(word: number, shift: number): number {\n  return (word << shift) | ((word >>> (32 - shift)) >>> 0);\n}\n\n/** Is current platform little-endian? Most are. Big-Endian platform: IBM */\nexport const isLE: boolean = /* @__PURE__ */ (() =>\n  new Uint8Array(new Uint32Array([0x11223344]).buffer)[0] === 0x44)();\n\n/** The byte swap operation for uint32 */\nexport function byteSwap(word: number): number {\n  return (\n    ((word << 24) & 0xff000000) |\n    ((word << 8) & 0xff0000) |\n    ((word >>> 8) & 0xff00) |\n    ((word >>> 24) & 0xff)\n  );\n}\n/** Conditionally byte swap if on a big-endian platform */\nexport const swap8IfBE: (n: number) => number = isLE\n  ? (n: number) => n\n  : (n: number) => byteSwap(n);\n\n/** @deprecated */\nexport const byteSwapIfBE: typeof swap8IfBE = swap8IfBE;\n/** In place byte swap for Uint32Array */\nexport function byteSwap32(arr: Uint32Array): Uint32Array {\n  for (let i = 0; i < arr.length; i++) {\n    arr[i] = byteSwap(arr[i]);\n  }\n  return arr;\n}\n\nexport const swap32IfBE: (u: Uint32Array) => Uint32Array = isLE\n  ? (u: Uint32Array) => u\n  : byteSwap32;\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean = /* @__PURE__ */ (() =>\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function')();\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\n  // pre-caching improves the speed 6x\n  let hex = '';\n  for (let i = 0; i < bytes.length; i++) {\n    hex += hexes[bytes[i]];\n  }\n  return hex;\n}\n\n// We use optimized technique to convert hex string to byte array\nconst asciis = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('hex string expected, got unpadded hex of length ' + hl);\n  const array = new Uint8Array(al);\n  for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {\n    const n1 = asciiToBase16(hex.charCodeAt(hi));\n    const n2 = asciiToBase16(hex.charCodeAt(hi + 1));\n    if (n1 === undefined || n2 === undefined) {\n      const char = hex[hi] + hex[hi + 1];\n      throw new Error('hex string expected, got non-hex character \"' + char + '\" at index ' + hi);\n    }\n    array[ai] = n1 * 16 + n2; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\n/**\n * There is no setImmediate in browser and setTimeout is slow.\n * Call of async fn will return Promise, which will be fullfiled only on\n * next scheduler queue processing step and this is exactly what we need.\n */\nexport const nextTick = async (): Promise<void> => {};\n\n/** Returns control to thread each 'tick' ms to avoid blocking. */\nexport async function asyncLoop(\n  iters: number,\n  tick: number,\n  cb: (i: number) => void\n): Promise<void> {\n  let ts = Date.now();\n  for (let i = 0; i < iters; i++) {\n    cb(i);\n    // Date.now() is not monotonic, so in case if clock goes backwards we return return control too\n    const diff = Date.now() - ts;\n    if (diff >= 0 && diff < tick) continue;\n    await nextTick();\n    ts += diff;\n  }\n}\n\n// Global symbols, but ts doesn't see them: https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\ndeclare const TextDecoder: any;\n\n/**\n * Converts string to bytes using UTF8 encoding.\n * @example utf8ToBytes('abc') // Uint8Array.from([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n/**\n * Converts bytes to string using UTF8 encoding.\n * @example bytesToUtf8(Uint8Array.from([97, 98, 99])) // 'abc'\n */\nexport function bytesToUtf8(bytes: Uint8Array): string {\n  return new TextDecoder().decode(bytes);\n}\n\n/** Accepted input of hash functions. Strings are converted to byte arrays. */\nexport type Input = string | Uint8Array;\n/**\n * Normalizes (non-hex) string or Uint8Array to Uint8Array.\n * Warning: when Uint8Array is passed, it would NOT get copied.\n * Keep in mind for future mutable operations.\n */\nexport function toBytes(data: Input): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** KDFs can accept string or Uint8Array for user convenience. */\nexport type KDFInput = string | Uint8Array;\n/**\n * Helper for KDFs: consumes uint8array or string.\n * When string is passed, does utf8 decoding, using TextDecoder.\n */\nexport function kdfInputToBytes(data: KDFInput): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** Copies several Uint8Arrays into one. */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\ntype EmptyObj = {};\nexport function checkOpts<T1 extends EmptyObj, T2 extends EmptyObj>(\n  defaults: T1,\n  opts?: T2\n): T1 & T2 {\n  if (opts !== undefined && {}.toString.call(opts) !== '[object Object]')\n    throw new Error('options should be object or undefined');\n  const merged = Object.assign(defaults, opts);\n  return merged as T1 & T2;\n}\n\n/** Hash interface. */\nexport type IHash = {\n  (data: Uint8Array): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create: any;\n};\n\n/** For runtime check if class implements interface */\nexport abstract class Hash<T extends Hash<T>> {\n  abstract blockLen: number; // Bytes per block\n  abstract outputLen: number; // Bytes in output\n  abstract update(buf: Input): this;\n  // Writes digest into buf\n  abstract digestInto(buf: Uint8Array): void;\n  abstract digest(): Uint8Array;\n  /**\n   * Resets internal state. Makes Hash instance unusable.\n   * Reset is impossible for keyed hashes if key is consumed into state. If digest is not consumed\n   * by user, they will need to manually call `destroy()` when zeroing is necessary.\n   */\n  abstract destroy(): void;\n  /**\n   * Clones hash instance. Unsafe: doesn't check whether `to` is valid. Can be used as `clone()`\n   * when no options are passed.\n   * Reasons to use `_cloneInto` instead of clone: 1) performance 2) reuse instance => all internal\n   * buffers are overwritten => causes buffer overwrite which is used for digest in some cases.\n   * There are no guarantees for clean-up because it's impossible in JS.\n   */\n  abstract _cloneInto(to?: T): T;\n  // Safe version that clones internal state\n  abstract clone(): T;\n}\n\n/**\n * XOF: streaming API to read digest in chunks.\n * Same as 'squeeze' in keccak/k12 and 'seek' in blake3, but more generic name.\n * When hash used in XOF mode it is up to user to call '.destroy' afterwards, since we cannot\n * destroy state, next call can require more bytes.\n */\nexport type HashXOF<T extends Hash<T>> = Hash<T> & {\n  xof(bytes: number): Uint8Array; // Read 'bytes' bytes from digest stream\n  xofInto(buf: Uint8Array): Uint8Array; // read buf.length bytes from digest stream into buf\n};\n\n/** Hash function */\nexport type CHash = ReturnType<typeof createHasher>;\n/** Hash function with output */\nexport type CHashO = ReturnType<typeof createOptHasher>;\n/** XOF with output */\nexport type CHashXO = ReturnType<typeof createXOFer>;\n\n/** Wraps hash function, creating an interface on top of it */\nexport function createHasher<T extends Hash<T>>(\n  hashCons: () => Hash<T>\n): {\n  (msg: Input): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(): Hash<T>;\n} {\n  const hashC = (msg: Input): Uint8Array => hashCons().update(toBytes(msg)).digest();\n  const tmp = hashCons();\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = () => hashCons();\n  return hashC;\n}\n\nexport function createOptHasher<H extends Hash<H>, T extends Object>(\n  hashCons: (opts?: T) => Hash<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): Hash<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\n\nexport function createXOFer<H extends HashXOF<H>, T extends Object>(\n  hashCons: (opts?: T) => HashXOF<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): HashXOF<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\nexport const wrapConstructor: typeof createHasher = createHasher;\nexport const wrapConstructorWithOpts: typeof createOptHasher = createOptHasher;\nexport const wrapXOFConstructorWithOpts: typeof createXOFer = createXOFer;\n\n/** Cryptographically secure PRNG. Uses internal OS-level `crypto.getRandomValues`. */\nexport function randomBytes(bytesLength = 32): Uint8Array {\n  if (crypto && typeof crypto.getRandomValues === 'function') {\n    return crypto.getRandomValues(new Uint8Array(bytesLength));\n  }\n  // Legacy Node.js compatibility\n  if (crypto && typeof crypto.randomBytes === 'function') {\n    return Uint8Array.from(crypto.randomBytes(bytesLength));\n  }\n  throw new Error('crypto.getRandomValues must be defined');\n}\n", "/**\n * Hex, bytes and number utilities.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\n// 100 lines of code in the file are duplicated from noble-hashes (utils).\n// This is OK: `abstract` directory does not use noble-hashes.\n// User may opt-in into using different hashing library. This way, noble-hashes\n// won't be included into their bundle.\nconst _0n = /* @__PURE__ */ BigInt(0);\nconst _1n = /* @__PURE__ */ BigInt(1);\nexport type Hex = Uint8Array | string; // hex strings are accepted for simplicity\nexport type PrivKey = Hex | bigint; // bigints are accepted to ease learning curve\nexport type CHash = {\n  (message: Uint8Array | string): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create(opts?: { dkLen?: number }): any; // For shake\n};\nexport type FHash = (message: Uint8Array | string) => Uint8Array;\n\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\nexport function abytes(item: unknown): void {\n  if (!isBytes(item)) throw new Error('Uint8Array expected');\n}\n\nexport function abool(title: string, value: boolean): void {\n  if (typeof value !== 'boolean') throw new Error(title + ' boolean expected, got ' + value);\n}\n\n// Used in weierstrass, der\nexport function numberToHexUnpadded(num: number | bigint): string {\n  const hex = num.toString(16);\n  return hex.length & 1 ? '0' + hex : hex;\n}\n\nexport function hexToNumber(hex: string): bigint {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  return hex === '' ? _0n : BigInt('0x' + hex); // Big Endian\n}\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean =\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function';\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\n  // pre-caching improves the speed 6x\n  let hex = '';\n  for (let i = 0; i < bytes.length; i++) {\n    hex += hexes[bytes[i]];\n  }\n  return hex;\n}\n\n// We use optimized technique to convert hex string to byte array\nconst asciis = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('hex string expected, got unpadded hex of length ' + hl);\n  const array = new Uint8Array(al);\n  for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {\n    const n1 = asciiToBase16(hex.charCodeAt(hi));\n    const n2 = asciiToBase16(hex.charCodeAt(hi + 1));\n    if (n1 === undefined || n2 === undefined) {\n      const char = hex[hi] + hex[hi + 1];\n      throw new Error('hex string expected, got non-hex character \"' + char + '\" at index ' + hi);\n    }\n    array[ai] = n1 * 16 + n2; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\n// BE: Big Endian, LE: Little Endian\nexport function bytesToNumberBE(bytes: Uint8Array): bigint {\n  return hexToNumber(bytesToHex(bytes));\n}\nexport function bytesToNumberLE(bytes: Uint8Array): bigint {\n  abytes(bytes);\n  return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));\n}\n\nexport function numberToBytesBE(n: number | bigint, len: number): Uint8Array {\n  return hexToBytes(n.toString(16).padStart(len * 2, '0'));\n}\nexport function numberToBytesLE(n: number | bigint, len: number): Uint8Array {\n  return numberToBytesBE(n, len).reverse();\n}\n// Unpadded, rarely used\nexport function numberToVarBytesBE(n: number | bigint): Uint8Array {\n  return hexToBytes(numberToHexUnpadded(n));\n}\n\n/**\n * Takes hex string or Uint8Array, converts to Uint8Array.\n * Validates output length.\n * Will throw error for other types.\n * @param title descriptive title for an error e.g. 'private key'\n * @param hex hex string or Uint8Array\n * @param expectedLength optional, will compare to result array's length\n * @returns\n */\nexport function ensureBytes(title: string, hex: Hex, expectedLength?: number): Uint8Array {\n  let res: Uint8Array;\n  if (typeof hex === 'string') {\n    try {\n      res = hexToBytes(hex);\n    } catch (e) {\n      throw new Error(title + ' must be hex string or Uint8Array, cause: ' + e);\n    }\n  } else if (isBytes(hex)) {\n    // Uint8Array.from() instead of hash.slice() because node.js Buffer\n    // is instance of Uint8Array, and its slice() creates **mutable** copy\n    res = Uint8Array.from(hex);\n  } else {\n    throw new Error(title + ' must be hex string or Uint8Array');\n  }\n  const len = res.length;\n  if (typeof expectedLength === 'number' && len !== expectedLength)\n    throw new Error(title + ' of length ' + expectedLength + ' expected, got ' + len);\n  return res;\n}\n\n/**\n * Copies several Uint8Arrays into one.\n */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\n// Compares 2 u8a-s in kinda constant time\nexport function equalBytes(a: Uint8Array, b: Uint8Array): boolean {\n  if (a.length !== b.length) return false;\n  let diff = 0;\n  for (let i = 0; i < a.length; i++) diff |= a[i] ^ b[i];\n  return diff === 0;\n}\n\n// Global symbols in both browsers and Node.js since v11\n// See https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\n\n/**\n * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n// Is positive bigint\nconst isPosBig = (n: bigint) => typeof n === 'bigint' && _0n <= n;\n\nexport function inRange(n: bigint, min: bigint, max: bigint): boolean {\n  return isPosBig(n) && isPosBig(min) && isPosBig(max) && min <= n && n < max;\n}\n\n/**\n * Asserts min <= n < max. NOTE: It's < max and not <= max.\n * @example\n * aInRange('x', x, 1n, 256n); // would assume x is in (1n..255n)\n */\nexport function aInRange(title: string, n: bigint, min: bigint, max: bigint): void {\n  // Why min <= n < max and not a (min < n < max) OR b (min <= n <= max)?\n  // consider P=256n, min=0n, max=P\n  // - a for min=0 would require -1:          `inRange('x', x, -1n, P)`\n  // - b would commonly require subtraction:  `inRange('x', x, 0n, P - 1n)`\n  // - our way is the cleanest:               `inRange('x', x, 0n, P)\n  if (!inRange(n, min, max))\n    throw new Error('expected valid ' + title + ': ' + min + ' <= n < ' + max + ', got ' + n);\n}\n\n// Bit operations\n\n/**\n * Calculates amount of bits in a bigint.\n * Same as `n.toString(2).length`\n * TODO: merge with nLength in modular\n */\nexport function bitLen(n: bigint): number {\n  let len;\n  for (len = 0; n > _0n; n >>= _1n, len += 1);\n  return len;\n}\n\n/**\n * Gets single bit at position.\n * NOTE: first bit position is 0 (same as arrays)\n * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`\n */\nexport function bitGet(n: bigint, pos: number): bigint {\n  return (n >> BigInt(pos)) & _1n;\n}\n\n/**\n * Sets single bit at position.\n */\nexport function bitSet(n: bigint, pos: number, value: boolean): bigint {\n  return n | ((value ? _1n : _0n) << BigInt(pos));\n}\n\n/**\n * Calculate mask for N bits. Not using ** operator with bigints because of old engines.\n * Same as BigInt(`0b${Array(i).fill('1').join('')}`)\n */\nexport const bitMask = (n: number): bigint => (_1n << BigInt(n)) - _1n;\n\n// DRBG\n\nconst u8n = (len: number) => new Uint8Array(len); // creates Uint8Array\nconst u8fr = (arr: ArrayLike<number>) => Uint8Array.from(arr); // another shortcut\ntype Pred<T> = (v: Uint8Array) => T | undefined;\n/**\n * Minimal HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n * @returns function that will call DRBG until 2nd arg returns something meaningful\n * @example\n *   const drbg = createHmacDRBG<Key>(32, 32, hmac);\n *   drbg(seed, bytesToKey); // bytesToKey must return Key or undefined\n */\nexport function createHmacDrbg<T>(\n  hashLen: number,\n  qByteLen: number,\n  hmacFn: (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array\n): (seed: Uint8Array, predicate: Pred<T>) => T {\n  if (typeof hashLen !== 'number' || hashLen < 2) throw new Error('hashLen must be a number');\n  if (typeof qByteLen !== 'number' || qByteLen < 2) throw new Error('qByteLen must be a number');\n  if (typeof hmacFn !== 'function') throw new Error('hmacFn must be a function');\n  // Step B, Step C: set hashLen to 8*ceil(hlen/8)\n  let v = u8n(hashLen); // Minimal non-full-spec HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n  let k = u8n(hashLen); // Steps B and C of RFC6979 3.2: set hashLen, in our case always same\n  let i = 0; // Iterations counter, will throw when over 1000\n  const reset = () => {\n    v.fill(1);\n    k.fill(0);\n    i = 0;\n  };\n  const h = (...b: Uint8Array[]) => hmacFn(k, v, ...b); // hmac(k)(v, ...values)\n  const reseed = (seed = u8n(0)) => {\n    // HMAC-DRBG reseed() function. Steps D-G\n    k = h(u8fr([0x00]), seed); // k = hmac(k || v || 0x00 || seed)\n    v = h(); // v = hmac(k || v)\n    if (seed.length === 0) return;\n    k = h(u8fr([0x01]), seed); // k = hmac(k || v || 0x01 || seed)\n    v = h(); // v = hmac(k || v)\n  };\n  const gen = () => {\n    // HMAC-DRBG generate() function\n    if (i++ >= 1000) throw new Error('drbg: tried 1000 values');\n    let len = 0;\n    const out: Uint8Array[] = [];\n    while (len < qByteLen) {\n      v = h();\n      const sl = v.slice();\n      out.push(sl);\n      len += v.length;\n    }\n    return concatBytes(...out);\n  };\n  const genUntil = (seed: Uint8Array, pred: Pred<T>): T => {\n    reset();\n    reseed(seed); // Steps D-G\n    let res: T | undefined = undefined; // Step H: grind until k is in [1..n-1]\n    while (!(res = pred(gen()))) reseed();\n    reset();\n    return res;\n  };\n  return genUntil;\n}\n\n// Validating curves and fields\n\nconst validatorFns = {\n  bigint: (val: any): boolean => typeof val === 'bigint',\n  function: (val: any): boolean => typeof val === 'function',\n  boolean: (val: any): boolean => typeof val === 'boolean',\n  string: (val: any): boolean => typeof val === 'string',\n  stringOrUint8Array: (val: any): boolean => typeof val === 'string' || isBytes(val),\n  isSafeInteger: (val: any): boolean => Number.isSafeInteger(val),\n  array: (val: any): boolean => Array.isArray(val),\n  field: (val: any, object: any): any => (object as any).Fp.isValid(val),\n  hash: (val: any): boolean => typeof val === 'function' && Number.isSafeInteger(val.outputLen),\n} as const;\ntype Validator = keyof typeof validatorFns;\ntype ValMap<T extends Record<string, any>> = { [K in keyof T]?: Validator };\n// type Record<K extends string | number | symbol, T> = { [P in K]: T; }\n\nexport function validateObject<T extends Record<string, any>>(\n  object: T,\n  validators: ValMap<T>,\n  optValidators: ValMap<T> = {}\n): T {\n  const checkField = (fieldName: keyof T, type: Validator, isOptional: boolean) => {\n    const checkVal = validatorFns[type];\n    if (typeof checkVal !== 'function') throw new Error('invalid validator function');\n\n    const val = object[fieldName as keyof typeof object];\n    if (isOptional && val === undefined) return;\n    if (!checkVal(val, object)) {\n      throw new Error(\n        'param ' + String(fieldName) + ' is invalid. Expected ' + type + ', got ' + val\n      );\n    }\n  };\n  for (const [fieldName, type] of Object.entries(validators)) checkField(fieldName, type!, false);\n  for (const [fieldName, type] of Object.entries(optValidators)) checkField(fieldName, type!, true);\n  return object;\n}\n// validate type tests\n// const o: { a: number; b: number; c: number } = { a: 1, b: 5, c: 6 };\n// const z0 = validateObject(o, { a: 'isSafeInteger' }, { c: 'bigint' }); // Ok!\n// // Should fail type-check\n// const z1 = validateObject(o, { a: 'tmp' }, { c: 'zz' });\n// const z2 = validateObject(o, { a: 'isSafeInteger' }, { c: 'zz' });\n// const z3 = validateObject(o, { test: 'boolean', z: 'bug' });\n// const z4 = validateObject(o, { a: 'boolean', z: 'bug' });\n\n/**\n * throws not implemented error\n */\nexport const notImplemented = (): never => {\n  throw new Error('not implemented');\n};\n\n/**\n * Memoizes (caches) computation result.\n * Uses WeakMap: the value is going auto-cleaned by GC after last reference is removed.\n */\nexport function memoized<T extends object, R, O extends any[]>(\n  fn: (arg: T, ...args: O) => R\n): (arg: T, ...args: O) => R {\n  const map = new WeakMap<T, R>();\n  return (arg: T, ...args: O): R => {\n    const val = map.get(arg);\n    if (val !== undefined) return val;\n    const computed = fn(arg, ...args);\n    map.set(arg, computed);\n    return computed;\n  };\n}\n", "/**\n * Utils for modular division and finite fields.\n * A finite field over 11 is integer number operations `mod 11`.\n * There is no division: it is replaced by modular multiplicative inverse.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { anumber } from '@noble/hashes/utils';\nimport {\n  bitMask,\n  bytesToNumberBE,\n  bytesToNumberLE,\n  ensureBytes,\n  numberToBytesBE,\n  numberToBytesLE,\n  validateObject,\n} from './utils.ts';\n\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _3n = /* @__PURE__ */ BigInt(3);\n// prettier-ignore\nconst _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5), _8n = /* @__PURE__ */ BigInt(8);\n// prettier-ignore\nconst _9n =/* @__PURE__ */ BigInt(9), _16n = /* @__PURE__ */ BigInt(16);\n\n// Calculates a modulo b\nexport function mod(a: bigint, b: bigint): bigint {\n  const result = a % b;\n  return result >= _0n ? result : b + result;\n}\n/**\n * Efficiently raise num to power and do modular division.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n * TODO: remove.\n * @example\n * pow(2n, 6n, 11n) // 64n % 11n == 9n\n */\nexport function pow(num: bigint, power: bigint, modulo: bigint): bigint {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (modulo <= _0n) throw new Error('invalid modulus');\n  if (modulo === _1n) return _0n;\n  let res = _1n;\n  while (power > _0n) {\n    if (power & _1n) res = (res * num) % modulo;\n    num = (num * num) % modulo;\n    power >>= _1n;\n  }\n  return res;\n}\n\n/** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */\nexport function pow2(x: bigint, power: bigint, modulo: bigint): bigint {\n  let res = x;\n  while (power-- > _0n) {\n    res *= res;\n    res %= modulo;\n  }\n  return res;\n}\n\n/**\n * Inverses number over modulo.\n * Implemented using [Euclidean GCD](https://brilliant.org/wiki/extended-euclidean-algorithm/).\n */\nexport function invert(number: bigint, modulo: bigint): bigint {\n  if (number === _0n) throw new Error('invert: expected non-zero number');\n  if (modulo <= _0n) throw new Error('invert: expected positive modulus, got ' + modulo);\n  // Fermat's little theorem \"CT-like\" version inv(n) = n^(m-2) mod m is 30x slower.\n  let a = mod(number, modulo);\n  let b = modulo;\n  // prettier-ignore\n  let x = _0n, y = _1n, u = _1n, v = _0n;\n  while (a !== _0n) {\n    // JIT applies optimization if those two lines follow each other\n    const q = b / a;\n    const r = b % a;\n    const m = x - u * q;\n    const n = y - v * q;\n    // prettier-ignore\n    b = a, a = r, x = u, y = v, u = m, v = n;\n  }\n  const gcd = b;\n  if (gcd !== _1n) throw new Error('invert: does not exist');\n  return mod(x, modulo);\n}\n\n/**\n * Tonelli-Shanks square root search algorithm.\n * 1. https://eprint.iacr.org/2012/685.pdf (page 12)\n * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks\n * @param P field order\n * @returns function that takes field Fp (created from P) and number n\n */\nexport function tonelliShanks(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // Do expensive precomputation step\n  // Step 1: By factoring out powers of 2 from p - 1,\n  // find q and s such that p-1 == q*(2^s) with q odd\n  let Q = P - _1n;\n  let S = 0;\n  while (Q % _2n === _0n) {\n    Q /= _2n;\n    S++;\n  }\n\n  // Step 2: Select a non-square z such that (z | p) \u2261 -1 and set c \u2261 zq\n  let Z = _2n;\n  const _Fp = Field(P);\n  while (Z < P && FpIsSquare(_Fp, Z)) {\n    if (Z++ > 1000) throw new Error('Cannot find square root: probably non-prime P');\n  }\n\n  // Fast-path\n  if (S === 1) {\n    const p1div4 = (P + _1n) / _4n;\n    return function tonelliFast<T>(Fp: IField<T>, n: T) {\n      const root = Fp.pow(n, p1div4);\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n  // Slow-path\n  const Q1div2 = (Q + _1n) / _2n;\n  return function tonelliSlow<T>(Fp: IField<T>, n: T): T {\n    // Step 0: Check that n is indeed a square: (n | p) should not be \u2261 -1\n    if (!FpIsSquare(Fp, n)) throw new Error('Cannot find square root');\n    let r = S;\n    // TODO: test on Fp2 and others\n    let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b\n    let x = Fp.pow(n, Q1div2); // first guess at the square root\n    let b = Fp.pow(n, Q); // first guess at the fudge factor\n\n    while (!Fp.eql(b, Fp.ONE)) {\n      // (4. If t = 0, return r = 0)\n      // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm\n      if (Fp.eql(b, Fp.ZERO)) return Fp.ZERO;\n      // Find m such b^(2^m)==1\n      let m = 1;\n      for (let t2 = Fp.sqr(b); m < r; m++) {\n        if (Fp.eql(t2, Fp.ONE)) break;\n        t2 = Fp.sqr(t2); // t2 *= t2\n      }\n      // NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift,\n      // otherwise there will be overflow.\n      const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)\n      g = Fp.sqr(ge); // g = ge * ge\n      x = Fp.mul(x, ge); // x *= ge\n      b = Fp.mul(b, g); // b *= g\n      r = m;\n    }\n    return x;\n  };\n}\n\n/**\n * Square root for a finite field. It will try to check if optimizations are applicable and fall back to 4:\n *\n * 1. P \u2261 3 (mod 4)\n * 2. P \u2261 5 (mod 8)\n * 3. P \u2261 9 (mod 16)\n * 4. Tonelli-Shanks algorithm\n *\n * Different algorithms can give different roots, it is up to user to decide which one they want.\n * For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).\n */\nexport function FpSqrt(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // P \u2261 3 (mod 4)\n  // \u221An = n^((P+1)/4)\n  if (P % _4n === _3n) {\n    // Not all roots possible!\n    // const ORDER =\n    //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;\n    // const NUM = 72057594037927816n;\n    return function sqrt3mod4<T>(Fp: IField<T>, n: T) {\n      const p1div4 = (P + _1n) / _4n;\n      const root = Fp.pow(n, p1div4);\n      // Throw if root**2 != n\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // Atkin algorithm for q \u2261 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)\n  if (P % _8n === _5n) {\n    return function sqrt5mod8<T>(Fp: IField<T>, n: T) {\n      const n2 = Fp.mul(n, _2n);\n      const c1 = (P - _5n) / _8n;\n      const v = Fp.pow(n2, c1);\n      const nv = Fp.mul(n, v);\n      const i = Fp.mul(Fp.mul(nv, _2n), v);\n      const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // P \u2261 9 (mod 16)\n  if (P % _16n === _9n) {\n    // NOTE: tonelli is too slow for bls-Fp2 calculations even on start\n    // Means we cannot use sqrt for constants at all!\n    //\n    // const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F\n    // const c2 = Fp.sqrt(c1);                //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F\n    // const c3 = Fp.sqrt(Fp.negate(c1));     //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F\n    // const c4 = (P + _7n) / _16n;           //  4. c4 = (q + 7) / 16        # Integer arithmetic\n    // sqrt = (x) => {\n    //   let tv1 = Fp.pow(x, c4);             //  1. tv1 = x^c4\n    //   let tv2 = Fp.mul(c1, tv1);           //  2. tv2 = c1 * tv1\n    //   const tv3 = Fp.mul(c2, tv1);         //  3. tv3 = c2 * tv1\n    //   let tv4 = Fp.mul(c3, tv1);           //  4. tv4 = c3 * tv1\n    //   const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x\n    //   const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x\n    //   tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x\n    //   tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x\n    //   const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x\n    //   return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2\n    // }\n  }\n  // Other cases: Tonelli-Shanks algorithm\n  return tonelliShanks(P);\n}\n\n// Little-endian check for first LE bit (last BE bit);\nexport const isNegativeLE = (num: bigint, modulo: bigint): boolean =>\n  (mod(num, modulo) & _1n) === _1n;\n\n/** Field is not always over prime: for example, Fp2 has ORDER(q)=p^m. */\nexport interface IField<T> {\n  ORDER: bigint;\n  isLE: boolean;\n  BYTES: number;\n  BITS: number;\n  MASK: bigint;\n  ZERO: T;\n  ONE: T;\n  // 1-arg\n  create: (num: T) => T;\n  isValid: (num: T) => boolean;\n  is0: (num: T) => boolean;\n  neg(num: T): T;\n  inv(num: T): T;\n  sqrt(num: T): T;\n  sqr(num: T): T;\n  // 2-args\n  eql(lhs: T, rhs: T): boolean;\n  add(lhs: T, rhs: T): T;\n  sub(lhs: T, rhs: T): T;\n  mul(lhs: T, rhs: T | bigint): T;\n  pow(lhs: T, power: bigint): T;\n  div(lhs: T, rhs: T | bigint): T;\n  // N for NonNormalized (for now)\n  addN(lhs: T, rhs: T): T;\n  subN(lhs: T, rhs: T): T;\n  mulN(lhs: T, rhs: T | bigint): T;\n  sqrN(num: T): T;\n\n  // Optional\n  // Should be same as sgn0 function in\n  // [RFC9380](https://www.rfc-editor.org/rfc/rfc9380#section-4.1).\n  // NOTE: sgn0 is 'negative in LE', which is same as odd. And negative in LE is kinda strange definition anyway.\n  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2\n  // legendre?(num: T): T;\n  pow(lhs: T, power: bigint): T;\n  invertBatch: (lst: T[]) => T[];\n  toBytes(num: T): Uint8Array;\n  fromBytes(bytes: Uint8Array): T;\n  // If c is False, CMOV returns a, otherwise it returns b.\n  cmov(a: T, b: T, c: boolean): T;\n}\n// prettier-ignore\nconst FIELD_FIELDS = [\n  'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',\n  'eql', 'add', 'sub', 'mul', 'pow', 'div',\n  'addN', 'subN', 'mulN', 'sqrN'\n] as const;\nexport function validateField<T>(field: IField<T>): IField<T> {\n  const initial = {\n    ORDER: 'bigint',\n    MASK: 'bigint',\n    BYTES: 'isSafeInteger',\n    BITS: 'isSafeInteger',\n  } as Record<string, string>;\n  const opts = FIELD_FIELDS.reduce((map, val: string) => {\n    map[val] = 'function';\n    return map;\n  }, initial);\n  return validateObject(field, opts);\n}\n\n// Generic field functions\n\n/**\n * Same as `pow` but for Fp: non-constant-time.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n */\nexport function FpPow<T>(Fp: IField<T>, num: T, power: bigint): T {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (power === _0n) return Fp.ONE;\n  if (power === _1n) return num;\n  // @ts-ignore\n  let p = Fp.ONE;\n  let d = num;\n  while (power > _0n) {\n    if (power & _1n) p = Fp.mul(p, d);\n    d = Fp.sqr(d);\n    power >>= _1n;\n  }\n  return p;\n}\n\n/**\n * Efficiently invert an array of Field elements.\n * Exception-free. Will return `undefined` for 0 elements.\n * @param passZero map 0 to 0 (instead of undefined)\n */\nexport function FpInvertBatch<T>(Fp: IField<T>, nums: T[], passZero = false): T[] {\n  const inverted = new Array(nums.length).fill(passZero ? Fp.ZERO : undefined);\n  // Walk from first to last, multiply them by each other MOD p\n  const multipliedAcc = nums.reduce((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = acc;\n    return Fp.mul(acc, num);\n  }, Fp.ONE);\n  // Invert last element\n  const invertedAcc = Fp.inv(multipliedAcc);\n  // Walk from last to first, multiply them by inverted each other MOD p\n  nums.reduceRight((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = Fp.mul(acc, inverted[i]);\n    return Fp.mul(acc, num);\n  }, invertedAcc);\n  return inverted;\n}\n\n// TODO: remove\nexport function FpDiv<T>(Fp: IField<T>, lhs: T, rhs: T | bigint): T {\n  return Fp.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, Fp.ORDER) : Fp.inv(rhs));\n}\n\n/**\n * Legendre symbol.\n * Legendre constant is used to calculate Legendre symbol (a | p)\n * which denotes the value of a^((p-1)/2) (mod p)..\n *\n * * (a | p) \u2261 1    if a is a square (mod p), quadratic residue\n * * (a | p) \u2261 -1   if a is not a square (mod p), quadratic non residue\n * * (a | p) \u2261 0    if a \u2261 0 (mod p)\n */\nexport function FpLegendre<T>(Fp: IField<T>, n: T): number {\n  const legc = (Fp.ORDER - _1n) / _2n;\n  const powered = Fp.pow(n, legc);\n  const yes = Fp.eql(powered, Fp.ONE);\n  const zero = Fp.eql(powered, Fp.ZERO);\n  const no = Fp.eql(powered, Fp.neg(Fp.ONE));\n  if (!yes && !zero && !no) throw new Error('Cannot find square root: probably non-prime P');\n  return yes ? 1 : zero ? 0 : -1;\n}\n\n// This function returns True whenever the value x is a square in the field F.\nexport function FpIsSquare<T>(Fp: IField<T>, n: T): boolean {\n  const l = FpLegendre(Fp, n);\n  return l === 0 || l === 1;\n}\n\n// CURVE.n lengths\nexport function nLength(\n  n: bigint,\n  nBitLength?: number\n): {\n  nBitLength: number;\n  nByteLength: number;\n} {\n  // Bit size, byte size of CURVE.n\n  if (nBitLength !== undefined) anumber(nBitLength);\n  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;\n  const nByteLength = Math.ceil(_nBitLength / 8);\n  return { nBitLength: _nBitLength, nByteLength };\n}\n\ntype FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;\n/**\n * Initializes a finite field over prime.\n * Major performance optimizations:\n * * a) denormalized operations like mulN instead of mul\n * * b) same object shape: never add or remove keys\n * * c) Object.freeze\n * Fragile: always run a benchmark on a change.\n * Security note: operations don't check 'isValid' for all elements for performance reasons,\n * it is caller responsibility to check this.\n * This is low-level code, please make sure you know what you're doing.\n * @param ORDER prime positive bigint\n * @param bitLen how many bits the field consumes\n * @param isLE (def: false) if encoding / decoding should be in little-endian\n * @param redef optional faster redefinitions of sqrt and other methods\n */\nexport function Field(\n  ORDER: bigint,\n  bitLen?: number,\n  isLE = false,\n  redef: Partial<IField<bigint>> = {}\n): Readonly<FpField> {\n  if (ORDER <= _0n) throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);\n  const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);\n  if (BYTES > 2048) throw new Error('invalid field: expected ORDER of <= 2048 bytes');\n  let sqrtP: ReturnType<typeof FpSqrt>; // cached sqrtP\n  const f: Readonly<FpField> = Object.freeze({\n    ORDER,\n    isLE,\n    BITS,\n    BYTES,\n    MASK: bitMask(BITS),\n    ZERO: _0n,\n    ONE: _1n,\n    create: (num) => mod(num, ORDER),\n    isValid: (num) => {\n      if (typeof num !== 'bigint')\n        throw new Error('invalid field element: expected bigint, got ' + typeof num);\n      return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible\n    },\n    is0: (num) => num === _0n,\n    isOdd: (num) => (num & _1n) === _1n,\n    neg: (num) => mod(-num, ORDER),\n    eql: (lhs, rhs) => lhs === rhs,\n\n    sqr: (num) => mod(num * num, ORDER),\n    add: (lhs, rhs) => mod(lhs + rhs, ORDER),\n    sub: (lhs, rhs) => mod(lhs - rhs, ORDER),\n    mul: (lhs, rhs) => mod(lhs * rhs, ORDER),\n    pow: (num, power) => FpPow(f, num, power),\n    div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),\n\n    // Same as above, but doesn't normalize\n    sqrN: (num) => num * num,\n    addN: (lhs, rhs) => lhs + rhs,\n    subN: (lhs, rhs) => lhs - rhs,\n    mulN: (lhs, rhs) => lhs * rhs,\n\n    inv: (num) => invert(num, ORDER),\n    sqrt:\n      redef.sqrt ||\n      ((n) => {\n        if (!sqrtP) sqrtP = FpSqrt(ORDER);\n        return sqrtP(f, n);\n      }),\n    toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),\n    fromBytes: (bytes) => {\n      if (bytes.length !== BYTES)\n        throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);\n      return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);\n    },\n    // TODO: we don't need it here, move out to separate fn\n    invertBatch: (lst) => FpInvertBatch(f, lst),\n    // We can't move this out because Fp6, Fp12 implement it\n    // and it's unclear what to return in there.\n    cmov: (a, b, c) => (c ? b : a),\n  } as FpField);\n  return Object.freeze(f);\n}\n\nexport function FpSqrtOdd<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n  const root = Fp.sqrt(elm);\n  return Fp.isOdd(root) ? root : Fp.neg(root);\n}\n\nexport function FpSqrtEven<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n  const root = Fp.sqrt(elm);\n  return Fp.isOdd(root) ? Fp.neg(root) : root;\n}\n\n/**\n * \"Constant-time\" private key generation utility.\n * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).\n * Which makes it slightly more biased, less secure.\n * @deprecated use `mapKeyToField` instead\n */\nexport function hashToPrivateScalar(\n  hash: string | Uint8Array,\n  groupOrder: bigint,\n  isLE = false\n): bigint {\n  hash = ensureBytes('privateHash', hash);\n  const hashLen = hash.length;\n  const minLen = nLength(groupOrder).nByteLength + 8;\n  if (minLen < 24 || hashLen < minLen || hashLen > 1024)\n    throw new Error(\n      'hashToPrivateScalar: expected ' + minLen + '-1024 bytes of input, got ' + hashLen\n    );\n  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);\n  return mod(num, groupOrder - _1n) + _1n;\n}\n\n/**\n * Returns total number of bytes consumed by the field element.\n * For example, 32 bytes for usual 256-bit weierstrass curve.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of field\n */\nexport function getFieldBytesLength(fieldOrder: bigint): number {\n  if (typeof fieldOrder !== 'bigint') throw new Error('field order must be bigint');\n  const bitLength = fieldOrder.toString(2).length;\n  return Math.ceil(bitLength / 8);\n}\n\n/**\n * Returns minimal amount of bytes that can be safely reduced\n * by field order.\n * Should be 2^-128 for 128-bit curve such as P256.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of target hash\n */\nexport function getMinHashLength(fieldOrder: bigint): number {\n  const length = getFieldBytesLength(fieldOrder);\n  return length + Math.ceil(length / 2);\n}\n\n/**\n * \"Constant-time\" private key generation utility.\n * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF\n * and convert them into private scalar, with the modulo bias being negligible.\n * Needs at least 48 bytes of input for 32-byte private key.\n * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/\n * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final\n * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5\n * @param hash hash output from SHA3 or a similar function\n * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)\n * @param isLE interpret hash bytes as LE num\n * @returns valid private scalar\n */\nexport function mapHashToField(key: Uint8Array, fieldOrder: bigint, isLE = false): Uint8Array {\n  const len = key.length;\n  const fieldLen = getFieldBytesLength(fieldOrder);\n  const minLen = getMinHashLength(fieldOrder);\n  // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.\n  if (len < 16 || len < minLen || len > 1024)\n    throw new Error('expected ' + minLen + '-1024 bytes of input, got ' + len);\n  const num = isLE ? bytesToNumberLE(key) : bytesToNumberBE(key);\n  // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0\n  const reduced = mod(num, fieldOrder - _1n) + _1n;\n  return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);\n}\n", "/**\n * hash-to-curve from RFC 9380.\n * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.\n * https://www.rfc-editor.org/rfc/rfc9380\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport type { AffinePoint, Group, GroupConstructor } from './curve.ts';\nimport { FpInvertBatch, type IField, mod } from './modular.ts';\nimport type { CHash } from './utils.ts';\nimport { abytes, bytesToNumberBE, concatBytes, utf8ToBytes, validateObject } from './utils.ts';\n\nexport type UnicodeOrBytes = string | Uint8Array;\n\n/**\n * * `DST` is a domain separation tag, defined in section 2.2.5\n * * `p` characteristic of F, where F is a finite field of characteristic p and order q = p^m\n * * `m` is extension degree (1 for prime fields)\n * * `k` is the target security target in bits (e.g. 128), from section 5.1\n * * `expand` is `xmd` (SHA2, SHA3, BLAKE) or `xof` (SHAKE, BLAKE-XOF)\n * * `hash` conforming to `utils.CHash` interface, with `outputLen` / `blockLen` props\n */\nexport type Opts = {\n  DST: UnicodeOrBytes;\n  p: bigint;\n  m: number;\n  k: number;\n  expand: 'xmd' | 'xof';\n  hash: CHash;\n};\n\n// Octet Stream to Integer. \"spec\" implementation of os2ip is 2.5x slower vs bytesToNumberBE.\nconst os2ip = bytesToNumberBE;\n\n// Integer to Octet Stream (numberToBytesBE)\nfunction i2osp(value: number, length: number): Uint8Array {\n  anum(value);\n  anum(length);\n  if (value < 0 || value >= 1 << (8 * length)) throw new Error('invalid I2OSP input: ' + value);\n  const res = Array.from({ length }).fill(0) as number[];\n  for (let i = length - 1; i >= 0; i--) {\n    res[i] = value & 0xff;\n    value >>>= 8;\n  }\n  return new Uint8Array(res);\n}\n\nfunction strxor(a: Uint8Array, b: Uint8Array): Uint8Array {\n  const arr = new Uint8Array(a.length);\n  for (let i = 0; i < a.length; i++) {\n    arr[i] = a[i] ^ b[i];\n  }\n  return arr;\n}\n\nfunction anum(item: unknown): void {\n  if (!Number.isSafeInteger(item)) throw new Error('number expected');\n}\n\n/**\n * Produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.\n * [RFC 9380 5.3.1](https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1).\n */\nexport function expand_message_xmd(\n  msg: Uint8Array,\n  DST: Uint8Array,\n  lenInBytes: number,\n  H: CHash\n): Uint8Array {\n  abytes(msg);\n  abytes(DST);\n  anum(lenInBytes);\n  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n  if (DST.length > 255) DST = H(concatBytes(utf8ToBytes('H2C-OVERSIZE-DST-'), DST));\n  const { outputLen: b_in_bytes, blockLen: r_in_bytes } = H;\n  const ell = Math.ceil(lenInBytes / b_in_bytes);\n  if (lenInBytes > 65535 || ell > 255) throw new Error('expand_message_xmd: invalid lenInBytes');\n  const DST_prime = concatBytes(DST, i2osp(DST.length, 1));\n  const Z_pad = i2osp(0, r_in_bytes);\n  const l_i_b_str = i2osp(lenInBytes, 2); // len_in_bytes_str\n  const b = new Array<Uint8Array>(ell);\n  const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));\n  b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));\n  for (let i = 1; i <= ell; i++) {\n    const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];\n    b[i] = H(concatBytes(...args));\n  }\n  const pseudo_random_bytes = concatBytes(...b);\n  return pseudo_random_bytes.slice(0, lenInBytes);\n}\n\n/**\n * Produces a uniformly random byte string using an extendable-output function (XOF) H.\n * 1. The collision resistance of H MUST be at least k bits.\n * 2. H MUST be an XOF that has been proved indifferentiable from\n *    a random oracle under a reasonable cryptographic assumption.\n * [RFC 9380 5.3.2](https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2).\n */\nexport function expand_message_xof(\n  msg: Uint8Array,\n  DST: Uint8Array,\n  lenInBytes: number,\n  k: number,\n  H: CHash\n): Uint8Array {\n  abytes(msg);\n  abytes(DST);\n  anum(lenInBytes);\n  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n  // DST = H('H2C-OVERSIZE-DST-' || a_very_long_DST, Math.ceil((lenInBytes * k) / 8));\n  if (DST.length > 255) {\n    const dkLen = Math.ceil((2 * k) / 8);\n    DST = H.create({ dkLen }).update(utf8ToBytes('H2C-OVERSIZE-DST-')).update(DST).digest();\n  }\n  if (lenInBytes > 65535 || DST.length > 255)\n    throw new Error('expand_message_xof: invalid lenInBytes');\n  return (\n    H.create({ dkLen: lenInBytes })\n      .update(msg)\n      .update(i2osp(lenInBytes, 2))\n      // 2. DST_prime = DST || I2OSP(len(DST), 1)\n      .update(DST)\n      .update(i2osp(DST.length, 1))\n      .digest()\n  );\n}\n\n/**\n * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.\n * [RFC 9380 5.2](https://www.rfc-editor.org/rfc/rfc9380#section-5.2).\n * @param msg a byte string containing the message to hash\n * @param count the number of elements of F to output\n * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above\n * @returns [u_0, ..., u_(count - 1)], a list of field elements.\n */\nexport function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][] {\n  validateObject(options, {\n    DST: 'stringOrUint8Array',\n    p: 'bigint',\n    m: 'isSafeInteger',\n    k: 'isSafeInteger',\n    hash: 'hash',\n  });\n  const { p, k, m, hash, expand, DST: _DST } = options;\n  abytes(msg);\n  anum(count);\n  const DST = typeof _DST === 'string' ? utf8ToBytes(_DST) : _DST;\n  const log2p = p.toString(2).length;\n  const L = Math.ceil((log2p + k) / 8); // section 5.1 of ietf draft link above\n  const len_in_bytes = count * m * L;\n  let prb; // pseudo_random_bytes\n  if (expand === 'xmd') {\n    prb = expand_message_xmd(msg, DST, len_in_bytes, hash);\n  } else if (expand === 'xof') {\n    prb = expand_message_xof(msg, DST, len_in_bytes, k, hash);\n  } else if (expand === '_internal_pass') {\n    // for internal tests only\n    prb = msg;\n  } else {\n    throw new Error('expand must be \"xmd\" or \"xof\"');\n  }\n  const u = new Array(count);\n  for (let i = 0; i < count; i++) {\n    const e = new Array(m);\n    for (let j = 0; j < m; j++) {\n      const elm_offset = L * (j + i * m);\n      const tv = prb.subarray(elm_offset, elm_offset + L);\n      e[j] = mod(os2ip(tv), p);\n    }\n    u[i] = e;\n  }\n  return u;\n}\n\nexport type XY<T> = (x: T, y: T) => { x: T; y: T };\nexport type XYRatio<T> = [T[], T[], T[], T[]]; // xn/xd, yn/yd\nexport function isogenyMap<T, F extends IField<T>>(field: F, map: XYRatio<T>): XY<T> {\n  // Make same order as in spec\n  const coeff = map.map((i) => Array.from(i).reverse());\n  return (x: T, y: T) => {\n    const [xn, xd, yn, yd] = coeff.map((val) =>\n      val.reduce((acc, i) => field.add(field.mul(acc, x), i))\n    );\n    // 6.6.3\n    // Exceptional cases of iso_map are inputs that cause the denominator of\n    // either rational function to evaluate to zero; such cases MUST return\n    // the identity point on E.\n    const [xd_inv, yd_inv] = FpInvertBatch(field, [xd, yd], true);\n    x = field.mul(xn, xd_inv); // xNum / xDen\n    y = field.mul(y, field.mul(yn, yd_inv)); // y * (yNum / yDev)\n    return { x, y };\n  };\n}\n\n/** Point interface, which curves must implement to work correctly with the module. */\nexport interface H2CPoint<T> extends Group<H2CPoint<T>> {\n  add(rhs: H2CPoint<T>): H2CPoint<T>;\n  toAffine(iz?: bigint): AffinePoint<T>;\n  clearCofactor(): H2CPoint<T>;\n  assertValidity(): void;\n}\n\nexport interface H2CPointConstructor<T> extends GroupConstructor<H2CPoint<T>> {\n  fromAffine(ap: AffinePoint<T>): H2CPoint<T>;\n}\n\nexport type MapToCurve<T> = (scalar: bigint[]) => AffinePoint<T>;\n\n// Separated from initialization opts, so users won't accidentally change per-curve parameters\n// (changing DST is ok!)\nexport type htfBasicOpts = { DST: UnicodeOrBytes };\nexport type HTFMethod<T> = (msg: Uint8Array, options?: htfBasicOpts) => H2CPoint<T>;\nexport type MapMethod<T> = (scalars: bigint[]) => H2CPoint<T>;\nexport type Hasher<T> = {\n  hashToCurve: HTFMethod<T>;\n  encodeToCurve: HTFMethod<T>;\n  mapToCurve: MapMethod<T>;\n  defaults: Opts & { encodeDST?: UnicodeOrBytes };\n};\n\n/** Creates hash-to-curve methods from EC Point and mapToCurve function. */\nexport function createHasher<T>(\n  Point: H2CPointConstructor<T>,\n  mapToCurve: MapToCurve<T>,\n  defaults: Opts & { encodeDST?: UnicodeOrBytes }\n): Hasher<T> {\n  if (typeof mapToCurve !== 'function') throw new Error('mapToCurve() must be defined');\n  function map(num: bigint[]) {\n    return Point.fromAffine(mapToCurve(num));\n  }\n  function clear(initial: H2CPoint<T>) {\n    const P = initial.clearCofactor();\n    if (P.equals(Point.ZERO)) return Point.ZERO; // zero will throw in assert\n    P.assertValidity();\n    return P;\n  }\n\n  return {\n    defaults,\n\n    // Encodes byte string to elliptic curve.\n    // hash_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n    hashToCurve(msg: Uint8Array, options?: htfBasicOpts): H2CPoint<T> {\n      const u = hash_to_field(msg, 2, { ...defaults, DST: defaults.DST, ...options } as Opts);\n      const u0 = map(u[0]);\n      const u1 = map(u[1]);\n      return clear(u0.add(u1));\n    },\n\n    // Encodes byte string to elliptic curve.\n    // encode_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n    encodeToCurve(msg: Uint8Array, options?: htfBasicOpts): H2CPoint<T> {\n      const u = hash_to_field(msg, 1, { ...defaults, DST: defaults.encodeDST, ...options } as Opts);\n      return clear(map(u[0]));\n    },\n\n    // Same as encodeToCurve, but without hash\n    mapToCurve(scalars: bigint[]): H2CPoint<T> {\n      if (!Array.isArray(scalars)) throw new Error('expected array of bigints');\n      for (const i of scalars)\n        if (typeof i !== 'bigint') throw new Error('expected array of bigints');\n      return clear(map(scalars));\n    },\n  };\n}\n", "/**\n * Methods for elliptic curve multiplication by scalars.\n * Contains wNAF, pippenger\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { type IField, nLength, validateField } from './modular.ts';\nimport { bitLen, bitMask, validateObject } from './utils.ts';\n\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\n\nexport type AffinePoint<T> = {\n  x: T;\n  y: T;\n} & { z?: never; t?: never };\n\nexport interface Group<T extends Group<T>> {\n  double(): T;\n  negate(): T;\n  add(other: T): T;\n  subtract(other: T): T;\n  equals(other: T): boolean;\n  multiply(scalar: bigint): T;\n}\n\nexport type GroupConstructor<T> = {\n  BASE: T;\n  ZERO: T;\n};\nexport type Mapper<T> = (i: T[]) => T[];\n\nfunction constTimeNegate<T extends Group<T>>(condition: boolean, item: T): T {\n  const neg = item.negate();\n  return condition ? neg : item;\n}\n\nfunction validateW(W: number, bits: number) {\n  if (!Number.isSafeInteger(W) || W <= 0 || W > bits)\n    throw new Error('invalid window size, expected [1..' + bits + '], got W=' + W);\n}\n\n/** Internal wNAF opts for specific W and scalarBits */\nexport type WOpts = {\n  windows: number;\n  windowSize: number;\n  mask: bigint;\n  maxNumber: number;\n  shiftBy: bigint;\n};\n\nfunction calcWOpts(W: number, scalarBits: number): WOpts {\n  validateW(W, scalarBits);\n  const windows = Math.ceil(scalarBits / W) + 1; // W=8 33. Not 32, because we skip zero\n  const windowSize = 2 ** (W - 1); // W=8 128. Not 256, because we skip zero\n  const maxNumber = 2 ** W; // W=8 256\n  const mask = bitMask(W); // W=8 255 == mask 0b11111111\n  const shiftBy = BigInt(W); // W=8 8\n  return { windows, windowSize, mask, maxNumber, shiftBy };\n}\n\nfunction calcOffsets(n: bigint, window: number, wOpts: WOpts) {\n  const { windowSize, mask, maxNumber, shiftBy } = wOpts;\n  let wbits = Number(n & mask); // extract W bits.\n  let nextN = n >> shiftBy; // shift number by W bits.\n\n  // What actually happens here:\n  // const highestBit = Number(mask ^ (mask >> 1n));\n  // let wbits2 = wbits - 1; // skip zero\n  // if (wbits2 & highestBit) { wbits2 ^= Number(mask); // (~);\n\n  // split if bits > max: +224 => 256-32\n  if (wbits > windowSize) {\n    // we skip zero, which means instead of `>= size-1`, we do `> size`\n    wbits -= maxNumber; // -32, can be maxNumber - wbits, but then we need to set isNeg here.\n    nextN += _1n; // +256 (carry)\n  }\n  const offsetStart = window * windowSize;\n  const offset = offsetStart + Math.abs(wbits) - 1; // -1 because we skip zero\n  const isZero = wbits === 0; // is current window slice a 0?\n  const isNeg = wbits < 0; // is current window slice negative?\n  const isNegF = window % 2 !== 0; // fake random statement for noise\n  const offsetF = offsetStart; // fake offset for noise\n  return { nextN, offset, isZero, isNeg, isNegF, offsetF };\n}\n\nfunction validateMSMPoints(points: any[], c: any) {\n  if (!Array.isArray(points)) throw new Error('array expected');\n  points.forEach((p, i) => {\n    if (!(p instanceof c)) throw new Error('invalid point at index ' + i);\n  });\n}\nfunction validateMSMScalars(scalars: any[], field: any) {\n  if (!Array.isArray(scalars)) throw new Error('array of scalars expected');\n  scalars.forEach((s, i) => {\n    if (!field.isValid(s)) throw new Error('invalid scalar at index ' + i);\n  });\n}\n\n// Since points in different groups cannot be equal (different object constructor),\n// we can have single place to store precomputes.\n// Allows to make points frozen / immutable.\nconst pointPrecomputes = new WeakMap<any, any[]>();\nconst pointWindowSizes = new WeakMap<any, number>();\n\nfunction getW(P: any): number {\n  return pointWindowSizes.get(P) || 1;\n}\n\nexport type IWNAF<T extends Group<T>> = {\n  constTimeNegate: <T extends Group<T>>(condition: boolean, item: T) => T;\n  hasPrecomputes(elm: T): boolean;\n  unsafeLadder(elm: T, n: bigint, p?: T): T;\n  precomputeWindow(elm: T, W: number): Group<T>[];\n  getPrecomputes(W: number, P: T, transform: Mapper<T>): T[];\n  wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T };\n  wNAFUnsafe(W: number, precomputes: T[], n: bigint, acc?: T): T;\n  wNAFCached(P: T, n: bigint, transform: Mapper<T>): { p: T; f: T };\n  wNAFCachedUnsafe(P: T, n: bigint, transform: Mapper<T>, prev?: T): T;\n  setWindowSize(P: T, W: number): void;\n};\n\n/**\n * Elliptic curve multiplication of Point by scalar. Fragile.\n * Scalars should always be less than curve order: this should be checked inside of a curve itself.\n * Creates precomputation tables for fast multiplication:\n * - private scalar is split by fixed size windows of W bits\n * - every window point is collected from window's table & added to accumulator\n * - since windows are different, same point inside tables won't be accessed more than once per calc\n * - each multiplication is 'Math.ceil(CURVE_ORDER / \uD835\uDC4A) + 1' point additions (fixed for any scalar)\n * - +1 window is neccessary for wNAF\n * - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication\n *\n * @todo Research returning 2d JS array of windows, instead of a single window.\n * This would allow windows to be in different memory locations\n */\nexport function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number): IWNAF<T> {\n  return {\n    constTimeNegate,\n\n    hasPrecomputes(elm: T) {\n      return getW(elm) !== 1;\n    },\n\n    // non-const time multiplication ladder\n    unsafeLadder(elm: T, n: bigint, p = c.ZERO) {\n      let d: T = elm;\n      while (n > _0n) {\n        if (n & _1n) p = p.add(d);\n        d = d.double();\n        n >>= _1n;\n      }\n      return p;\n    },\n\n    /**\n     * Creates a wNAF precomputation window. Used for caching.\n     * Default window size is set by `utils.precompute()` and is equal to 8.\n     * Number of precomputed points depends on the curve size:\n     * 2^(\uD835\uDC4A\u22121) * (Math.ceil(\uD835\uDC5B / \uD835\uDC4A) + 1), where:\n     * - \uD835\uDC4A is the window size\n     * - \uD835\uDC5B is the bitlength of the curve order.\n     * For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.\n     * @param elm Point instance\n     * @param W window size\n     * @returns precomputed point tables flattened to a single array\n     */\n    precomputeWindow(elm: T, W: number): Group<T>[] {\n      const { windows, windowSize } = calcWOpts(W, bits);\n      const points: T[] = [];\n      let p: T = elm;\n      let base = p;\n      for (let window = 0; window < windows; window++) {\n        base = p;\n        points.push(base);\n        // i=1, bc we skip 0\n        for (let i = 1; i < windowSize; i++) {\n          base = base.add(p);\n          points.push(base);\n        }\n        p = base.double();\n      }\n      return points;\n    },\n\n    /**\n     * Implements ec multiplication using precomputed tables and w-ary non-adjacent form.\n     * @param W window size\n     * @param precomputes precomputed tables\n     * @param n scalar (we don't check here, but should be less than curve order)\n     * @returns real and fake (for const-time) points\n     */\n    wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T } {\n      // Smaller version:\n      // https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541\n      // TODO: check the scalar is less than group order?\n      // wNAF behavior is undefined otherwise. But have to carefully remove\n      // other checks before wNAF. ORDER == bits here.\n      // Accumulators\n      let p = c.ZERO;\n      let f = c.BASE;\n      // This code was first written with assumption that 'f' and 'p' will never be infinity point:\n      // since each addition is multiplied by 2 ** W, it cannot cancel each other. However,\n      // there is negate now: it is possible that negated element from low value\n      // would be the same as high element, which will create carry into next window.\n      // It's not obvious how this can fail, but still worth investigating later.\n      const wo = calcWOpts(W, bits);\n      for (let window = 0; window < wo.windows; window++) {\n        // (n === _0n) is handled and not early-exited. isEven and offsetF are used for noise\n        const { nextN, offset, isZero, isNeg, isNegF, offsetF } = calcOffsets(n, window, wo);\n        n = nextN;\n        if (isZero) {\n          // bits are 0: add garbage to fake point\n          // Important part for const-time getPublicKey: add random \"noise\" point to f.\n          f = f.add(constTimeNegate(isNegF, precomputes[offsetF]));\n        } else {\n          // bits are 1: add to result point\n          p = p.add(constTimeNegate(isNeg, precomputes[offset]));\n        }\n      }\n      // Return both real and fake points: JIT won't eliminate f.\n      // At this point there is a way to F be infinity-point even if p is not,\n      // which makes it less const-time: around 1 bigint multiply.\n      return { p, f };\n    },\n\n    /**\n     * Implements ec unsafe (non const-time) multiplication using precomputed tables and w-ary non-adjacent form.\n     * @param W window size\n     * @param precomputes precomputed tables\n     * @param n scalar (we don't check here, but should be less than curve order)\n     * @param acc accumulator point to add result of multiplication\n     * @returns point\n     */\n    wNAFUnsafe(W: number, precomputes: T[], n: bigint, acc: T = c.ZERO): T {\n      const wo = calcWOpts(W, bits);\n      for (let window = 0; window < wo.windows; window++) {\n        if (n === _0n) break; // Early-exit, skip 0 value\n        const { nextN, offset, isZero, isNeg } = calcOffsets(n, window, wo);\n        n = nextN;\n        if (isZero) {\n          // Window bits are 0: skip processing.\n          // Move to next window.\n          continue;\n        } else {\n          const item = precomputes[offset];\n          acc = acc.add(isNeg ? item.negate() : item); // Re-using acc allows to save adds in MSM\n        }\n      }\n      return acc;\n    },\n\n    getPrecomputes(W: number, P: T, transform: Mapper<T>): T[] {\n      // Calculate precomputes on a first run, reuse them after\n      let comp = pointPrecomputes.get(P);\n      if (!comp) {\n        comp = this.precomputeWindow(P, W) as T[];\n        if (W !== 1) pointPrecomputes.set(P, transform(comp));\n      }\n      return comp;\n    },\n\n    wNAFCached(P: T, n: bigint, transform: Mapper<T>): { p: T; f: T } {\n      const W = getW(P);\n      return this.wNAF(W, this.getPrecomputes(W, P, transform), n);\n    },\n\n    wNAFCachedUnsafe(P: T, n: bigint, transform: Mapper<T>, prev?: T): T {\n      const W = getW(P);\n      if (W === 1) return this.unsafeLadder(P, n, prev); // For W=1 ladder is ~x2 faster\n      return this.wNAFUnsafe(W, this.getPrecomputes(W, P, transform), n, prev);\n    },\n\n    // We calculate precomputes for elliptic curve point multiplication\n    // using windowed method. This specifies window size and\n    // stores precomputed values. Usually only base point would be precomputed.\n\n    setWindowSize(P: T, W: number) {\n      validateW(W, bits);\n      pointWindowSizes.set(P, W);\n      pointPrecomputes.delete(P);\n    },\n  };\n}\n\n/**\n * Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).\n * 30x faster vs naive addition on L=4096, 10x faster than precomputes.\n * For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.\n * Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.\n * @param c Curve Point constructor\n * @param fieldN field over CURVE.N - important that it's not over CURVE.P\n * @param points array of L curve points\n * @param scalars array of L scalars (aka private keys / bigints)\n */\nexport function pippenger<T extends Group<T>>(\n  c: GroupConstructor<T>,\n  fieldN: IField<bigint>,\n  points: T[],\n  scalars: bigint[]\n): T {\n  // If we split scalars by some window (let's say 8 bits), every chunk will only\n  // take 256 buckets even if there are 4096 scalars, also re-uses double.\n  // TODO:\n  // - https://eprint.iacr.org/2024/750.pdf\n  // - https://tches.iacr.org/index.php/TCHES/article/view/10287\n  // 0 is accepted in scalars\n  validateMSMPoints(points, c);\n  validateMSMScalars(scalars, fieldN);\n  if (points.length !== scalars.length)\n    throw new Error('arrays of points and scalars must have equal length');\n  const zero = c.ZERO;\n  const wbits = bitLen(BigInt(points.length));\n  const windowSize = wbits > 12 ? wbits - 3 : wbits > 4 ? wbits - 2 : wbits ? 2 : 1; // in bits\n  const MASK = bitMask(windowSize);\n  const buckets = new Array(Number(MASK) + 1).fill(zero); // +1 for zero array\n  const lastBits = Math.floor((fieldN.BITS - 1) / windowSize) * windowSize;\n  let sum = zero;\n  for (let i = lastBits; i >= 0; i -= windowSize) {\n    buckets.fill(zero);\n    for (let j = 0; j < scalars.length; j++) {\n      const scalar = scalars[j];\n      const wbits = Number((scalar >> BigInt(i)) & MASK);\n      buckets[wbits] = buckets[wbits].add(points[j]);\n    }\n    let resI = zero; // not using this will do small speed-up, but will lose ct\n    // Skip first bucket, because it is zero\n    for (let j = buckets.length - 1, sumI = zero; j > 0; j--) {\n      sumI = sumI.add(buckets[j]);\n      resI = resI.add(sumI);\n    }\n    sum = sum.add(resI);\n    if (i !== 0) for (let j = 0; j < windowSize; j++) sum = sum.double();\n  }\n  return sum as T;\n}\n/**\n * Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).\n * @param c Curve Point constructor\n * @param fieldN field over CURVE.N - important that it's not over CURVE.P\n * @param points array of L curve points\n * @returns function which multiplies points with scaars\n */\nexport function precomputeMSMUnsafe<T extends Group<T>>(\n  c: GroupConstructor<T>,\n  fieldN: IField<bigint>,\n  points: T[],\n  windowSize: number\n): (scalars: bigint[]) => T {\n  /**\n   * Performance Analysis of Window-based Precomputation\n   *\n   * Base Case (256-bit scalar, 8-bit window):\n   * - Standard precomputation requires:\n   *   - 31 additions per scalar \u00D7 256 scalars = 7,936 ops\n   *   - Plus 255 summary additions = 8,191 total ops\n   *   Note: Summary additions can be optimized via accumulator\n   *\n   * Chunked Precomputation Analysis:\n   * - Using 32 chunks requires:\n   *   - 255 additions per chunk\n   *   - 256 doublings\n   *   - Total: (255 \u00D7 32) + 256 = 8,416 ops\n   *\n   * Memory Usage Comparison:\n   * Window Size | Standard Points | Chunked Points\n   * ------------|-----------------|---------------\n   *     4-bit   |     520         |      15\n   *     8-bit   |    4,224        |     255\n   *    10-bit   |   13,824        |   1,023\n   *    16-bit   |  557,056        |  65,535\n   *\n   * Key Advantages:\n   * 1. Enables larger window sizes due to reduced memory overhead\n   * 2. More efficient for smaller scalar counts:\n   *    - 16 chunks: (16 \u00D7 255) + 256 = 4,336 ops\n   *    - ~2x faster than standard 8,191 ops\n   *\n   * Limitations:\n   * - Not suitable for plain precomputes (requires 256 constant doublings)\n   * - Performance degrades with larger scalar counts:\n   *   - Optimal for ~256 scalars\n   *   - Less efficient for 4096+ scalars (Pippenger preferred)\n   */\n  validateW(windowSize, fieldN.BITS);\n  validateMSMPoints(points, c);\n  const zero = c.ZERO;\n  const tableSize = 2 ** windowSize - 1; // table size (without zero)\n  const chunks = Math.ceil(fieldN.BITS / windowSize); // chunks of item\n  const MASK = bitMask(windowSize);\n  const tables = points.map((p: T) => {\n    const res = [];\n    for (let i = 0, acc = p; i < tableSize; i++) {\n      res.push(acc);\n      acc = acc.add(p);\n    }\n    return res;\n  });\n  return (scalars: bigint[]): T => {\n    validateMSMScalars(scalars, fieldN);\n    if (scalars.length > points.length)\n      throw new Error('array of scalars must be smaller than array of points');\n    let res = zero;\n    for (let i = 0; i < chunks; i++) {\n      // No need to double if accumulator is still zero.\n      if (res !== zero) for (let j = 0; j < windowSize; j++) res = res.double();\n      const shiftBy = BigInt(chunks * windowSize - (i + 1) * windowSize);\n      for (let j = 0; j < scalars.length; j++) {\n        const n = scalars[j];\n        const curr = Number((n >> shiftBy) & MASK);\n        if (!curr) continue; // skip zero scalars chunks\n        res = res.add(tables[j][curr - 1]);\n      }\n    }\n    return res;\n  };\n}\n\n/**\n * Generic BasicCurve interface: works even for polynomial fields (BLS): P, n, h would be ok.\n * Though generator can be different (Fp2 / Fp6 for BLS).\n */\nexport type BasicCurve<T> = {\n  Fp: IField<T>; // Field over which we'll do calculations (Fp)\n  n: bigint; // Curve order, total count of valid points in the field\n  nBitLength?: number; // bit length of curve order\n  nByteLength?: number; // byte length of curve order\n  h: bigint; // cofactor. we can assign default=1, but users will just ignore it w/o validation\n  hEff?: bigint; // Number to multiply to clear cofactor\n  Gx: T; // base point X coordinate\n  Gy: T; // base point Y coordinate\n  allowInfinityPoint?: boolean; // bls12-381 requires it. ZERO point is valid, but invalid pubkey\n};\n\nexport function validateBasic<FP, T>(\n  curve: BasicCurve<FP> & T\n): Readonly<\n  {\n    readonly nBitLength: number;\n    readonly nByteLength: number;\n  } & BasicCurve<FP> &\n    T & {\n      p: bigint;\n    }\n> {\n  validateField(curve.Fp);\n  validateObject(\n    curve,\n    {\n      n: 'bigint',\n      h: 'bigint',\n      Gx: 'field',\n      Gy: 'field',\n    },\n    {\n      nBitLength: 'isSafeInteger',\n      nByteLength: 'isSafeInteger',\n    }\n  );\n  // Set defaults\n  return Object.freeze({\n    ...nLength(curve.n, curve.nBitLength),\n    ...curve,\n    ...{ p: curve.Fp.ORDER },\n  } as const);\n}\n", "/**\n * Short Weierstrass curve methods. The formula is: y\u00B2 = x\u00B3 + ax + b.\n *\n * ### Parameters\n *\n * To initialize a weierstrass curve, one needs to pass following params:\n *\n * * a: formula param\n * * b: formula param\n * * Fp: finite Field over which we'll do calculations. Can be complex (Fp2, Fp12)\n * * n: Curve prime subgroup order, total count of valid points in the field\n * * Gx: Base point (x, y) aka generator point x coordinate\n * * Gy: ...y coordinate\n * * h: cofactor, usually 1. h*n = curve group order (n is only subgroup order)\n * * lowS: whether to enable (default) or disable \"low-s\" non-malleable signatures\n *\n * ### Design rationale for types\n *\n * * Interaction between classes from different curves should fail:\n *   `k256.Point.BASE.add(p256.Point.BASE)`\n * * For this purpose we want to use `instanceof` operator, which is fast and works during runtime\n * * Different calls of `curve()` would return different classes -\n *   `curve(params) !== curve(params)`: if somebody decided to monkey-patch their curve,\n *   it won't affect others\n *\n * TypeScript can't infer types for classes created inside a function. Classes is one instance\n * of nominative types in TypeScript and interfaces only check for shape, so it's hard to create\n * unique type for every function call.\n *\n * We can use generic types via some param, like curve opts, but that would:\n *     1. Enable interaction between `curve(params)` and `curve(params)` (curves of same params)\n *     which is hard to debug.\n *     2. Params can be generic and we can't enforce them to be constant value:\n *     if somebody creates curve from non-constant params,\n *     it would be allowed to interact with other curves with non-constant params\n *\n * @todo https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// prettier-ignore\nimport {\n  type AffinePoint, type BasicCurve, type Group, type GroupConstructor,\n  pippenger, validateBasic, wNAF\n} from './curve.ts';\n// prettier-ignore\nimport {\n  Field,\n  FpInvertBatch,\n  type IField, getMinHashLength, invert, mapHashToField, mod, validateField\n} from './modular.ts';\n// prettier-ignore\nimport {\n  type CHash, type Hex, type PrivKey,\n  aInRange, abool,\n  bitMask,\n  bytesToHex, bytesToNumberBE, concatBytes, createHmacDrbg, ensureBytes, hexToBytes,\n  inRange, isBytes, memoized, numberToBytesBE, numberToHexUnpadded, validateObject\n} from './utils.ts';\n\nexport type { AffinePoint };\ntype HmacFnSync = (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array;\ntype EndomorphismOpts = {\n  beta: bigint;\n  splitScalar: (k: bigint) => { k1neg: boolean; k1: bigint; k2neg: boolean; k2: bigint };\n};\nexport type BasicWCurve<T> = BasicCurve<T> & {\n  // Params: a, b\n  a: T;\n  b: T;\n\n  // Optional params\n  allowedPrivateKeyLengths?: readonly number[]; // for P521\n  wrapPrivateKey?: boolean; // bls12-381 requires mod(n) instead of rejecting keys >= n\n  endo?: EndomorphismOpts; // Endomorphism options for Koblitz curves\n  // When a cofactor != 1, there can be an effective methods to:\n  // 1. Determine whether a point is torsion-free\n  isTorsionFree?: (c: ProjConstructor<T>, point: ProjPointType<T>) => boolean;\n  // 2. Clear torsion component\n  clearCofactor?: (c: ProjConstructor<T>, point: ProjPointType<T>) => ProjPointType<T>;\n};\n\nexport type Entropy = Hex | boolean;\nexport type SignOpts = { lowS?: boolean; extraEntropy?: Entropy; prehash?: boolean };\nexport type VerOpts = { lowS?: boolean; prehash?: boolean; format?: 'compact' | 'der' | undefined };\n\nfunction validateSigVerOpts(opts: SignOpts | VerOpts) {\n  if (opts.lowS !== undefined) abool('lowS', opts.lowS);\n  if (opts.prehash !== undefined) abool('prehash', opts.prehash);\n}\n\n// Instance for 3d XYZ points\nexport interface ProjPointType<T> extends Group<ProjPointType<T>> {\n  readonly px: T;\n  readonly py: T;\n  readonly pz: T;\n  get x(): T;\n  get y(): T;\n  toAffine(iz?: T): AffinePoint<T>;\n  toHex(isCompressed?: boolean): string;\n  toRawBytes(isCompressed?: boolean): Uint8Array;\n\n  assertValidity(): void;\n  hasEvenY(): boolean;\n  multiplyUnsafe(scalar: bigint): ProjPointType<T>;\n  multiplyAndAddUnsafe(Q: ProjPointType<T>, a: bigint, b: bigint): ProjPointType<T> | undefined;\n  isTorsionFree(): boolean;\n  clearCofactor(): ProjPointType<T>;\n  _setWindowSize(windowSize: number): void;\n}\n// Static methods for 3d XYZ points\nexport interface ProjConstructor<T> extends GroupConstructor<ProjPointType<T>> {\n  new (x: T, y: T, z: T): ProjPointType<T>;\n  fromAffine(p: AffinePoint<T>): ProjPointType<T>;\n  fromHex(hex: Hex): ProjPointType<T>;\n  fromPrivateKey(privateKey: PrivKey): ProjPointType<T>;\n  normalizeZ(points: ProjPointType<T>[]): ProjPointType<T>[];\n  msm(points: ProjPointType<T>[], scalars: bigint[]): ProjPointType<T>;\n}\n\nexport type CurvePointsType<T> = BasicWCurve<T> & {\n  // Bytes\n  fromBytes?: (bytes: Uint8Array) => AffinePoint<T>;\n  toBytes?: (c: ProjConstructor<T>, point: ProjPointType<T>, isCompressed: boolean) => Uint8Array;\n};\n\nexport type CurvePointsTypeWithLength<T> = Readonly<\n  CurvePointsType<T> & { nByteLength: number; nBitLength: number }\n>;\n\nfunction validatePointOpts<T>(curve: CurvePointsType<T>): CurvePointsTypeWithLength<T> {\n  const opts = validateBasic(curve);\n  validateObject(\n    opts,\n    {\n      a: 'field',\n      b: 'field',\n    },\n    {\n      allowedPrivateKeyLengths: 'array',\n      wrapPrivateKey: 'boolean',\n      isTorsionFree: 'function',\n      clearCofactor: 'function',\n      allowInfinityPoint: 'boolean',\n      fromBytes: 'function',\n      toBytes: 'function',\n    }\n  );\n  const { endo, Fp, a } = opts;\n  if (endo) {\n    if (!Fp.eql(a, Fp.ZERO)) {\n      throw new Error('invalid endomorphism, can only be defined for Koblitz curves that have a=0');\n    }\n    if (\n      typeof endo !== 'object' ||\n      typeof endo.beta !== 'bigint' ||\n      typeof endo.splitScalar !== 'function'\n    ) {\n      throw new Error('invalid endomorphism, expected beta: bigint and splitScalar: function');\n    }\n  }\n  return Object.freeze({ ...opts } as const);\n}\n\nexport type CurvePointsRes<T> = {\n  CURVE: ReturnType<typeof validatePointOpts<T>>;\n  ProjectivePoint: ProjConstructor<T>;\n  normPrivateKeyToScalar: (key: PrivKey) => bigint;\n  weierstrassEquation: (x: T) => T;\n  isWithinCurveOrder: (num: bigint) => boolean;\n};\n\nexport class DERErr extends Error {\n  constructor(m = '') {\n    super(m);\n  }\n}\nexport type IDER = {\n  // asn.1 DER encoding utils\n  Err: typeof DERErr;\n  // Basic building block is TLV (Tag-Length-Value)\n  _tlv: {\n    encode: (tag: number, data: string) => string;\n    // v - value, l - left bytes (unparsed)\n    decode(tag: number, data: Uint8Array): { v: Uint8Array; l: Uint8Array };\n  };\n  // https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,\n  // since we always use positive integers here. It must always be empty:\n  // - add zero byte if exists\n  // - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)\n  _int: {\n    encode(num: bigint): string;\n    decode(data: Uint8Array): bigint;\n  };\n  toSig(hex: string | Uint8Array): { r: bigint; s: bigint };\n  hexFromSig(sig: { r: bigint; s: bigint }): string;\n};\n/**\n * ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:\n *\n *     [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]\n *\n * Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html\n */\nexport const DER: IDER = {\n  // asn.1 DER encoding utils\n  Err: DERErr,\n  // Basic building block is TLV (Tag-Length-Value)\n  _tlv: {\n    encode: (tag: number, data: string): string => {\n      const { Err: E } = DER;\n      if (tag < 0 || tag > 256) throw new E('tlv.encode: wrong tag');\n      if (data.length & 1) throw new E('tlv.encode: unpadded data');\n      const dataLen = data.length / 2;\n      const len = numberToHexUnpadded(dataLen);\n      if ((len.length / 2) & 0b1000_0000) throw new E('tlv.encode: long form length too big');\n      // length of length with long form flag\n      const lenLen = dataLen > 127 ? numberToHexUnpadded((len.length / 2) | 0b1000_0000) : '';\n      const t = numberToHexUnpadded(tag);\n      return t + lenLen + len + data;\n    },\n    // v - value, l - left bytes (unparsed)\n    decode(tag: number, data: Uint8Array): { v: Uint8Array; l: Uint8Array } {\n      const { Err: E } = DER;\n      let pos = 0;\n      if (tag < 0 || tag > 256) throw new E('tlv.encode: wrong tag');\n      if (data.length < 2 || data[pos++] !== tag) throw new E('tlv.decode: wrong tlv');\n      const first = data[pos++];\n      const isLong = !!(first & 0b1000_0000); // First bit of first length byte is flag for short/long form\n      let length = 0;\n      if (!isLong) length = first;\n      else {\n        // Long form: [longFlag(1bit), lengthLength(7bit), length (BE)]\n        const lenLen = first & 0b0111_1111;\n        if (!lenLen) throw new E('tlv.decode(long): indefinite length not supported');\n        if (lenLen > 4) throw new E('tlv.decode(long): byte length is too big'); // this will overflow u32 in js\n        const lengthBytes = data.subarray(pos, pos + lenLen);\n        if (lengthBytes.length !== lenLen) throw new E('tlv.decode: length bytes not complete');\n        if (lengthBytes[0] === 0) throw new E('tlv.decode(long): zero leftmost byte');\n        for (const b of lengthBytes) length = (length << 8) | b;\n        pos += lenLen;\n        if (length < 128) throw new E('tlv.decode(long): not minimal encoding');\n      }\n      const v = data.subarray(pos, pos + length);\n      if (v.length !== length) throw new E('tlv.decode: wrong value length');\n      return { v, l: data.subarray(pos + length) };\n    },\n  },\n  // https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,\n  // since we always use positive integers here. It must always be empty:\n  // - add zero byte if exists\n  // - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)\n  _int: {\n    encode(num: bigint): string {\n      const { Err: E } = DER;\n      if (num < _0n) throw new E('integer: negative integers are not allowed');\n      let hex = numberToHexUnpadded(num);\n      // Pad with zero byte if negative flag is present\n      if (Number.parseInt(hex[0], 16) & 0b1000) hex = '00' + hex;\n      if (hex.length & 1) throw new E('unexpected DER parsing assertion: unpadded hex');\n      return hex;\n    },\n    decode(data: Uint8Array): bigint {\n      const { Err: E } = DER;\n      if (data[0] & 0b1000_0000) throw new E('invalid signature integer: negative');\n      if (data[0] === 0x00 && !(data[1] & 0b1000_0000))\n        throw new E('invalid signature integer: unnecessary leading zero');\n      return bytesToNumberBE(data);\n    },\n  },\n  toSig(hex: string | Uint8Array): { r: bigint; s: bigint } {\n    // parse DER signature\n    const { Err: E, _int: int, _tlv: tlv } = DER;\n    const data = ensureBytes('signature', hex);\n    const { v: seqBytes, l: seqLeftBytes } = tlv.decode(0x30, data);\n    if (seqLeftBytes.length) throw new E('invalid signature: left bytes after parsing');\n    const { v: rBytes, l: rLeftBytes } = tlv.decode(0x02, seqBytes);\n    const { v: sBytes, l: sLeftBytes } = tlv.decode(0x02, rLeftBytes);\n    if (sLeftBytes.length) throw new E('invalid signature: left bytes after parsing');\n    return { r: int.decode(rBytes), s: int.decode(sBytes) };\n  },\n  hexFromSig(sig: { r: bigint; s: bigint }): string {\n    const { _tlv: tlv, _int: int } = DER;\n    const rs = tlv.encode(0x02, int.encode(sig.r));\n    const ss = tlv.encode(0x02, int.encode(sig.s));\n    const seq = rs + ss;\n    return tlv.encode(0x30, seq);\n  },\n};\n\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);\n\nexport function weierstrassPoints<T>(opts: CurvePointsType<T>): CurvePointsRes<T> {\n  const CURVE = validatePointOpts(opts);\n  const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ\n  const Fn = Field(CURVE.n, CURVE.nBitLength);\n\n  const toBytes =\n    CURVE.toBytes ||\n    ((_c: ProjConstructor<T>, point: ProjPointType<T>, _isCompressed: boolean) => {\n      const a = point.toAffine();\n      return concatBytes(Uint8Array.from([0x04]), Fp.toBytes(a.x), Fp.toBytes(a.y));\n    });\n  const fromBytes =\n    CURVE.fromBytes ||\n    ((bytes: Uint8Array) => {\n      // const head = bytes[0];\n      const tail = bytes.subarray(1);\n      // if (head !== 0x04) throw new Error('Only non-compressed encoding is supported');\n      const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n      const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n      return { x, y };\n    });\n\n  /**\n   * y\u00B2 = x\u00B3 + ax + b: Short weierstrass curve formula. Takes x, returns y\u00B2.\n   * @returns y\u00B2\n   */\n  function weierstrassEquation(x: T): T {\n    const { a, b } = CURVE;\n    const x2 = Fp.sqr(x); // x * x\n    const x3 = Fp.mul(x2, x); // x2 * x\n    return Fp.add(Fp.add(x3, Fp.mul(x, a)), b); // x3 + a * x + b\n  }\n  // Validate whether the passed curve params are valid.\n  // We check if curve equation works for generator point.\n  // `assertValidity()` won't work: `isTorsionFree()` is not available at this point in bls12-381.\n  // ProjectivePoint class has not been initialized yet.\n  if (!Fp.eql(Fp.sqr(CURVE.Gy), weierstrassEquation(CURVE.Gx)))\n    throw new Error('bad generator point: equation left != right');\n\n  // Valid group elements reside in range 1..n-1\n  function isWithinCurveOrder(num: bigint): boolean {\n    return inRange(num, _1n, CURVE.n);\n  }\n  // Validates if priv key is valid and converts it to bigint.\n  // Supports options allowedPrivateKeyLengths and wrapPrivateKey.\n  function normPrivateKeyToScalar(key: PrivKey): bigint {\n    const { allowedPrivateKeyLengths: lengths, nByteLength, wrapPrivateKey, n: N } = CURVE;\n    if (lengths && typeof key !== 'bigint') {\n      if (isBytes(key)) key = bytesToHex(key);\n      // Normalize to hex string, pad. E.g. P521 would norm 130-132 char hex to 132-char bytes\n      if (typeof key !== 'string' || !lengths.includes(key.length))\n        throw new Error('invalid private key');\n      key = key.padStart(nByteLength * 2, '0');\n    }\n    let num: bigint;\n    try {\n      num =\n        typeof key === 'bigint'\n          ? key\n          : bytesToNumberBE(ensureBytes('private key', key, nByteLength));\n    } catch (error) {\n      throw new Error(\n        'invalid private key, expected hex or ' + nByteLength + ' bytes, got ' + typeof key\n      );\n    }\n    if (wrapPrivateKey) num = mod(num, N); // disabled by default, enabled for BLS\n    aInRange('private key', num, _1n, N); // num in range [1..N-1]\n    return num;\n  }\n\n  function aprjpoint(other: unknown) {\n    if (!(other instanceof Point)) throw new Error('ProjectivePoint expected');\n  }\n\n  // Memoized toAffine / validity check. They are heavy. Points are immutable.\n\n  // Converts Projective point to affine (x, y) coordinates.\n  // Can accept precomputed Z^-1 - for example, from invertBatch.\n  // (x, y, z) \u220B (x=x/z, y=y/z)\n  const toAffineMemo = memoized((p: Point, iz?: T): AffinePoint<T> => {\n    const { px: x, py: y, pz: z } = p;\n    // Fast-path for normalized points\n    if (Fp.eql(z, Fp.ONE)) return { x, y };\n    const is0 = p.is0();\n    // If invZ was 0, we return zero point. However we still want to execute\n    // all operations, so we replace invZ with a random number, 1.\n    if (iz == null) iz = is0 ? Fp.ONE : Fp.inv(z);\n    const ax = Fp.mul(x, iz);\n    const ay = Fp.mul(y, iz);\n    const zz = Fp.mul(z, iz);\n    if (is0) return { x: Fp.ZERO, y: Fp.ZERO };\n    if (!Fp.eql(zz, Fp.ONE)) throw new Error('invZ was invalid');\n    return { x: ax, y: ay };\n  });\n  // NOTE: on exception this will crash 'cached' and no value will be set.\n  // Otherwise true will be return\n  const assertValidMemo = memoized((p: Point) => {\n    if (p.is0()) {\n      // (0, 1, 0) aka ZERO is invalid in most contexts.\n      // In BLS, ZERO can be serialized, so we allow it.\n      // (0, 0, 0) is invalid representation of ZERO.\n      if (CURVE.allowInfinityPoint && !Fp.is0(p.py)) return;\n      throw new Error('bad point: ZERO');\n    }\n    // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`\n    const { x, y } = p.toAffine();\n    // Check if x, y are valid field elements\n    if (!Fp.isValid(x) || !Fp.isValid(y)) throw new Error('bad point: x or y not FE');\n    const left = Fp.sqr(y); // y\u00B2\n    const right = weierstrassEquation(x); // x\u00B3 + ax + b\n    if (!Fp.eql(left, right)) throw new Error('bad point: equation left != right');\n    if (!p.isTorsionFree()) throw new Error('bad point: not in prime-order subgroup');\n    return true;\n  });\n\n  /**\n   * Projective Point works in 3d / projective (homogeneous) coordinates: (x, y, z) \u220B (x=x/z, y=y/z)\n   * Default Point works in 2d / affine coordinates: (x, y)\n   * We're doing calculations in projective, because its operations don't require costly inversion.\n   */\n  class Point implements ProjPointType<T> {\n    static readonly BASE = new Point(CURVE.Gx, CURVE.Gy, Fp.ONE);\n    static readonly ZERO = new Point(Fp.ZERO, Fp.ONE, Fp.ZERO); // 0, 1, 0\n    readonly px: T;\n    readonly py: T;\n    readonly pz: T;\n\n    constructor(px: T, py: T, pz: T) {\n      if (px == null || !Fp.isValid(px)) throw new Error('x required');\n      if (py == null || !Fp.isValid(py) || Fp.is0(py)) throw new Error('y required');\n      if (pz == null || !Fp.isValid(pz)) throw new Error('z required');\n      this.px = px;\n      this.py = py;\n      this.pz = pz;\n      Object.freeze(this);\n    }\n\n    // Does not validate if the point is on-curve.\n    // Use fromHex instead, or call assertValidity() later.\n    static fromAffine(p: AffinePoint<T>): Point {\n      const { x, y } = p || {};\n      if (!p || !Fp.isValid(x) || !Fp.isValid(y)) throw new Error('invalid affine point');\n      if (p instanceof Point) throw new Error('projective point not allowed');\n      const is0 = (i: T) => Fp.eql(i, Fp.ZERO);\n      // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0)\n      if (is0(x) && is0(y)) return Point.ZERO;\n      return new Point(x, y, Fp.ONE);\n    }\n\n    get x(): T {\n      return this.toAffine().x;\n    }\n    get y(): T {\n      return this.toAffine().y;\n    }\n\n    /**\n     * Takes a bunch of Projective Points but executes only one\n     * inversion on all of them. Inversion is very slow operation,\n     * so this improves performance massively.\n     * Optimization: converts a list of projective points to a list of identical points with Z=1.\n     */\n    static normalizeZ(points: Point[]): Point[] {\n      const toInv = FpInvertBatch(\n        Fp,\n        points.map((p) => p.pz)\n      );\n      return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);\n    }\n\n    /**\n     * Converts hash string or Uint8Array to Point.\n     * @param hex short/long ECDSA hex\n     */\n    static fromHex(hex: Hex): Point {\n      const P = Point.fromAffine(fromBytes(ensureBytes('pointHex', hex)));\n      P.assertValidity();\n      return P;\n    }\n\n    // Multiplies generator point by privateKey.\n    static fromPrivateKey(privateKey: PrivKey) {\n      return Point.BASE.multiply(normPrivateKeyToScalar(privateKey));\n    }\n\n    // Multiscalar Multiplication\n    static msm(points: Point[], scalars: bigint[]): Point {\n      return pippenger(Point, Fn, points, scalars);\n    }\n\n    // \"Private method\", don't use it directly\n    _setWindowSize(windowSize: number) {\n      wnaf.setWindowSize(this, windowSize);\n    }\n\n    // A point on curve is valid if it conforms to equation.\n    assertValidity(): void {\n      assertValidMemo(this);\n    }\n\n    hasEvenY(): boolean {\n      const { y } = this.toAffine();\n      if (Fp.isOdd) return !Fp.isOdd(y);\n      throw new Error(\"Field doesn't support isOdd\");\n    }\n\n    /**\n     * Compare one point to another.\n     */\n    equals(other: Point): boolean {\n      aprjpoint(other);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      const { px: X2, py: Y2, pz: Z2 } = other;\n      const U1 = Fp.eql(Fp.mul(X1, Z2), Fp.mul(X2, Z1));\n      const U2 = Fp.eql(Fp.mul(Y1, Z2), Fp.mul(Y2, Z1));\n      return U1 && U2;\n    }\n\n    /**\n     * Flips point to one corresponding to (x, -y) in Affine coordinates.\n     */\n    negate(): Point {\n      return new Point(this.px, Fp.neg(this.py), this.pz);\n    }\n\n    // Renes-Costello-Batina exception-free doubling formula.\n    // There is 30% faster Jacobian formula, but it is not complete.\n    // https://eprint.iacr.org/2015/1060, algorithm 3\n    // Cost: 8M + 3S + 3*a + 2*b3 + 15add.\n    double() {\n      const { a, b } = CURVE;\n      const b3 = Fp.mul(b, _3n);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n      let t0 = Fp.mul(X1, X1); // step 1\n      let t1 = Fp.mul(Y1, Y1);\n      let t2 = Fp.mul(Z1, Z1);\n      let t3 = Fp.mul(X1, Y1);\n      t3 = Fp.add(t3, t3); // step 5\n      Z3 = Fp.mul(X1, Z1);\n      Z3 = Fp.add(Z3, Z3);\n      X3 = Fp.mul(a, Z3);\n      Y3 = Fp.mul(b3, t2);\n      Y3 = Fp.add(X3, Y3); // step 10\n      X3 = Fp.sub(t1, Y3);\n      Y3 = Fp.add(t1, Y3);\n      Y3 = Fp.mul(X3, Y3);\n      X3 = Fp.mul(t3, X3);\n      Z3 = Fp.mul(b3, Z3); // step 15\n      t2 = Fp.mul(a, t2);\n      t3 = Fp.sub(t0, t2);\n      t3 = Fp.mul(a, t3);\n      t3 = Fp.add(t3, Z3);\n      Z3 = Fp.add(t0, t0); // step 20\n      t0 = Fp.add(Z3, t0);\n      t0 = Fp.add(t0, t2);\n      t0 = Fp.mul(t0, t3);\n      Y3 = Fp.add(Y3, t0);\n      t2 = Fp.mul(Y1, Z1); // step 25\n      t2 = Fp.add(t2, t2);\n      t0 = Fp.mul(t2, t3);\n      X3 = Fp.sub(X3, t0);\n      Z3 = Fp.mul(t2, t1);\n      Z3 = Fp.add(Z3, Z3); // step 30\n      Z3 = Fp.add(Z3, Z3);\n      return new Point(X3, Y3, Z3);\n    }\n\n    // Renes-Costello-Batina exception-free addition formula.\n    // There is 30% faster Jacobian formula, but it is not complete.\n    // https://eprint.iacr.org/2015/1060, algorithm 1\n    // Cost: 12M + 0S + 3*a + 3*b3 + 23add.\n    add(other: Point): Point {\n      aprjpoint(other);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      const { px: X2, py: Y2, pz: Z2 } = other;\n      let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n      const a = CURVE.a;\n      const b3 = Fp.mul(CURVE.b, _3n);\n      let t0 = Fp.mul(X1, X2); // step 1\n      let t1 = Fp.mul(Y1, Y2);\n      let t2 = Fp.mul(Z1, Z2);\n      let t3 = Fp.add(X1, Y1);\n      let t4 = Fp.add(X2, Y2); // step 5\n      t3 = Fp.mul(t3, t4);\n      t4 = Fp.add(t0, t1);\n      t3 = Fp.sub(t3, t4);\n      t4 = Fp.add(X1, Z1);\n      let t5 = Fp.add(X2, Z2); // step 10\n      t4 = Fp.mul(t4, t5);\n      t5 = Fp.add(t0, t2);\n      t4 = Fp.sub(t4, t5);\n      t5 = Fp.add(Y1, Z1);\n      X3 = Fp.add(Y2, Z2); // step 15\n      t5 = Fp.mul(t5, X3);\n      X3 = Fp.add(t1, t2);\n      t5 = Fp.sub(t5, X3);\n      Z3 = Fp.mul(a, t4);\n      X3 = Fp.mul(b3, t2); // step 20\n      Z3 = Fp.add(X3, Z3);\n      X3 = Fp.sub(t1, Z3);\n      Z3 = Fp.add(t1, Z3);\n      Y3 = Fp.mul(X3, Z3);\n      t1 = Fp.add(t0, t0); // step 25\n      t1 = Fp.add(t1, t0);\n      t2 = Fp.mul(a, t2);\n      t4 = Fp.mul(b3, t4);\n      t1 = Fp.add(t1, t2);\n      t2 = Fp.sub(t0, t2); // step 30\n      t2 = Fp.mul(a, t2);\n      t4 = Fp.add(t4, t2);\n      t0 = Fp.mul(t1, t4);\n      Y3 = Fp.add(Y3, t0);\n      t0 = Fp.mul(t5, t4); // step 35\n      X3 = Fp.mul(t3, X3);\n      X3 = Fp.sub(X3, t0);\n      t0 = Fp.mul(t3, t1);\n      Z3 = Fp.mul(t5, Z3);\n      Z3 = Fp.add(Z3, t0); // step 40\n      return new Point(X3, Y3, Z3);\n    }\n\n    subtract(other: Point) {\n      return this.add(other.negate());\n    }\n\n    is0() {\n      return this.equals(Point.ZERO);\n    }\n\n    private wNAF(n: bigint): { p: Point; f: Point } {\n      return wnaf.wNAFCached(this, n, Point.normalizeZ);\n    }\n\n    /**\n     * Non-constant-time multiplication. Uses double-and-add algorithm.\n     * It's faster, but should only be used when you don't care about\n     * an exposed private key e.g. sig verification, which works over *public* keys.\n     */\n    multiplyUnsafe(sc: bigint): Point {\n      const { endo, n: N } = CURVE;\n      aInRange('scalar', sc, _0n, N);\n      const I = Point.ZERO;\n      if (sc === _0n) return I;\n      if (this.is0() || sc === _1n) return this;\n\n      // Case a: no endomorphism. Case b: has precomputes.\n      if (!endo || wnaf.hasPrecomputes(this))\n        return wnaf.wNAFCachedUnsafe(this, sc, Point.normalizeZ);\n\n      // Case c: endomorphism\n      let { k1neg, k1, k2neg, k2 } = endo.splitScalar(sc);\n      let k1p = I;\n      let k2p = I;\n      let d: Point = this;\n      while (k1 > _0n || k2 > _0n) {\n        if (k1 & _1n) k1p = k1p.add(d);\n        if (k2 & _1n) k2p = k2p.add(d);\n        d = d.double();\n        k1 >>= _1n;\n        k2 >>= _1n;\n      }\n      if (k1neg) k1p = k1p.negate();\n      if (k2neg) k2p = k2p.negate();\n      k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n      return k1p.add(k2p);\n    }\n\n    /**\n     * Constant time multiplication.\n     * Uses wNAF method. Windowed method may be 10% faster,\n     * but takes 2x longer to generate and consumes 2x memory.\n     * Uses precomputes when available.\n     * Uses endomorphism for Koblitz curves.\n     * @param scalar by which the point would be multiplied\n     * @returns New point\n     */\n    multiply(scalar: bigint): Point {\n      const { endo, n: N } = CURVE;\n      aInRange('scalar', scalar, _1n, N);\n      let point: Point, fake: Point; // Fake point is used to const-time mult\n      if (endo) {\n        const { k1neg, k1, k2neg, k2 } = endo.splitScalar(scalar);\n        let { p: k1p, f: f1p } = this.wNAF(k1);\n        let { p: k2p, f: f2p } = this.wNAF(k2);\n        k1p = wnaf.constTimeNegate(k1neg, k1p);\n        k2p = wnaf.constTimeNegate(k2neg, k2p);\n        k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n        point = k1p.add(k2p);\n        fake = f1p.add(f2p);\n      } else {\n        const { p, f } = this.wNAF(scalar);\n        point = p;\n        fake = f;\n      }\n      // Normalize `z` for both points, but return only real one\n      return Point.normalizeZ([point, fake])[0];\n    }\n\n    /**\n     * Efficiently calculate `aP + bQ`. Unsafe, can expose private key, if used incorrectly.\n     * Not using Strauss-Shamir trick: precomputation tables are faster.\n     * The trick could be useful if both P and Q are not G (not in our case).\n     * @returns non-zero affine point\n     */\n    multiplyAndAddUnsafe(Q: Point, a: bigint, b: bigint): Point | undefined {\n      const G = Point.BASE; // No Strauss-Shamir trick: we have 10% faster G precomputes\n      const mul = (\n        P: Point,\n        a: bigint // Select faster multiply() method\n      ) => (a === _0n || a === _1n || !P.equals(G) ? P.multiplyUnsafe(a) : P.multiply(a));\n      const sum = mul(this, a).add(mul(Q, b));\n      return sum.is0() ? undefined : sum;\n    }\n\n    // Converts Projective point to affine (x, y) coordinates.\n    // Can accept precomputed Z^-1 - for example, from invertBatch.\n    // (x, y, z) \u220B (x=x/z, y=y/z)\n    toAffine(iz?: T): AffinePoint<T> {\n      return toAffineMemo(this, iz);\n    }\n    isTorsionFree(): boolean {\n      const { h: cofactor, isTorsionFree } = CURVE;\n      if (cofactor === _1n) return true; // No subgroups, always torsion-free\n      if (isTorsionFree) return isTorsionFree(Point, this);\n      throw new Error('isTorsionFree() has not been declared for the elliptic curve');\n    }\n    clearCofactor(): Point {\n      const { h: cofactor, clearCofactor } = CURVE;\n      if (cofactor === _1n) return this; // Fast-path\n      if (clearCofactor) return clearCofactor(Point, this) as Point;\n      return this.multiplyUnsafe(CURVE.h);\n    }\n\n    toRawBytes(isCompressed = true): Uint8Array {\n      abool('isCompressed', isCompressed);\n      this.assertValidity();\n      return toBytes(Point, this, isCompressed);\n    }\n\n    toHex(isCompressed = true): string {\n      abool('isCompressed', isCompressed);\n      return bytesToHex(this.toRawBytes(isCompressed));\n    }\n  }\n  const _bits = CURVE.nBitLength;\n  const wnaf = wNAF(Point, CURVE.endo ? Math.ceil(_bits / 2) : _bits);\n  return {\n    CURVE,\n    ProjectivePoint: Point as ProjConstructor<T>,\n    normPrivateKeyToScalar,\n    weierstrassEquation,\n    isWithinCurveOrder,\n  };\n}\n\n// Instance\nexport interface SignatureType {\n  readonly r: bigint;\n  readonly s: bigint;\n  readonly recovery?: number;\n  assertValidity(): void;\n  addRecoveryBit(recovery: number): RecoveredSignatureType;\n  hasHighS(): boolean;\n  normalizeS(): SignatureType;\n  recoverPublicKey(msgHash: Hex): ProjPointType<bigint>;\n  toCompactRawBytes(): Uint8Array;\n  toCompactHex(): string;\n  toDERRawBytes(isCompressed?: boolean): Uint8Array;\n  toDERHex(isCompressed?: boolean): string;\n}\nexport type RecoveredSignatureType = SignatureType & {\n  readonly recovery: number;\n};\n// Static methods\nexport type SignatureConstructor = {\n  new (r: bigint, s: bigint): SignatureType;\n  fromCompact(hex: Hex): SignatureType;\n  fromDER(hex: Hex): SignatureType;\n};\ntype SignatureLike = { r: bigint; s: bigint };\n\nexport type PubKey = Hex | ProjPointType<bigint>;\n\nexport type CurveType = BasicWCurve<bigint> & {\n  hash: CHash; // CHash not FHash because we need outputLen for DRBG\n  hmac: HmacFnSync;\n  randomBytes: (bytesLength?: number) => Uint8Array;\n  lowS?: boolean;\n  bits2int?: (bytes: Uint8Array) => bigint;\n  bits2int_modN?: (bytes: Uint8Array) => bigint;\n};\n\nfunction validateOpts(\n  curve: CurveType\n): Readonly<CurveType & { nByteLength: number; nBitLength: number }> {\n  const opts = validateBasic(curve);\n  validateObject(\n    opts,\n    {\n      hash: 'hash',\n      hmac: 'function',\n      randomBytes: 'function',\n    },\n    {\n      bits2int: 'function',\n      bits2int_modN: 'function',\n      lowS: 'boolean',\n    }\n  );\n  return Object.freeze({ lowS: true, ...opts } as const);\n}\n\nexport type CurveFn = {\n  CURVE: ReturnType<typeof validateOpts>;\n  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;\n  getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;\n  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => RecoveredSignatureType;\n  verify: (signature: Hex | SignatureLike, msgHash: Hex, publicKey: Hex, opts?: VerOpts) => boolean;\n  ProjectivePoint: ProjConstructor<bigint>;\n  Signature: SignatureConstructor;\n  utils: {\n    normPrivateKeyToScalar: (key: PrivKey) => bigint;\n    isValidPrivateKey(privateKey: PrivKey): boolean;\n    randomPrivateKey: () => Uint8Array;\n    precompute: (windowSize?: number, point?: ProjPointType<bigint>) => ProjPointType<bigint>;\n  };\n};\n\n/**\n * Creates short weierstrass curve and ECDSA signature methods for it.\n * @example\n * import { Field } from '@noble/curves/abstract/modular';\n * // Before that, define BigInt-s: a, b, p, n, Gx, Gy\n * const curve = weierstrass({ a, b, Fp: Field(p), n, Gx, Gy, h: 1n })\n */\nexport function weierstrass(curveDef: CurveType): CurveFn {\n  const CURVE = validateOpts(curveDef) as ReturnType<typeof validateOpts>;\n  const { Fp, n: CURVE_ORDER } = CURVE;\n  const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32\n  const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32\n\n  function modN(a: bigint) {\n    return mod(a, CURVE_ORDER);\n  }\n  function invN(a: bigint) {\n    return invert(a, CURVE_ORDER);\n  }\n\n  const {\n    ProjectivePoint: Point,\n    normPrivateKeyToScalar,\n    weierstrassEquation,\n    isWithinCurveOrder,\n  } = weierstrassPoints({\n    ...CURVE,\n    toBytes(_c, point, isCompressed: boolean): Uint8Array {\n      const a = point.toAffine();\n      const x = Fp.toBytes(a.x);\n      const cat = concatBytes;\n      abool('isCompressed', isCompressed);\n      if (isCompressed) {\n        return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);\n      } else {\n        return cat(Uint8Array.from([0x04]), x, Fp.toBytes(a.y));\n      }\n    },\n    fromBytes(bytes: Uint8Array) {\n      const len = bytes.length;\n      const head = bytes[0];\n      const tail = bytes.subarray(1);\n      // this.assertValidity() is done inside of fromHex\n      if (len === compressedLen && (head === 0x02 || head === 0x03)) {\n        const x = bytesToNumberBE(tail);\n        if (!inRange(x, _1n, Fp.ORDER)) throw new Error('Point is not on curve');\n        const y2 = weierstrassEquation(x); // y\u00B2 = x\u00B3 + ax + b\n        let y: bigint;\n        try {\n          y = Fp.sqrt(y2); // y = y\u00B2 ^ (p+1)/4\n        } catch (sqrtError) {\n          const suffix = sqrtError instanceof Error ? ': ' + sqrtError.message : '';\n          throw new Error('Point is not on curve' + suffix);\n        }\n        const isYOdd = (y & _1n) === _1n;\n        // ECDSA\n        const isHeadOdd = (head & 1) === 1;\n        if (isHeadOdd !== isYOdd) y = Fp.neg(y);\n        return { x, y };\n      } else if (len === uncompressedLen && head === 0x04) {\n        const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n        const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n        return { x, y };\n      } else {\n        const cl = compressedLen;\n        const ul = uncompressedLen;\n        throw new Error(\n          'invalid Point, expected length of ' + cl + ', or uncompressed ' + ul + ', got ' + len\n        );\n      }\n    },\n  });\n  const numToNByteHex = (num: bigint): string =>\n    bytesToHex(numberToBytesBE(num, CURVE.nByteLength));\n\n  function isBiggerThanHalfOrder(number: bigint) {\n    const HALF = CURVE_ORDER >> _1n;\n    return number > HALF;\n  }\n\n  function normalizeS(s: bigint) {\n    return isBiggerThanHalfOrder(s) ? modN(-s) : s;\n  }\n  // slice bytes num\n  const slcNum = (b: Uint8Array, from: number, to: number) => bytesToNumberBE(b.slice(from, to));\n\n  /**\n   * ECDSA signature with its (r, s) properties. Supports DER & compact representations.\n   */\n  class Signature implements SignatureType {\n    readonly r: bigint;\n    readonly s: bigint;\n    readonly recovery?: number;\n    constructor(r: bigint, s: bigint, recovery?: number) {\n      aInRange('r', r, _1n, CURVE_ORDER); // r in [1..N]\n      aInRange('s', s, _1n, CURVE_ORDER); // s in [1..N]\n      this.r = r;\n      this.s = s;\n      if (recovery != null) this.recovery = recovery;\n      Object.freeze(this);\n    }\n\n    // pair (bytes of r, bytes of s)\n    static fromCompact(hex: Hex) {\n      const l = CURVE.nByteLength;\n      hex = ensureBytes('compactSignature', hex, l * 2);\n      return new Signature(slcNum(hex, 0, l), slcNum(hex, l, 2 * l));\n    }\n\n    // DER encoded ECDSA signature\n    // https://bitcoin.stackexchange.com/questions/57644/what-are-the-parts-of-a-bitcoin-transaction-input-script\n    static fromDER(hex: Hex) {\n      const { r, s } = DER.toSig(ensureBytes('DER', hex));\n      return new Signature(r, s);\n    }\n\n    /**\n     * @todo remove\n     * @deprecated\n     */\n    assertValidity(): void {}\n\n    addRecoveryBit(recovery: number): RecoveredSignature {\n      return new Signature(this.r, this.s, recovery) as RecoveredSignature;\n    }\n\n    recoverPublicKey(msgHash: Hex): typeof Point.BASE {\n      const { r, s, recovery: rec } = this;\n      const h = bits2int_modN(ensureBytes('msgHash', msgHash)); // Truncate hash\n      if (rec == null || ![0, 1, 2, 3].includes(rec)) throw new Error('recovery id invalid');\n      const radj = rec === 2 || rec === 3 ? r + CURVE.n : r;\n      if (radj >= Fp.ORDER) throw new Error('recovery id 2 or 3 invalid');\n      const prefix = (rec & 1) === 0 ? '02' : '03';\n      const R = Point.fromHex(prefix + numToNByteHex(radj));\n      const ir = invN(radj); // r^-1\n      const u1 = modN(-h * ir); // -hr^-1\n      const u2 = modN(s * ir); // sr^-1\n      const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)\n      if (!Q) throw new Error('point at infinify'); // unsafe is fine: no priv data leaked\n      Q.assertValidity();\n      return Q;\n    }\n\n    // Signatures should be low-s, to prevent malleability.\n    hasHighS(): boolean {\n      return isBiggerThanHalfOrder(this.s);\n    }\n\n    normalizeS() {\n      return this.hasHighS() ? new Signature(this.r, modN(-this.s), this.recovery) : this;\n    }\n\n    // DER-encoded\n    toDERRawBytes() {\n      return hexToBytes(this.toDERHex());\n    }\n    toDERHex() {\n      return DER.hexFromSig(this);\n    }\n\n    // padded bytes of r, then padded bytes of s\n    toCompactRawBytes() {\n      return hexToBytes(this.toCompactHex());\n    }\n    toCompactHex() {\n      return numToNByteHex(this.r) + numToNByteHex(this.s);\n    }\n  }\n  type RecoveredSignature = Signature & { recovery: number };\n\n  const utils = {\n    isValidPrivateKey(privateKey: PrivKey) {\n      try {\n        normPrivateKeyToScalar(privateKey);\n        return true;\n      } catch (error) {\n        return false;\n      }\n    },\n    normPrivateKeyToScalar: normPrivateKeyToScalar,\n\n    /**\n     * Produces cryptographically secure private key from random of size\n     * (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.\n     */\n    randomPrivateKey: (): Uint8Array => {\n      const length = getMinHashLength(CURVE.n);\n      return mapHashToField(CURVE.randomBytes(length), CURVE.n);\n    },\n\n    /**\n     * Creates precompute table for an arbitrary EC point. Makes point \"cached\".\n     * Allows to massively speed-up `point.multiply(scalar)`.\n     * @returns cached point\n     * @example\n     * const fast = utils.precompute(8, ProjectivePoint.fromHex(someonesPubKey));\n     * fast.multiply(privKey); // much faster ECDH now\n     */\n    precompute(windowSize = 8, point = Point.BASE): typeof Point.BASE {\n      point._setWindowSize(windowSize);\n      point.multiply(BigInt(3)); // 3 is arbitrary, just need any number here\n      return point;\n    },\n  };\n\n  /**\n   * Computes public key for a private key. Checks for validity of the private key.\n   * @param privateKey private key\n   * @param isCompressed whether to return compact (default), or full key\n   * @returns Public key, full when isCompressed=false; short when isCompressed=true\n   */\n  function getPublicKey(privateKey: PrivKey, isCompressed = true): Uint8Array {\n    return Point.fromPrivateKey(privateKey).toRawBytes(isCompressed);\n  }\n\n  /**\n   * Quick and dirty check for item being public key. Does not validate hex, or being on-curve.\n   */\n  function isProbPub(item: PrivKey | PubKey): boolean {\n    const arr = isBytes(item);\n    const str = typeof item === 'string';\n    const len = (arr || str) && (item as Hex).length;\n    if (arr) return len === compressedLen || len === uncompressedLen;\n    if (str) return len === 2 * compressedLen || len === 2 * uncompressedLen;\n    if (item instanceof Point) return true;\n    return false;\n  }\n\n  /**\n   * ECDH (Elliptic Curve Diffie Hellman).\n   * Computes shared public key from private key and public key.\n   * Checks: 1) private key validity 2) shared key is on-curve.\n   * Does NOT hash the result.\n   * @param privateA private key\n   * @param publicB different public key\n   * @param isCompressed whether to return compact (default), or full key\n   * @returns shared public key\n   */\n  function getSharedSecret(privateA: PrivKey, publicB: Hex, isCompressed = true): Uint8Array {\n    if (isProbPub(privateA)) throw new Error('first arg must be private key');\n    if (!isProbPub(publicB)) throw new Error('second arg must be public key');\n    const b = Point.fromHex(publicB); // check for being on-curve\n    return b.multiply(normPrivateKeyToScalar(privateA)).toRawBytes(isCompressed);\n  }\n\n  // RFC6979: ensure ECDSA msg is X bytes and < N. RFC suggests optional truncating via bits2octets.\n  // FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which matches bits2int.\n  // bits2int can produce res>N, we can do mod(res, N) since the bitLen is the same.\n  // int2octets can't be used; pads small msgs with 0: unacceptatble for trunc as per RFC vectors\n  const bits2int =\n    CURVE.bits2int ||\n    function (bytes: Uint8Array): bigint {\n      // Our custom check \"just in case\"\n      if (bytes.length > 8192) throw new Error('input is too large');\n      // For curves with nBitLength % 8 !== 0: bits2octets(bits2octets(m)) !== bits2octets(m)\n      // for some cases, since bytes.length * 8 is not actual bitLength.\n      const num = bytesToNumberBE(bytes); // check for == u8 done here\n      const delta = bytes.length * 8 - CURVE.nBitLength; // truncate to nBitLength leftmost bits\n      return delta > 0 ? num >> BigInt(delta) : num;\n    };\n  const bits2int_modN =\n    CURVE.bits2int_modN ||\n    function (bytes: Uint8Array): bigint {\n      return modN(bits2int(bytes)); // can't use bytesToNumberBE here\n    };\n  // NOTE: pads output with zero as per spec\n  const ORDER_MASK = bitMask(CURVE.nBitLength);\n  /**\n   * Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.\n   */\n  function int2octets(num: bigint): Uint8Array {\n    aInRange('num < 2^' + CURVE.nBitLength, num, _0n, ORDER_MASK);\n    // works with order, can have different size than numToField!\n    return numberToBytesBE(num, CURVE.nByteLength);\n  }\n\n  // Steps A, D of RFC6979 3.2\n  // Creates RFC6979 seed; converts msg/privKey to numbers.\n  // Used only in sign, not in verify.\n  // NOTE: we cannot assume here that msgHash has same amount of bytes as curve order,\n  // this will be invalid at least for P521. Also it can be bigger for P224 + SHA256\n  function prepSig(msgHash: Hex, privateKey: PrivKey, opts = defaultSigOpts) {\n    if (['recovered', 'canonical'].some((k) => k in opts))\n      throw new Error('sign() legacy options not supported');\n    const { hash, randomBytes } = CURVE;\n    let { lowS, prehash, extraEntropy: ent } = opts; // generates low-s sigs by default\n    if (lowS == null) lowS = true; // RFC6979 3.2: we skip step A, because we already provide hash\n    msgHash = ensureBytes('msgHash', msgHash);\n    validateSigVerOpts(opts);\n    if (prehash) msgHash = ensureBytes('prehashed msgHash', hash(msgHash));\n\n    // We can't later call bits2octets, since nested bits2int is broken for curves\n    // with nBitLength % 8 !== 0. Because of that, we unwrap it here as int2octets call.\n    // const bits2octets = (bits) => int2octets(bits2int_modN(bits))\n    const h1int = bits2int_modN(msgHash);\n    const d = normPrivateKeyToScalar(privateKey); // validate private key, convert to bigint\n    const seedArgs = [int2octets(d), int2octets(h1int)];\n    // extraEntropy. RFC6979 3.6: additional k' (optional).\n    if (ent != null && ent !== false) {\n      // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')\n      const e = ent === true ? randomBytes(Fp.BYTES) : ent; // generate random bytes OR pass as-is\n      seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes\n    }\n    const seed = concatBytes(...seedArgs); // Step D of RFC6979 3.2\n    const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!\n    // Converts signature params into point w r/s, checks result for validity.\n    function k2sig(kBytes: Uint8Array): RecoveredSignature | undefined {\n      // RFC 6979 Section 3.2, step 3: k = bits2int(T)\n      const k = bits2int(kBytes); // Cannot use fields methods, since it is group element\n      if (!isWithinCurveOrder(k)) return; // Important: all mod() calls here must be done over N\n      const ik = invN(k); // k^-1 mod n\n      const q = Point.BASE.multiply(k).toAffine(); // q = Gk\n      const r = modN(q.x); // r = q.x mod n\n      if (r === _0n) return;\n      // Can use scalar blinding b^-1(bm + bdr) where b \u2208 [1,q\u22121] according to\n      // https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:\n      // a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT\n      const s = modN(ik * modN(m + r * d)); // Not using blinding here\n      if (s === _0n) return;\n      let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n); // recovery bit (2 or 3, when q.x > n)\n      let normS = s;\n      if (lowS && isBiggerThanHalfOrder(s)) {\n        normS = normalizeS(s); // if lowS was passed, ensure s is always\n        recovery ^= 1; // // in the bottom half of N\n      }\n      return new Signature(r, normS, recovery) as RecoveredSignature; // use normS, not s\n    }\n    return { seed, k2sig };\n  }\n  const defaultSigOpts: SignOpts = { lowS: CURVE.lowS, prehash: false };\n  const defaultVerOpts: VerOpts = { lowS: CURVE.lowS, prehash: false };\n\n  /**\n   * Signs message hash with a private key.\n   * ```\n   * sign(m, d, k) where\n   *   (x, y) = G \u00D7 k\n   *   r = x mod n\n   *   s = (m + dr)/k mod n\n   * ```\n   * @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.\n   * @param privKey private key\n   * @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.\n   * @returns signature with recovery param\n   */\n  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): RecoveredSignature {\n    const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.\n    const C = CURVE;\n    const drbg = createHmacDrbg<RecoveredSignature>(C.hash.outputLen, C.nByteLength, C.hmac);\n    return drbg(seed, k2sig); // Steps B, C, D, E, F, G\n  }\n\n  // Enable precomputes. Slows down first publicKey computation by 20ms.\n  Point.BASE._setWindowSize(8);\n  // utils.precompute(8, ProjectivePoint.BASE)\n\n  /**\n   * Verifies a signature against message hash and public key.\n   * Rejects lowS signatures by default: to override,\n   * specify option `{lowS: false}`. Implements section 4.1.4 from https://www.secg.org/sec1-v2.pdf:\n   *\n   * ```\n   * verify(r, s, h, P) where\n   *   U1 = hs^-1 mod n\n   *   U2 = rs^-1 mod n\n   *   R = U1\u22C5G - U2\u22C5P\n   *   mod(R.x, n) == r\n   * ```\n   */\n  function verify(\n    signature: Hex | SignatureLike,\n    msgHash: Hex,\n    publicKey: Hex,\n    opts = defaultVerOpts\n  ): boolean {\n    const sg = signature;\n    msgHash = ensureBytes('msgHash', msgHash);\n    publicKey = ensureBytes('publicKey', publicKey);\n    const { lowS, prehash, format } = opts;\n\n    // Verify opts, deduce signature format\n    validateSigVerOpts(opts);\n    if ('strict' in opts) throw new Error('options.strict was renamed to lowS');\n    if (format !== undefined && format !== 'compact' && format !== 'der')\n      throw new Error('format must be compact or der');\n    const isHex = typeof sg === 'string' || isBytes(sg);\n    const isObj =\n      !isHex &&\n      !format &&\n      typeof sg === 'object' &&\n      sg !== null &&\n      typeof sg.r === 'bigint' &&\n      typeof sg.s === 'bigint';\n    if (!isHex && !isObj)\n      throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');\n\n    let _sig: Signature | undefined = undefined;\n    let P: ProjPointType<bigint>;\n    try {\n      if (isObj) _sig = new Signature(sg.r, sg.s);\n      if (isHex) {\n        // Signature can be represented in 2 ways: compact (2*nByteLength) & DER (variable-length).\n        // Since DER can also be 2*nByteLength bytes, we check for it first.\n        try {\n          if (format !== 'compact') _sig = Signature.fromDER(sg);\n        } catch (derError) {\n          if (!(derError instanceof DER.Err)) throw derError;\n        }\n        if (!_sig && format !== 'der') _sig = Signature.fromCompact(sg);\n      }\n      P = Point.fromHex(publicKey);\n    } catch (error) {\n      return false;\n    }\n    if (!_sig) return false;\n    if (lowS && _sig.hasHighS()) return false;\n    if (prehash) msgHash = CURVE.hash(msgHash);\n    const { r, s } = _sig;\n    const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element\n    const is = invN(s); // s^-1\n    const u1 = modN(h * is); // u1 = hs^-1 mod n\n    const u2 = modN(r * is); // u2 = rs^-1 mod n\n    const R = Point.BASE.multiplyAndAddUnsafe(P, u1, u2)?.toAffine(); // R = u1\u22C5G + u2\u22C5P\n    if (!R) return false;\n    const v = modN(R.x);\n    return v === r;\n  }\n  return {\n    CURVE,\n    getPublicKey,\n    getSharedSecret,\n    sign,\n    verify,\n    ProjectivePoint: Point,\n    Signature,\n    utils,\n  };\n}\n\n/**\n * Implementation of the Shallue and van de Woestijne method for any weierstrass curve.\n * TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.\n * b = True and y = sqrt(u / v) if (u / v) is square in F, and\n * b = False and y = sqrt(Z * (u / v)) otherwise.\n * @param Fp\n * @param Z\n * @returns\n */\nexport function SWUFpSqrtRatio<T>(\n  Fp: IField<T>,\n  Z: T\n): (u: T, v: T) => { isValid: boolean; value: T } {\n  // Generic implementation\n  const q = Fp.ORDER;\n  let l = _0n;\n  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;\n  const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.\n  // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.\n  // 2n ** c1 == 2n << (c1-1)\n  const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);\n  const _2n_pow_c1 = _2n_pow_c1_1 * _2n;\n  const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1)  # Integer arithmetic\n  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic\n  const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic\n  const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1)                  # Integer arithmetic\n  const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2\n  const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)\n  let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {\n    let tv1 = c6; // 1. tv1 = c6\n    let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4\n    let tv3 = Fp.sqr(tv2); // 3. tv3 = tv2^2\n    tv3 = Fp.mul(tv3, v); // 4. tv3 = tv3 * v\n    let tv5 = Fp.mul(u, tv3); // 5. tv5 = u * tv3\n    tv5 = Fp.pow(tv5, c3); // 6. tv5 = tv5^c3\n    tv5 = Fp.mul(tv5, tv2); // 7. tv5 = tv5 * tv2\n    tv2 = Fp.mul(tv5, v); // 8. tv2 = tv5 * v\n    tv3 = Fp.mul(tv5, u); // 9. tv3 = tv5 * u\n    let tv4 = Fp.mul(tv3, tv2); // 10. tv4 = tv3 * tv2\n    tv5 = Fp.pow(tv4, c5); // 11. tv5 = tv4^c5\n    let isQR = Fp.eql(tv5, Fp.ONE); // 12. isQR = tv5 == 1\n    tv2 = Fp.mul(tv3, c7); // 13. tv2 = tv3 * c7\n    tv5 = Fp.mul(tv4, tv1); // 14. tv5 = tv4 * tv1\n    tv3 = Fp.cmov(tv2, tv3, isQR); // 15. tv3 = CMOV(tv2, tv3, isQR)\n    tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)\n    // 17. for i in (c1, c1 - 1, ..., 2):\n    for (let i = c1; i > _1n; i--) {\n      let tv5 = i - _2n; // 18.    tv5 = i - 2\n      tv5 = _2n << (tv5 - _1n); // 19.    tv5 = 2^tv5\n      let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5\n      const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1\n      tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1\n      tv1 = Fp.mul(tv1, tv1); // 23.    tv1 = tv1 * tv1\n      tvv5 = Fp.mul(tv4, tv1); // 24.    tv5 = tv4 * tv1\n      tv3 = Fp.cmov(tv2, tv3, e1); // 25.    tv3 = CMOV(tv2, tv3, e1)\n      tv4 = Fp.cmov(tvv5, tv4, e1); // 26.    tv4 = CMOV(tv5, tv4, e1)\n    }\n    return { isValid: isQR, value: tv3 };\n  };\n  if (Fp.ORDER % _4n === _3n) {\n    // sqrt_ratio_3mod4(u, v)\n    const c1 = (Fp.ORDER - _3n) / _4n; // 1. c1 = (q - 3) / 4     # Integer arithmetic\n    const c2 = Fp.sqrt(Fp.neg(Z)); // 2. c2 = sqrt(-Z)\n    sqrtRatio = (u: T, v: T) => {\n      let tv1 = Fp.sqr(v); // 1. tv1 = v^2\n      const tv2 = Fp.mul(u, v); // 2. tv2 = u * v\n      tv1 = Fp.mul(tv1, tv2); // 3. tv1 = tv1 * tv2\n      let y1 = Fp.pow(tv1, c1); // 4. y1 = tv1^c1\n      y1 = Fp.mul(y1, tv2); // 5. y1 = y1 * tv2\n      const y2 = Fp.mul(y1, c2); // 6. y2 = y1 * c2\n      const tv3 = Fp.mul(Fp.sqr(y1), v); // 7. tv3 = y1^2; 8. tv3 = tv3 * v\n      const isQR = Fp.eql(tv3, u); // 9. isQR = tv3 == u\n      let y = Fp.cmov(y2, y1, isQR); // 10. y = CMOV(y2, y1, isQR)\n      return { isValid: isQR, value: y }; // 11. return (isQR, y) isQR ? y : y*c2\n    };\n  }\n  // No curves uses that\n  // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8\n  return sqrtRatio;\n}\n/**\n * Simplified Shallue-van de Woestijne-Ulas Method\n * https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2\n */\nexport function mapToCurveSimpleSWU<T>(\n  Fp: IField<T>,\n  opts: {\n    A: T;\n    B: T;\n    Z: T;\n  }\n): (u: T) => { x: T; y: T } {\n  validateField(Fp);\n  if (!Fp.isValid(opts.A) || !Fp.isValid(opts.B) || !Fp.isValid(opts.Z))\n    throw new Error('mapToCurveSimpleSWU: invalid opts');\n  const sqrtRatio = SWUFpSqrtRatio(Fp, opts.Z);\n  if (!Fp.isOdd) throw new Error('Fp.isOdd is not implemented!');\n  // Input: u, an element of F.\n  // Output: (x, y), a point on E.\n  return (u: T): { x: T; y: T } => {\n    // prettier-ignore\n    let tv1, tv2, tv3, tv4, tv5, tv6, x, y;\n    tv1 = Fp.sqr(u); // 1.  tv1 = u^2\n    tv1 = Fp.mul(tv1, opts.Z); // 2.  tv1 = Z * tv1\n    tv2 = Fp.sqr(tv1); // 3.  tv2 = tv1^2\n    tv2 = Fp.add(tv2, tv1); // 4.  tv2 = tv2 + tv1\n    tv3 = Fp.add(tv2, Fp.ONE); // 5.  tv3 = tv2 + 1\n    tv3 = Fp.mul(tv3, opts.B); // 6.  tv3 = B * tv3\n    tv4 = Fp.cmov(opts.Z, Fp.neg(tv2), !Fp.eql(tv2, Fp.ZERO)); // 7.  tv4 = CMOV(Z, -tv2, tv2 != 0)\n    tv4 = Fp.mul(tv4, opts.A); // 8.  tv4 = A * tv4\n    tv2 = Fp.sqr(tv3); // 9.  tv2 = tv3^2\n    tv6 = Fp.sqr(tv4); // 10. tv6 = tv4^2\n    tv5 = Fp.mul(tv6, opts.A); // 11. tv5 = A * tv6\n    tv2 = Fp.add(tv2, tv5); // 12. tv2 = tv2 + tv5\n    tv2 = Fp.mul(tv2, tv3); // 13. tv2 = tv2 * tv3\n    tv6 = Fp.mul(tv6, tv4); // 14. tv6 = tv6 * tv4\n    tv5 = Fp.mul(tv6, opts.B); // 15. tv5 = B * tv6\n    tv2 = Fp.add(tv2, tv5); // 16. tv2 = tv2 + tv5\n    x = Fp.mul(tv1, tv3); // 17.   x = tv1 * tv3\n    const { isValid, value } = sqrtRatio(tv2, tv6); // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)\n    y = Fp.mul(tv1, u); // 19.   y = tv1 * u  -> Z * u^3 * y1\n    y = Fp.mul(y, value); // 20.   y = y * y1\n    x = Fp.cmov(x, tv3, isValid); // 21.   x = CMOV(x, tv3, is_gx1_square)\n    y = Fp.cmov(y, value, isValid); // 22.   y = CMOV(y, y1, is_gx1_square)\n    const e1 = Fp.isOdd!(u) === Fp.isOdd!(y); // 23.  e1 = sgn0(u) == sgn0(y)\n    y = Fp.cmov(Fp.neg(y), y, e1); // 24.   y = CMOV(-y, y, e1)\n    const tv4_inv = FpInvertBatch(Fp, [tv4], true)[0];\n    x = Fp.mul(x, tv4_inv); // 25.   x = x / tv4\n    return { x, y };\n  };\n}\n", "/**\n * BLS (Barreto-Lynn-Scott) family of pairing-friendly curves.\n * BLS != BLS.\n * The file implements BLS (Boneh-Lynn-Shacham) signatures.\n * Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig)\n * families of pairing-friendly curves.\n * Consists of two curves: G1 and G2:\n * - G1 is a subgroup of (x, y) E(Fq) over y\u00B2 = x\u00B3 + 4.\n * - G2 is a subgroup of ((x\u2081, x\u2082+i), (y\u2081, y\u2082+i)) E(Fq\u00B2) over y\u00B2 = x\u00B3 + 4(1 + i) where i is \u221A-1\n * - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in\n *   Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.\n * Pairing is used to aggregate and verify signatures.\n * There are two main ways to use it:\n * 1. Fp for short private keys, Fp\u2082 for signatures\n * 2. Fp for short signatures, Fp\u2082 for private keys\n * @module\n **/\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// TODO: import { AffinePoint } from './curve.ts';\nimport {\n  type H2CPointConstructor,\n  type htfBasicOpts,\n  type Opts as HTFOpts,\n  type MapToCurve,\n  createHasher,\n} from './hash-to-curve.ts';\nimport { type IField, getMinHashLength, mapHashToField } from './modular.ts';\nimport type { Fp12, Fp12Bls, Fp2, Fp2Bls, Fp6 } from './tower.ts';\nimport { type CHash, type Hex, type PrivKey, ensureBytes, memoized } from './utils.ts';\nimport {\n  type CurvePointsRes,\n  type CurvePointsType,\n  type ProjPointType,\n  weierstrassPoints,\n} from './weierstrass.ts';\n\ntype Fp = bigint; // Can be different field?\n\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n\nexport type TwistType = 'multiplicative' | 'divisive';\n\nexport type ShortSignatureCoder<Fp> = {\n  fromHex(hex: Hex): ProjPointType<Fp>;\n  toRawBytes(point: ProjPointType<Fp>): Uint8Array;\n  toHex(point: ProjPointType<Fp>): string;\n};\n\nexport type SignatureCoder<Fp> = {\n  fromHex(hex: Hex): ProjPointType<Fp>;\n  toRawBytes(point: ProjPointType<Fp>): Uint8Array;\n  toHex(point: ProjPointType<Fp>): string;\n};\n\nexport type PostPrecomputePointAddFn = (\n  Rx: Fp2,\n  Ry: Fp2,\n  Rz: Fp2,\n  Qx: Fp2,\n  Qy: Fp2\n) => { Rx: Fp2; Ry: Fp2; Rz: Fp2 };\nexport type PostPrecomputeFn = (\n  Rx: Fp2,\n  Ry: Fp2,\n  Rz: Fp2,\n  Qx: Fp2,\n  Qy: Fp2,\n  pointAdd: PostPrecomputePointAddFn\n) => void;\nexport type CurveType = {\n  G1: Omit<CurvePointsType<Fp>, 'n'> & {\n    ShortSignature: SignatureCoder<Fp>;\n    mapToCurve: MapToCurve<Fp>;\n    htfDefaults: HTFOpts;\n  };\n  G2: Omit<CurvePointsType<Fp2>, 'n'> & {\n    Signature: SignatureCoder<Fp2>;\n    mapToCurve: MapToCurve<Fp2>;\n    htfDefaults: HTFOpts;\n  };\n  fields: {\n    Fp: IField<Fp>;\n    Fr: IField<bigint>;\n    Fp2: Fp2Bls;\n    Fp6: IField<Fp6>;\n    Fp12: Fp12Bls;\n  };\n  params: {\n    // NOTE: MSB is always ignored and used as marker for length,\n    // otherwise leading zeros will be lost.\n    // Can be different from 'X' (seed) param!\n    ateLoopSize: bigint;\n    xNegative: boolean;\n    r: bigint;\n    twistType: TwistType; // BLS12-381: Multiplicative, BN254: Divisive\n  };\n  htfDefaults: HTFOpts;\n  hash: CHash; // Because we need outputLen for DRBG\n  randomBytes: (bytesLength?: number) => Uint8Array;\n  // This is super ugly hack for untwist point in BN254 after miller loop\n  postPrecompute?: PostPrecomputeFn;\n};\n\ntype PrecomputeSingle = [Fp2, Fp2, Fp2][];\ntype Precompute = PrecomputeSingle[];\n\nexport type CurveFn = {\n  getPublicKey: (privateKey: PrivKey) => Uint8Array;\n  getPublicKeyForShortSignatures: (privateKey: PrivKey) => Uint8Array;\n  sign: {\n    (message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n    (message: ProjPointType<Fp2>, privateKey: PrivKey, htfOpts?: htfBasicOpts): ProjPointType<Fp2>;\n  };\n  signShortSignature: {\n    (message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n    (message: ProjPointType<Fp>, privateKey: PrivKey, htfOpts?: htfBasicOpts): ProjPointType<Fp>;\n  };\n  verify: (\n    signature: Hex | ProjPointType<Fp2>,\n    message: Hex | ProjPointType<Fp2>,\n    publicKey: Hex | ProjPointType<Fp>,\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  verifyShortSignature: (\n    signature: Hex | ProjPointType<Fp>,\n    message: Hex | ProjPointType<Fp>,\n    publicKey: Hex | ProjPointType<Fp2>,\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  verifyBatch: (\n    signature: Hex | ProjPointType<Fp2>,\n    messages: (Hex | ProjPointType<Fp2>)[],\n    publicKeys: (Hex | ProjPointType<Fp>)[],\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  aggregatePublicKeys: {\n    (publicKeys: Hex[]): Uint8Array;\n    (publicKeys: ProjPointType<Fp>[]): ProjPointType<Fp>;\n  };\n  aggregateSignatures: {\n    (signatures: Hex[]): Uint8Array;\n    (signatures: ProjPointType<Fp2>[]): ProjPointType<Fp2>;\n  };\n  aggregateShortSignatures: {\n    (signatures: Hex[]): Uint8Array;\n    (signatures: ProjPointType<Fp>[]): ProjPointType<Fp>;\n  };\n  millerLoopBatch: (pairs: [Precompute, Fp, Fp][]) => Fp12;\n  pairing: (P: ProjPointType<Fp>, Q: ProjPointType<Fp2>, withFinalExponent?: boolean) => Fp12;\n  pairingBatch: (\n    pairs: { g1: ProjPointType<Fp>; g2: ProjPointType<Fp2> }[],\n    withFinalExponent?: boolean\n  ) => Fp12;\n  G1: CurvePointsRes<Fp> & ReturnType<typeof createHasher<Fp>>;\n  G2: CurvePointsRes<Fp2> & ReturnType<typeof createHasher<Fp2>>;\n  Signature: SignatureCoder<Fp2>;\n  ShortSignature: ShortSignatureCoder<Fp>;\n  params: {\n    ateLoopSize: bigint;\n    r: bigint;\n    G1b: bigint;\n    G2b: Fp2;\n  };\n  fields: {\n    Fp: IField<Fp>;\n    Fp2: Fp2Bls;\n    Fp6: IField<Fp6>;\n    Fp12: Fp12Bls;\n    Fr: IField<bigint>;\n  };\n  utils: {\n    randomPrivateKey: () => Uint8Array;\n    calcPairingPrecomputes: (p: ProjPointType<Fp2>) => Precompute;\n  };\n};\n\n// Not used with BLS12-381 (no sequential `11` in X). Useful for other curves.\nfunction NAfDecomposition(a: bigint) {\n  const res = [];\n  // a>1 because of marker bit\n  for (; a > _1n; a >>= _1n) {\n    if ((a & _1n) === _0n) res.unshift(0);\n    else if ((a & _3n) === _3n) {\n      res.unshift(-1);\n      a += _1n;\n    } else res.unshift(1);\n  }\n  return res;\n}\n\nexport function bls(CURVE: CurveType): CurveFn {\n  // Fields are specific for curve, so for now we'll need to pass them with opts\n  const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields;\n  const BLS_X_IS_NEGATIVE = CURVE.params.xNegative;\n  const TWIST: TwistType = CURVE.params.twistType;\n  // Point on G1 curve: (x, y)\n  const G1_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G1 });\n  const G1 = Object.assign(\n    G1_,\n    createHasher(G1_.ProjectivePoint, CURVE.G1.mapToCurve, {\n      ...CURVE.htfDefaults,\n      ...CURVE.G1.htfDefaults,\n    })\n  );\n  // Point on G2 curve (complex numbers): (x\u2081, x\u2082+i), (y\u2081, y\u2082+i)\n  const G2_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G2 });\n  const G2 = Object.assign(\n    G2_,\n    createHasher(G2_.ProjectivePoint as H2CPointConstructor<Fp2>, CURVE.G2.mapToCurve, {\n      ...CURVE.htfDefaults,\n      ...CURVE.G2.htfDefaults,\n    })\n  );\n  type G1 = typeof G1.ProjectivePoint.BASE;\n  type G2 = typeof G2.ProjectivePoint.BASE;\n\n  // Applies sparse multiplication as line function\n  let lineFunction: (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) => Fp12;\n  if (TWIST === 'multiplicative') {\n    lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>\n      Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py));\n  } else if (TWIST === 'divisive') {\n    // NOTE: it should be [c0, c1, c2], but we use different order here to reduce complexity of\n    // precompute calculations.\n    lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>\n      Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0);\n  } else throw new Error('bls: unknown twist type');\n\n  const Fp2div2 = Fp2.div(Fp2.ONE, Fp2.mul(Fp2.ONE, _2n));\n  function pointDouble(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2) {\n    const t0 = Fp2.sqr(Ry); // Ry\u00B2\n    const t1 = Fp2.sqr(Rz); // Rz\u00B2\n    const t2 = Fp2.mulByB(Fp2.mul(t1, _3n)); // 3 * T1 * B\n    const t3 = Fp2.mul(t2, _3n); // 3 * T2\n    const t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)\u00B2 - T1 - T0\n    const c0 = Fp2.sub(t2, t0); // T2 - T0 (i)\n    const c1 = Fp2.mul(Fp2.sqr(Rx), _3n); // 3 * Rx\u00B2\n    const c2 = Fp2.neg(t4); // -T4 (-h)\n\n    ell.push([c0, c1, c2]);\n\n    Rx = Fp2.mul(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), Fp2div2); // ((T0 - T3) * Rx * Ry) / 2\n    Ry = Fp2.sub(Fp2.sqr(Fp2.mul(Fp2.add(t0, t3), Fp2div2)), Fp2.mul(Fp2.sqr(t2), _3n)); // ((T0 + T3) / 2)\u00B2 - 3 * T2\u00B2\n    Rz = Fp2.mul(t0, t4); // T0 * T4\n    return { Rx, Ry, Rz };\n  }\n  function pointAdd(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2, Qx: Fp2, Qy: Fp2) {\n    // Addition\n    const t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz\n    const t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz\n    const c0 = Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)); // T0 * Qx - T1 * Qy == Ry * Qx  - Rx * Qy\n    const c1 = Fp2.neg(t0); // -T0 == Qy * Rz - Ry\n    const c2 = t1; // == Rx - Qx * Rz\n\n    ell.push([c0, c1, c2]);\n\n    const t2 = Fp2.sqr(t1); // T1\u00B2\n    const t3 = Fp2.mul(t2, t1); // T2 * T1\n    const t4 = Fp2.mul(t2, Rx); // T2 * Rx\n    const t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0\u00B2 * Rz\n    Rx = Fp2.mul(t1, t5); // T1 * T5\n    Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry\n    Rz = Fp2.mul(Rz, t3); // Rz * T3\n    return { Rx, Ry, Rz };\n  }\n\n  // Pre-compute coefficients for sparse multiplication\n  // Point addition and point double calculations is reused for coefficients\n  // pointAdd happens only if bit set, so wNAF is reasonable. Unfortunately we cannot combine\n  // add + double in windowed precomputes here, otherwise it would be single op (since X is static)\n  const ATE_NAF = NAfDecomposition(CURVE.params.ateLoopSize);\n\n  const calcPairingPrecomputes = memoized((point: G2) => {\n    const p = point;\n    const { x, y } = p.toAffine();\n    // prettier-ignore\n    const Qx = x, Qy = y, negQy = Fp2.neg(y);\n    // prettier-ignore\n    let Rx = Qx, Ry = Qy, Rz = Fp2.ONE;\n    const ell: Precompute = [];\n    for (const bit of ATE_NAF) {\n      const cur: PrecomputeSingle = [];\n      ({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz));\n      if (bit) ({ Rx, Ry, Rz } = pointAdd(cur, Rx, Ry, Rz, Qx, bit === -1 ? negQy : Qy));\n      ell.push(cur);\n    }\n    if (CURVE.postPrecompute) {\n      const last = ell[ell.length - 1];\n      CURVE.postPrecompute(Rx, Ry, Rz, Qx, Qy, pointAdd.bind(null, last));\n    }\n    return ell;\n  });\n\n  // Main pairing logic is here. Computes product of miller loops + final exponentiate\n  // Applies calculated precomputes\n  type MillerInput = [Precompute, Fp, Fp][];\n  function millerLoopBatch(pairs: MillerInput, withFinalExponent: boolean = false) {\n    let f12 = Fp12.ONE;\n    if (pairs.length) {\n      const ellLen = pairs[0][0].length;\n      for (let i = 0; i < ellLen; i++) {\n        f12 = Fp12.sqr(f12); // This allows us to do sqr only one time for all pairings\n        // NOTE: we apply multiple pairings in parallel here\n        for (const [ell, Px, Py] of pairs) {\n          for (const [c0, c1, c2] of ell[i]) f12 = lineFunction(c0, c1, c2, f12, Px, Py);\n        }\n      }\n    }\n    if (BLS_X_IS_NEGATIVE) f12 = Fp12.conjugate(f12);\n    return withFinalExponent ? Fp12.finalExponentiate(f12) : f12;\n  }\n  type PairingInput = { g1: G1; g2: G2 };\n  // Calculates product of multiple pairings\n  // This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))`\n  function pairingBatch(pairs: PairingInput[], withFinalExponent: boolean = true) {\n    const res: MillerInput = [];\n    // Cache precomputed toAffine for all points\n    G1.ProjectivePoint.normalizeZ(pairs.map(({ g1 }) => g1));\n    G2.ProjectivePoint.normalizeZ(pairs.map(({ g2 }) => g2));\n    for (const { g1, g2 } of pairs) {\n      if (g1.equals(G1.ProjectivePoint.ZERO) || g2.equals(G2.ProjectivePoint.ZERO))\n        throw new Error('pairing is not available for ZERO point');\n      // This uses toAffine inside\n      g1.assertValidity();\n      g2.assertValidity();\n      const Qa = g1.toAffine();\n      res.push([calcPairingPrecomputes(g2), Qa.x, Qa.y]);\n    }\n    return millerLoopBatch(res, withFinalExponent);\n  }\n  // Calculates bilinear pairing\n  function pairing(Q: G1, P: G2, withFinalExponent: boolean = true): Fp12 {\n    return pairingBatch([{ g1: Q, g2: P }], withFinalExponent);\n  }\n\n  const utils = {\n    randomPrivateKey: (): Uint8Array => {\n      const length = getMinHashLength(Fr.ORDER);\n      return mapHashToField(CURVE.randomBytes(length), Fr.ORDER);\n    },\n    calcPairingPrecomputes,\n  };\n\n  const { ShortSignature } = CURVE.G1;\n  const { Signature } = CURVE.G2;\n\n  type G1Hex = Hex | G1;\n  type G2Hex = Hex | G2;\n  function normP1(point: G1Hex): G1 {\n    return point instanceof G1.ProjectivePoint ? (point as G1) : G1.ProjectivePoint.fromHex(point);\n  }\n  function normP1Hash(point: G1Hex, htfOpts?: htfBasicOpts): G1 {\n    return point instanceof G1.ProjectivePoint\n      ? point\n      : (G1.hashToCurve(ensureBytes('point', point), htfOpts) as G1);\n  }\n  function normP2(point: G2Hex): G2 {\n    return point instanceof G2.ProjectivePoint ? point : Signature.fromHex(point);\n  }\n  function normP2Hash(point: G2Hex, htfOpts?: htfBasicOpts): G2 {\n    return point instanceof G2.ProjectivePoint\n      ? point\n      : (G2.hashToCurve(ensureBytes('point', point), htfOpts) as G2);\n  }\n\n  // Multiplies generator (G1) by private key.\n  // P = pk x G\n  function getPublicKey(privateKey: PrivKey): Uint8Array {\n    return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n  }\n\n  // Multiplies generator (G2) by private key.\n  // P = pk x G\n  function getPublicKeyForShortSignatures(privateKey: PrivKey): Uint8Array {\n    return G2.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n  }\n\n  // Executes `hashToCurve` on the message and then multiplies the result by private key.\n  // S = pk x H(m)\n  function sign(message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n  function sign(message: G2, privateKey: PrivKey, htfOpts?: htfBasicOpts): G2;\n  function sign(message: G2Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array | G2 {\n    const msgPoint = normP2Hash(message, htfOpts);\n    msgPoint.assertValidity();\n    const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n    if (message instanceof G2.ProjectivePoint) return sigPoint;\n    return Signature.toRawBytes(sigPoint);\n  }\n\n  function signShortSignature(\n    message: Hex,\n    privateKey: PrivKey,\n    htfOpts?: htfBasicOpts\n  ): Uint8Array;\n  function signShortSignature(message: G1, privateKey: PrivKey, htfOpts?: htfBasicOpts): G1;\n  function signShortSignature(\n    message: G1Hex,\n    privateKey: PrivKey,\n    htfOpts?: htfBasicOpts\n  ): Uint8Array | G1 {\n    const msgPoint = normP1Hash(message, htfOpts);\n    msgPoint.assertValidity();\n    const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n    if (message instanceof G1.ProjectivePoint) return sigPoint;\n    return ShortSignature.toRawBytes(sigPoint);\n  }\n\n  // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n  // e(P, H(m)) == e(G, S)\n  function verify(\n    signature: G2Hex,\n    message: G2Hex,\n    publicKey: G1Hex,\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    const P = normP1(publicKey);\n    const Hm = normP2Hash(message, htfOpts);\n    const G = G1.ProjectivePoint.BASE;\n    const S = normP2(signature);\n    const exp = pairingBatch([\n      { g1: P.negate(), g2: Hm }, // ePHM = pairing(P.negate(), Hm, false);\n      { g1: G, g2: S }, // eGS = pairing(G, S, false);\n    ]);\n    return Fp12.eql(exp, Fp12.ONE);\n  }\n\n  // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n  // e(S, G) == e(H(m), P)\n  function verifyShortSignature(\n    signature: G1Hex,\n    message: G1Hex,\n    publicKey: G2Hex,\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    const P = normP2(publicKey);\n    const Hm = normP1Hash(message, htfOpts);\n    const G = G2.ProjectivePoint.BASE;\n    const S = normP1(signature);\n    const exp = pairingBatch([\n      { g1: Hm, g2: P }, // eHmP = pairing(Hm, P, false);\n      { g1: S, g2: G.negate() }, // eSG = pairing(S, G.negate(), false);\n    ]);\n    return Fp12.eql(exp, Fp12.ONE);\n  }\n\n  function aNonEmpty(arr: any[]) {\n    if (!Array.isArray(arr) || arr.length === 0) throw new Error('expected non-empty array');\n  }\n\n  // Adds a bunch of public key points together.\n  // pk1 + pk2 + pk3 = pkA\n  function aggregatePublicKeys(publicKeys: Hex[]): Uint8Array;\n  function aggregatePublicKeys(publicKeys: G1[]): G1;\n  function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {\n    aNonEmpty(publicKeys);\n    const agg = publicKeys.map(normP1).reduce((sum, p) => sum.add(p), G1.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (publicKeys[0] instanceof G1.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    // toRawBytes ensures point validity\n    return aggAffine.toRawBytes(true);\n  }\n\n  // Adds a bunch of signature points together.\n  function aggregateSignatures(signatures: Hex[]): Uint8Array;\n  function aggregateSignatures(signatures: G2[]): G2;\n  function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {\n    aNonEmpty(signatures);\n    const agg = signatures.map(normP2).reduce((sum, s) => sum.add(s), G2.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (signatures[0] instanceof G2.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    return Signature.toRawBytes(aggAffine);\n  }\n\n  // Adds a bunch of signature points together.\n  function aggregateShortSignatures(signatures: Hex[]): Uint8Array;\n  function aggregateShortSignatures(signatures: G1[]): G1;\n  function aggregateShortSignatures(signatures: G1Hex[]): Uint8Array | G1 {\n    aNonEmpty(signatures);\n    const agg = signatures.map(normP1).reduce((sum, s) => sum.add(s), G1.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (signatures[0] instanceof G1.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    return ShortSignature.toRawBytes(aggAffine);\n  }\n\n  // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407\n  // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))\n  function verifyBatch(\n    signature: G2Hex,\n    // TODO: maybe `{message: G2Hex, publicKey: G1Hex}[]` instead?\n    messages: G2Hex[],\n    publicKeys: G1Hex[],\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    aNonEmpty(messages);\n    if (publicKeys.length !== messages.length)\n      throw new Error('amount of public keys and messages should be equal');\n    const sig = normP2(signature);\n    const nMessages = messages.map((i) => normP2Hash(i, htfOpts));\n    const nPublicKeys = publicKeys.map(normP1);\n    // NOTE: this works only for exact same object\n    const messagePubKeyMap = new Map<G2, G1[]>();\n    for (let i = 0; i < nPublicKeys.length; i++) {\n      const pub = nPublicKeys[i];\n      const msg = nMessages[i];\n      let keys = messagePubKeyMap.get(msg);\n      if (keys === undefined) {\n        keys = [];\n        messagePubKeyMap.set(msg, keys);\n      }\n      keys.push(pub);\n    }\n    const paired = [];\n    try {\n      for (const [msg, keys] of messagePubKeyMap) {\n        const groupPublicKey = keys.reduce((acc, msg) => acc.add(msg));\n        paired.push({ g1: groupPublicKey, g2: msg });\n      }\n      paired.push({ g1: G1.ProjectivePoint.BASE.negate(), g2: sig });\n      return Fp12.eql(pairingBatch(paired), Fp12.ONE);\n    } catch {\n      return false;\n    }\n  }\n\n  G1.ProjectivePoint.BASE._setWindowSize(4);\n\n  return {\n    getPublicKey,\n    getPublicKeyForShortSignatures,\n    sign,\n    signShortSignature,\n    verify,\n    verifyBatch,\n    verifyShortSignature,\n    aggregatePublicKeys,\n    aggregateSignatures,\n    aggregateShortSignatures,\n    millerLoopBatch,\n    pairing,\n    pairingBatch,\n    G1,\n    G2,\n    Signature,\n    ShortSignature,\n    fields: {\n      Fr,\n      Fp,\n      Fp2,\n      Fp6,\n      Fp12,\n    },\n    params: {\n      ateLoopSize: CURVE.params.ateLoopSize,\n      r: CURVE.params.r,\n      G1b: CURVE.G1.b,\n      G2b: CURVE.G2.b,\n    },\n    utils,\n  };\n}\n", "/**\n * Towered extension fields.\n * Rather than implementing a massive 12th-degree extension directly, it is more efficient\n * to build it up from smaller extensions: a tower of extensions.\n *\n * For BLS12-381, the Fp12 field is implemented as a quadratic (degree two) extension,\n * on top of a cubic (degree three) extension, on top of a quadratic extension of Fp.\n *\n * For more info: \"Pairings for beginners\" by Costello, section 7.3.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport * as mod from './modular.ts';\nimport { bitLen, bitMask, concatBytes, notImplemented } from './utils.ts';\nimport type { ProjConstructor, ProjPointType } from './weierstrass.ts';\n\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n\n// Fp\u2082 over complex plane\nexport type BigintTuple = [bigint, bigint];\nexport type Fp = bigint;\n// Finite extension field over irreducible polynominal.\n// Fp(u) / (u\u00B2 - \u03B2) where \u03B2 = -1\nexport type Fp2 = { c0: bigint; c1: bigint };\nexport type BigintSix = [bigint, bigint, bigint, bigint, bigint, bigint];\nexport type Fp6 = { c0: Fp2; c1: Fp2; c2: Fp2 };\nexport type Fp12 = { c0: Fp6; c1: Fp6 }; // Fp\u2081\u2082 = Fp\u2086\u00B2 => Fp\u2082\u00B3, Fp\u2086(w) / (w\u00B2 - \u03B3) where \u03B3 = v\n// prettier-ignore\nexport type BigintTwelve = [\n  bigint, bigint, bigint, bigint, bigint, bigint,\n  bigint, bigint, bigint, bigint, bigint, bigint\n];\n\nexport type Fp2Bls = mod.IField<Fp2> & {\n  reim: (num: Fp2) => { re: Fp; im: Fp };\n  mulByB: (num: Fp2) => Fp2;\n  frobeniusMap(num: Fp2, power: number): Fp2;\n  fromBigTuple(num: [bigint, bigint]): Fp2;\n};\n\nexport type Fp12Bls = mod.IField<Fp12> & {\n  frobeniusMap(num: Fp12, power: number): Fp12;\n  mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n  mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n  conjugate(num: Fp12): Fp12;\n  finalExponentiate(num: Fp12): Fp12;\n  fromBigTwelve(num: BigintTwelve): Fp12;\n};\n\nfunction calcFrobeniusCoefficients<T>(\n  Fp: mod.IField<T>,\n  nonResidue: T,\n  modulus: bigint,\n  degree: number,\n  num: number = 1,\n  divisor?: number\n) {\n  const _divisor = BigInt(divisor === undefined ? degree : divisor);\n  const towerModulus: any = modulus ** BigInt(degree);\n  const res: T[][] = [];\n  for (let i = 0; i < num; i++) {\n    const a = BigInt(i + 1);\n    const powers: T[] = [];\n    for (let j = 0, qPower = _1n; j < degree; j++) {\n      const power = ((a * qPower - a) / _divisor) % towerModulus;\n      powers.push(Fp.pow(nonResidue, power));\n      qPower *= modulus;\n    }\n    res.push(powers);\n  }\n  return res;\n}\n\n// This works same at least for bls12-381, bn254 and bls12-377\nexport function psiFrobenius(\n  Fp: mod.IField<Fp>,\n  Fp2: Fp2Bls,\n  base: Fp2\n): {\n  psi: (x: Fp2, y: Fp2) => [Fp2, Fp2];\n  psi2: (x: Fp2, y: Fp2) => [Fp2, Fp2];\n  G2psi: (c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) => ProjPointType<Fp2>;\n  G2psi2: (c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) => ProjPointType<Fp2>;\n  PSI_X: Fp2;\n  PSI_Y: Fp2;\n  PSI2_X: Fp2;\n  PSI2_Y: Fp2;\n} {\n  // \u03A8 endomorphism\n  const PSI_X = Fp2.pow(base, (Fp.ORDER - _1n) / _3n); // u^((p-1)/3)\n  const PSI_Y = Fp2.pow(base, (Fp.ORDER - _1n) / _2n); // u^((p-1)/2)\n  function psi(x: Fp2, y: Fp2): [Fp2, Fp2] {\n    // This x10 faster than previous version in bls12-381\n    const x2 = Fp2.mul(Fp2.frobeniusMap(x, 1), PSI_X);\n    const y2 = Fp2.mul(Fp2.frobeniusMap(y, 1), PSI_Y);\n    return [x2, y2];\n  }\n  // \u03A8\u00B2(P) endomorphism (psi2(x) = psi(psi(x)))\n  const PSI2_X = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _3n); // u^((p^2 - 1)/3)\n  // This equals -1, which causes y to be Fp2.neg(y).\n  // But not sure if there are case when this is not true?\n  const PSI2_Y = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _2n); // u^((p^2 - 1)/3)\n  if (!Fp2.eql(PSI2_Y, Fp2.neg(Fp2.ONE))) throw new Error('psiFrobenius: PSI2_Y!==-1');\n  function psi2(x: Fp2, y: Fp2): [Fp2, Fp2] {\n    return [Fp2.mul(x, PSI2_X), Fp2.neg(y)];\n  }\n  // Map points\n  const mapAffine =\n    <T>(fn: (x: T, y: T) => [T, T]) =>\n    (c: ProjConstructor<T>, P: ProjPointType<T>) => {\n      const affine = P.toAffine();\n      const p = fn(affine.x, affine.y);\n      return c.fromAffine({ x: p[0], y: p[1] });\n    };\n  const G2psi = mapAffine(psi);\n  const G2psi2 = mapAffine(psi2);\n  return { psi, psi2, G2psi, G2psi2, PSI_X, PSI_Y, PSI2_X, PSI2_Y };\n}\n\nexport type Tower12Opts = {\n  ORDER: bigint;\n  NONRESIDUE?: Fp;\n  // Fp2\n  FP2_NONRESIDUE: BigintTuple;\n  Fp2sqrt?: (num: Fp2) => Fp2;\n  Fp2mulByB: (num: Fp2) => Fp2;\n  // Fp12\n  Fp12cyclotomicSquare: (num: Fp12) => Fp12;\n  Fp12cyclotomicExp: (num: Fp12, n: bigint) => Fp12;\n  Fp12finalExponentiate: (num: Fp12) => Fp12;\n};\n\nexport function tower12(opts: Tower12Opts): {\n  Fp: Readonly<mod.IField<bigint> & Required<Pick<mod.IField<bigint>, 'isOdd'>>>;\n  Fp2: mod.IField<Fp2> & {\n    NONRESIDUE: Fp2;\n    fromBigTuple: (tuple: BigintTuple | bigint[]) => Fp2;\n    reim: (num: Fp2) => { re: bigint; im: bigint };\n    mulByNonresidue: (num: Fp2) => Fp2;\n    mulByB: (num: Fp2) => Fp2;\n    frobeniusMap(num: Fp2, power: number): Fp2;\n  };\n  Fp6: mod.IField<Fp6> & {\n    fromBigSix: (tuple: BigintSix) => Fp6;\n    mulByNonresidue: (num: Fp6) => Fp6;\n    frobeniusMap(num: Fp6, power: number): Fp6;\n    mul1(num: Fp6, b1: Fp2): Fp6;\n    mul01(num: Fp6, b0: Fp2, b1: Fp2): Fp6;\n    mulByFp2(lhs: Fp6, rhs: Fp2): Fp6;\n  };\n  Fp4Square: (a: Fp2, b: Fp2) => { first: Fp2; second: Fp2 };\n  Fp12: mod.IField<Fp12> & {\n    fromBigTwelve: (t: BigintTwelve) => Fp12;\n    frobeniusMap(num: Fp12, power: number): Fp12;\n    mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n    mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n    mulByFp2(lhs: Fp12, rhs: Fp2): Fp12;\n    conjugate(num: Fp12): Fp12;\n    finalExponentiate(num: Fp12): Fp12;\n    _cyclotomicSquare(num: Fp12): Fp12;\n    _cyclotomicExp(num: Fp12, n: bigint): Fp12;\n  };\n} {\n  const { ORDER } = opts;\n  // Fp\n  const Fp = mod.Field(ORDER);\n  const FpNONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));\n  const Fpdiv2 = Fp.div(Fp.ONE, _2n); // 1/2\n\n  // Fp2\n  const FP2_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, FpNONRESIDUE, Fp.ORDER, 2)[0];\n  const Fp2Add = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({\n    c0: Fp.add(c0, r0),\n    c1: Fp.add(c1, r1),\n  });\n  const Fp2Subtract = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({\n    c0: Fp.sub(c0, r0),\n    c1: Fp.sub(c1, r1),\n  });\n  const Fp2Multiply = ({ c0, c1 }: Fp2, rhs: Fp2) => {\n    if (typeof rhs === 'bigint') return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };\n    // (a+bi)(c+di) = (ac\u2212bd) + (ad+bc)i\n    const { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp.mul(c0, r0); // c0 * o0\n    let t2 = Fp.mul(c1, r1); // c1 * o1\n    // (T1 - T2) + ((c0 + c1) * (r0 + r1) - (T1 + T2))*i\n    const o0 = Fp.sub(t1, t2);\n    const o1 = Fp.sub(Fp.mul(Fp.add(c0, c1), Fp.add(r0, r1)), Fp.add(t1, t2));\n    return { c0: o0, c1: o1 };\n  };\n  const Fp2Square = ({ c0, c1 }: Fp2) => {\n    const a = Fp.add(c0, c1);\n    const b = Fp.sub(c0, c1);\n    const c = Fp.add(c0, c0);\n    return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };\n  };\n  type Fp2Utils = {\n    NONRESIDUE: Fp2;\n    fromBigTuple: (tuple: BigintTuple | bigint[]) => Fp2;\n    reim: (num: Fp2) => { re: bigint; im: bigint };\n    mulByNonresidue: (num: Fp2) => Fp2;\n    mulByB: (num: Fp2) => Fp2;\n    frobeniusMap(num: Fp2, power: number): Fp2;\n  };\n  const Fp2fromBigTuple = (tuple: BigintTuple | bigint[]) => {\n    if (tuple.length !== 2) throw new Error('invalid tuple');\n    const fps = tuple.map((n) => Fp.create(n)) as [Fp, Fp];\n    return { c0: fps[0], c1: fps[1] };\n  };\n\n  const FP2_ORDER = ORDER * ORDER;\n  const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);\n  const Fp2: mod.IField<Fp2> & Fp2Utils = {\n    ORDER: FP2_ORDER,\n    isLE: Fp.isLE,\n    NONRESIDUE: Fp2Nonresidue,\n    BITS: bitLen(FP2_ORDER),\n    BYTES: Math.ceil(bitLen(FP2_ORDER) / 8),\n    MASK: bitMask(bitLen(FP2_ORDER)),\n    ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },\n    ONE: { c0: Fp.ONE, c1: Fp.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => typeof c0 === 'bigint' && typeof c1 === 'bigint',\n    is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),\n    eql: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.eql(c0, r0) && Fp.eql(c1, r1),\n    neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),\n    pow: (num, power) => mod.FpPow(Fp2, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),\n    // Normalized\n    add: Fp2Add,\n    sub: Fp2Subtract,\n    mul: Fp2Multiply,\n    sqr: Fp2Square,\n    // NonNormalized stuff\n    addN: Fp2Add,\n    subN: Fp2Subtract,\n    mulN: Fp2Multiply,\n    sqrN: Fp2Square,\n    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?\n    div: (lhs, rhs) =>\n      Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),\n    inv: ({ c0: a, c1: b }) => {\n      // We wish to find the multiplicative inverse of a nonzero\n      // element a + bu in Fp2. We leverage an identity\n      //\n      // (a + bu)(a - bu) = a\u00B2 + b\u00B2\n      //\n      // which holds because u\u00B2 = -1. This can be rewritten as\n      //\n      // (a + bu)(a - bu)/(a\u00B2 + b\u00B2) = 1\n      //\n      // because a\u00B2 + b\u00B2 = 0 has no nonzero solutions for (a, b).\n      // This gives that (a - bu)/(a\u00B2 + b\u00B2) is the inverse\n      // of (a + bu). Importantly, this can be computing using\n      // only a single inversion in Fp.\n      const factor = Fp.inv(Fp.create(a * a + b * b));\n      return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };\n    },\n    sqrt: (num) => {\n      if (opts.Fp2sqrt) return opts.Fp2sqrt(num);\n      // This is generic for all quadratic extensions (Fp2)\n      const { c0, c1 } = num;\n      if (Fp.is0(c1)) {\n        // if c0 is quadratic residue\n        if (mod.FpLegendre(Fp, c0) === 1) return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });\n        else return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, FpNONRESIDUE)) });\n      }\n      const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), FpNONRESIDUE)));\n      let d = Fp.mul(Fp.add(a, c0), Fpdiv2);\n      const legendre = mod.FpLegendre(Fp, d);\n      // -1, Quadratic non residue\n      if (legendre === -1) d = Fp.sub(d, a);\n      const a0 = Fp.sqrt(d);\n      const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, Fpdiv2), a0) });\n      if (!Fp2.eql(Fp2.sqr(candidateSqrt), num)) throw new Error('Cannot find square root');\n      // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num\n      const x1 = candidateSqrt;\n      const x2 = Fp2.neg(x1);\n      const { re: re1, im: im1 } = Fp2.reim(x1);\n      const { re: re2, im: im2 } = Fp2.reim(x2);\n      if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;\n      return x2;\n    },\n    // Same as sgn0_m_eq_2 in RFC 9380\n    isOdd: (x: Fp2) => {\n      const { re: x0, im: x1 } = Fp2.reim(x);\n      const sign_0 = x0 % _2n;\n      const zero_0 = x0 === _0n;\n      const sign_1 = x1 % _2n;\n      return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;\n    },\n    // Bytes util\n    fromBytes(b: Uint8Array): Fp2 {\n      if (b.length !== Fp2.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };\n    },\n    toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n      c0: Fp.cmov(c0, r0, c),\n      c1: Fp.cmov(c1, r1, c),\n    }),\n    reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),\n    // multiply by u + 1\n    mulByNonresidue: ({ c0, c1 }) => Fp2.mul({ c0, c1 }, Fp2Nonresidue),\n    mulByB: opts.Fp2mulByB,\n    fromBigTuple: Fp2fromBigTuple,\n    frobeniusMap: ({ c0, c1 }, power: number): Fp2 => ({\n      c0,\n      c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),\n    }),\n  };\n  // Fp6\n  const Fp6Add = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({\n    c0: Fp2.add(c0, r0),\n    c1: Fp2.add(c1, r1),\n    c2: Fp2.add(c2, r2),\n  });\n  const Fp6Subtract = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({\n    c0: Fp2.sub(c0, r0),\n    c1: Fp2.sub(c1, r1),\n    c2: Fp2.sub(c2, r2),\n  });\n  const Fp6Multiply = ({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) => {\n    if (typeof rhs === 'bigint') {\n      return {\n        c0: Fp2.mul(c0, rhs),\n        c1: Fp2.mul(c1, rhs),\n        c2: Fp2.mul(c2, rhs),\n      };\n    }\n    const { c0: r0, c1: r1, c2: r2 } = rhs;\n    const t0 = Fp2.mul(c0, r0); // c0 * o0\n    const t1 = Fp2.mul(c1, r1); // c1 * o1\n    const t2 = Fp2.mul(c2, r2); // c2 * o2\n    return {\n      // t0 + (c1 + c2) * (r1 * r2) - (T1 + T2) * (u + 1)\n      c0: Fp2.add(\n        t0,\n        Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), Fp2.add(r1, r2)), Fp2.add(t1, t2)))\n      ),\n      // (c0 + c1) * (r0 + r1) - (T0 + T1) + T2 * (u + 1)\n      c1: Fp2.add(\n        Fp2.sub(Fp2.mul(Fp2.add(c0, c1), Fp2.add(r0, r1)), Fp2.add(t0, t1)),\n        Fp2.mulByNonresidue(t2)\n      ),\n      // T1 + (c0 + c2) * (r0 + r2) - T0 + T2\n      c2: Fp2.sub(Fp2.add(t1, Fp2.mul(Fp2.add(c0, c2), Fp2.add(r0, r2))), Fp2.add(t0, t2)),\n    };\n  };\n  const Fp6Square = ({ c0, c1, c2 }: Fp6) => {\n    let t0 = Fp2.sqr(c0); // c0\u00B2\n    let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1\n    let t3 = Fp2.mul(Fp2.mul(c1, c2), _2n); // 2 * c1 * c2\n    let t4 = Fp2.sqr(c2); // c2\u00B2\n    return {\n      c0: Fp2.add(Fp2.mulByNonresidue(t3), t0), // T3 * (u + 1) + T0\n      c1: Fp2.add(Fp2.mulByNonresidue(t4), t1), // T4 * (u + 1) + T1\n      // T1 + (c0 - c1 + c2)\u00B2 + T3 - T0 - T4\n      c2: Fp2.sub(Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.sqr(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0), t4),\n    };\n  };\n  type Fp6Utils = {\n    fromBigSix: (tuple: BigintSix) => Fp6;\n    mulByNonresidue: (num: Fp6) => Fp6;\n    frobeniusMap(num: Fp6, power: number): Fp6;\n    mul1(num: Fp6, b1: Fp2): Fp6;\n    mul01(num: Fp6, b0: Fp2, b1: Fp2): Fp6;\n    mulByFp2(lhs: Fp6, rhs: Fp2): Fp6;\n  };\n\n  const [FP6_FROBENIUS_COEFFICIENTS_1, FP6_FROBENIUS_COEFFICIENTS_2] = calcFrobeniusCoefficients(\n    Fp2,\n    Fp2Nonresidue,\n    Fp.ORDER,\n    6,\n    2,\n    3\n  );\n\n  const Fp6: mod.IField<Fp6> & Fp6Utils = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    isLE: Fp2.isLE,\n    BITS: 3 * Fp2.BITS,\n    BYTES: 3 * Fp2.BYTES,\n    MASK: bitMask(3 * Fp2.BITS),\n    ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),\n    is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),\n    neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),\n    eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) =>\n      Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),\n    sqrt: notImplemented,\n    // Do we need division by bigint at all? Should be done via order:\n    div: (lhs, rhs) =>\n      Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp6, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),\n    // Normalized\n    add: Fp6Add,\n    sub: Fp6Subtract,\n    mul: Fp6Multiply,\n    sqr: Fp6Square,\n    // NonNormalized stuff\n    addN: Fp6Add,\n    subN: Fp6Subtract,\n    mulN: Fp6Multiply,\n    sqrN: Fp6Square,\n\n    inv: ({ c0, c1, c2 }) => {\n      let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0\u00B2 - c2 * c1 * (u + 1)\n      let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2\u00B2 * (u + 1) - c0 * c1\n      let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1\u00B2 - c0 * c2\n      // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)\n      let t4 = Fp2.inv(\n        Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0))\n      );\n      return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };\n    },\n    // Bytes utils\n    fromBytes: (b: Uint8Array): Fp6 => {\n      if (b.length !== Fp6.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return {\n        c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),\n        c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),\n        c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),\n      };\n    },\n    toBytes: ({ c0, c1, c2 }): Uint8Array =>\n      concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),\n    cmov: ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c) => ({\n      c0: Fp2.cmov(c0, r0, c),\n      c1: Fp2.cmov(c1, r1, c),\n      c2: Fp2.cmov(c2, r2, c),\n    }),\n    fromBigSix: (t: BigintSix): Fp6 => {\n      if (!Array.isArray(t) || t.length !== 6) throw new Error('invalid Fp6 usage');\n      return {\n        c0: Fp2.fromBigTuple(t.slice(0, 2)),\n        c1: Fp2.fromBigTuple(t.slice(2, 4)),\n        c2: Fp2.fromBigTuple(t.slice(4, 6)),\n      };\n    },\n    frobeniusMap: ({ c0, c1, c2 }, power: number) => ({\n      c0: Fp2.frobeniusMap(c0, power),\n      c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),\n      c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),\n    }),\n    mulByFp2: ({ c0, c1, c2 }, rhs: Fp2): Fp6 => ({\n      c0: Fp2.mul(c0, rhs),\n      c1: Fp2.mul(c1, rhs),\n      c2: Fp2.mul(c2, rhs),\n    }),\n    mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),\n    // Sparse multiplication\n    mul1: ({ c0, c1, c2 }, b1: Fp2): Fp6 => ({\n      c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),\n      c1: Fp2.mul(c0, b1),\n      c2: Fp2.mul(c1, b1),\n    }),\n    // Sparse multiplication\n    mul01({ c0, c1, c2 }, b0: Fp2, b1: Fp2): Fp6 {\n      let t0 = Fp2.mul(c0, b0); // c0 * b0\n      let t1 = Fp2.mul(c1, b1); // c1 * b1\n      return {\n        // ((c1 + c2) * b1 - T1) * (u + 1) + T0\n        c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),\n        // (b0 + b1) * (c0 + c1) - T0 - T1\n        c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),\n        // (c0 + c2) * b0 - T0 + T1\n        c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),\n      };\n    },\n  };\n\n  // Fp12\n  const FP12_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(\n    Fp2,\n    Fp2Nonresidue,\n    Fp.ORDER,\n    12,\n    1,\n    6\n  )[0];\n\n  const Fp12Add = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({\n    c0: Fp6.add(c0, r0),\n    c1: Fp6.add(c1, r1),\n  });\n  const Fp12Subtract = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({\n    c0: Fp6.sub(c0, r0),\n    c1: Fp6.sub(c1, r1),\n  });\n  const Fp12Multiply = ({ c0, c1 }: Fp12, rhs: Fp12 | bigint) => {\n    if (typeof rhs === 'bigint') return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };\n    let { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp6.mul(c0, r0); // c0 * r0\n    let t2 = Fp6.mul(c1, r1); // c1 * r1\n    return {\n      c0: Fp6.add(t1, Fp6.mulByNonresidue(t2)), // T1 + T2 * v\n      // (c0 + c1) * (r0 + r1) - (T1 + T2)\n      c1: Fp6.sub(Fp6.mul(Fp6.add(c0, c1), Fp6.add(r0, r1)), Fp6.add(t1, t2)),\n    };\n  };\n  const Fp12Square = ({ c0, c1 }: Fp12) => {\n    let ab = Fp6.mul(c0, c1); // c0 * c1\n    return {\n      // (c1 * v + c0) * (c0 + c1) - AB - AB * v\n      c0: Fp6.sub(\n        Fp6.sub(Fp6.mul(Fp6.add(Fp6.mulByNonresidue(c1), c0), Fp6.add(c0, c1)), ab),\n        Fp6.mulByNonresidue(ab)\n      ),\n      c1: Fp6.add(ab, ab),\n    }; // AB + AB\n  };\n  function Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } {\n    const a2 = Fp2.sqr(a);\n    const b2 = Fp2.sqr(b);\n    return {\n      first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b\u00B2 * Nonresidue + a\u00B2\n      second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)\u00B2 - a\u00B2 - b\u00B2\n    };\n  }\n  type Fp12Utils = {\n    fromBigTwelve: (t: BigintTwelve) => Fp12;\n    frobeniusMap(num: Fp12, power: number): Fp12;\n    mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n    mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n    mulByFp2(lhs: Fp12, rhs: Fp2): Fp12;\n    conjugate(num: Fp12): Fp12;\n    finalExponentiate(num: Fp12): Fp12;\n    _cyclotomicSquare(num: Fp12): Fp12;\n    _cyclotomicExp(num: Fp12, n: bigint): Fp12;\n  };\n\n  const Fp12: mod.IField<Fp12> & Fp12Utils = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    isLE: Fp6.isLE,\n    BITS: 2 * Fp6.BITS,\n    BYTES: 2 * Fp6.BYTES,\n    MASK: bitMask(2 * Fp6.BITS),\n    ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },\n    ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),\n    is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),\n    neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),\n    eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),\n    sqrt: notImplemented,\n    inv: ({ c0, c1 }) => {\n      let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0\u00B2 - c1\u00B2 * v)\n      return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w\n    },\n    div: (lhs, rhs) =>\n      Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp12, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),\n    // Normalized\n    add: Fp12Add,\n    sub: Fp12Subtract,\n    mul: Fp12Multiply,\n    sqr: Fp12Square,\n    // NonNormalized stuff\n    addN: Fp12Add,\n    subN: Fp12Subtract,\n    mulN: Fp12Multiply,\n    sqrN: Fp12Square,\n\n    // Bytes utils\n    fromBytes: (b: Uint8Array): Fp12 => {\n      if (b.length !== Fp12.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return {\n        c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),\n        c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),\n      };\n    },\n    toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n      c0: Fp6.cmov(c0, r0, c),\n      c1: Fp6.cmov(c1, r1, c),\n    }),\n    // Utils\n    // toString() {\n    //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');\n    // },\n    // fromTuple(c: [Fp6, Fp6]) {\n    //   return new Fp12(...c);\n    // }\n    fromBigTwelve: (t: BigintTwelve): Fp12 => ({\n      c0: Fp6.fromBigSix(t.slice(0, 6) as BigintSix),\n      c1: Fp6.fromBigSix(t.slice(6, 12) as BigintSix),\n    }),\n    // Raises to q**i -th power\n    frobeniusMap(lhs, power: number) {\n      const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);\n      const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];\n      return {\n        c0: Fp6.frobeniusMap(lhs.c0, power),\n        c1: Fp6.create({\n          c0: Fp2.mul(c0, coeff),\n          c1: Fp2.mul(c1, coeff),\n          c2: Fp2.mul(c2, coeff),\n        }),\n      };\n    },\n    mulByFp2: ({ c0, c1 }, rhs: Fp2): Fp12 => ({\n      c0: Fp6.mulByFp2(c0, rhs),\n      c1: Fp6.mulByFp2(c1, rhs),\n    }),\n    conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.neg(c1) }),\n    // Sparse multiplication\n    mul014: ({ c0, c1 }, o0: Fp2, o1: Fp2, o4: Fp2) => {\n      let t0 = Fp6.mul01(c0, o0, o1);\n      let t1 = Fp6.mul1(c1, o4);\n      return {\n        c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0\n        // (c1 + c0) * [o0, o1+o4] - T0 - T1\n        c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),\n      };\n    },\n    mul034: ({ c0, c1 }, o0: Fp2, o3: Fp2, o4: Fp2) => {\n      const a = Fp6.create({\n        c0: Fp2.mul(c0.c0, o0),\n        c1: Fp2.mul(c0.c1, o0),\n        c2: Fp2.mul(c0.c2, o0),\n      });\n      const b = Fp6.mul01(c1, o3, o4);\n      const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);\n      return {\n        c0: Fp6.add(Fp6.mulByNonresidue(b), a),\n        c1: Fp6.sub(e, Fp6.add(a, b)),\n      };\n    },\n\n    // A cyclotomic group is a subgroup of Fp^n defined by\n    //   G\u03A6\u2099(p) = {\u03B1 \u2208 Fp\u207F : \u03B1^\u03A6\u2099(p) = 1}\n    // The result of any pairing is in a cyclotomic subgroup\n    // https://eprint.iacr.org/2009/565.pdf\n    _cyclotomicSquare: opts.Fp12cyclotomicSquare,\n    _cyclotomicExp: opts.Fp12cyclotomicExp,\n    // https://eprint.iacr.org/2010/354.pdf\n    // https://eprint.iacr.org/2009/565.pdf\n    finalExponentiate: opts.Fp12finalExponentiate,\n  };\n\n  return { Fp, Fp2, Fp6, Fp4Square, Fp12 };\n}\n", "/**\n * Internal helpers for u64. BigUint64Array is too slow as per 2025, so we implement it using Uint32Array.\n * @todo re-check https://issues.chromium.org/issues/42212588\n * @module\n */\nconst U32_MASK64 = /* @__PURE__ */ BigInt(2 ** 32 - 1);\nconst _32n = /* @__PURE__ */ BigInt(32);\n\nfunction fromBig(\n  n: bigint,\n  le = false\n): {\n  h: number;\n  l: number;\n} {\n  if (le) return { h: Number(n & U32_MASK64), l: Number((n >> _32n) & U32_MASK64) };\n  return { h: Number((n >> _32n) & U32_MASK64) | 0, l: Number(n & U32_MASK64) | 0 };\n}\n\nfunction split(lst: bigint[], le = false): Uint32Array[] {\n  const len = lst.length;\n  let Ah = new Uint32Array(len);\n  let Al = new Uint32Array(len);\n  for (let i = 0; i < len; i++) {\n    const { h, l } = fromBig(lst[i], le);\n    [Ah[i], Al[i]] = [h, l];\n  }\n  return [Ah, Al];\n}\n\nconst toBig = (h: number, l: number): bigint => (BigInt(h >>> 0) << _32n) | BigInt(l >>> 0);\n// for Shift in [0, 32)\nconst shrSH = (h: number, _l: number, s: number): number => h >>> s;\nconst shrSL = (h: number, l: number, s: number): number => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in [1, 32)\nconst rotrSH = (h: number, l: number, s: number): number => (h >>> s) | (l << (32 - s));\nconst rotrSL = (h: number, l: number, s: number): number => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotrBH = (h: number, l: number, s: number): number => (h << (64 - s)) | (l >>> (s - 32));\nconst rotrBL = (h: number, l: number, s: number): number => (h >>> (s - 32)) | (l << (64 - s));\n// Right rotate for shift===32 (just swaps l&h)\nconst rotr32H = (_h: number, l: number): number => l;\nconst rotr32L = (h: number, _l: number): number => h;\n// Left rotate for Shift in [1, 32)\nconst rotlSH = (h: number, l: number, s: number): number => (h << s) | (l >>> (32 - s));\nconst rotlSL = (h: number, l: number, s: number): number => (l << s) | (h >>> (32 - s));\n// Left rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotlBH = (h: number, l: number, s: number): number => (l << (s - 32)) | (h >>> (64 - s));\nconst rotlBL = (h: number, l: number, s: number): number => (h << (s - 32)) | (l >>> (64 - s));\n\n// JS uses 32-bit signed integers for bitwise operations which means we cannot\n// simple take carry out of low bit sum by shift, we need to use division.\nfunction add(\n  Ah: number,\n  Al: number,\n  Bh: number,\n  Bl: number\n): {\n  h: number;\n  l: number;\n} {\n  const l = (Al >>> 0) + (Bl >>> 0);\n  return { h: (Ah + Bh + ((l / 2 ** 32) | 0)) | 0, l: l | 0 };\n}\n// Addition with more than 2 elements\nconst add3L = (Al: number, Bl: number, Cl: number): number => (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0);\nconst add3H = (low: number, Ah: number, Bh: number, Ch: number): number =>\n  (Ah + Bh + Ch + ((low / 2 ** 32) | 0)) | 0;\nconst add4L = (Al: number, Bl: number, Cl: number, Dl: number): number =>\n  (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0);\nconst add4H = (low: number, Ah: number, Bh: number, Ch: number, Dh: number): number =>\n  (Ah + Bh + Ch + Dh + ((low / 2 ** 32) | 0)) | 0;\nconst add5L = (Al: number, Bl: number, Cl: number, Dl: number, El: number): number =>\n  (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0) + (El >>> 0);\nconst add5H = (low: number, Ah: number, Bh: number, Ch: number, Dh: number, Eh: number): number =>\n  (Ah + Bh + Ch + Dh + Eh + ((low / 2 ** 32) | 0)) | 0;\n\n// prettier-ignore\nexport {\n  add, add3H, add3L, add4H, add4L, add5H, add5L, fromBig, rotlBH, rotlBL, rotlSH, rotlSL, rotr32H, rotr32L, rotrBH, rotrBL, rotrSH, rotrSL, shrSH, shrSL, split, toBig\n};\n// prettier-ignore\nconst u64: { fromBig: typeof fromBig; split: typeof split; toBig: (h: number, l: number) => bigint; shrSH: (h: number, _l: number, s: number) => number; shrSL: (h: number, l: number, s: number) => number; rotrSH: (h: number, l: number, s: number) => number; rotrSL: (h: number, l: number, s: number) => number; rotrBH: (h: number, l: number, s: number) => number; rotrBL: (h: number, l: number, s: number) => number; rotr32H: (_h: number, l: number) => number; rotr32L: (h: number, _l: number) => number; rotlSH: (h: number, l: number, s: number) => number; rotlSL: (h: number, l: number, s: number) => number; rotlBH: (h: number, l: number, s: number) => number; rotlBL: (h: number, l: number, s: number) => number; add: typeof add; add3L: (Al: number, Bl: number, Cl: number) => number; add3H: (low: number, Ah: number, Bh: number, Ch: number) => number; add4L: (Al: number, Bl: number, Cl: number, Dl: number) => number; add4H: (low: number, Ah: number, Bh: number, Ch: number, Dh: number) => number; add5H: (low: number, Ah: number, Bh: number, Ch: number, Dh: number, Eh: number) => number; add5L: (Al: number, Bl: number, Cl: number, Dl: number, El: number) => number; } = {\n  fromBig, split, toBig,\n  shrSH, shrSL,\n  rotrSH, rotrSL, rotrBH, rotrBL,\n  rotr32H, rotr32L,\n  rotlSH, rotlSL, rotlBH, rotlBL,\n  add, add3L, add3H, add4L, add4H, add5H, add5L,\n};\nexport default u64;\n", "/**\n * SHA3 (keccak) hash function, based on a new \"Sponge function\" design.\n * Different from older hashes, the internal state is bigger than output size.\n *\n * Check out [FIPS-202](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf),\n * [Website](https://keccak.team/keccak.html),\n * [the differences between SHA-3 and Keccak](https://crypto.stackexchange.com/questions/15727/what-are-the-key-differences-between-the-draft-sha-3-standard-and-the-keccak-sub).\n *\n * Check out `sha3-addons` module for cSHAKE, k12, and others.\n * @module\n */\nimport { rotlBH, rotlBL, rotlSH, rotlSL, split } from './_u64.ts';\n// prettier-ignore\nimport {\n  abytes, aexists, anumber, aoutput,\n  clean, createHasher, createXOFer, Hash,\n  swap32IfBE,\n  toBytes, u32,\n  type CHash, type CHashXO, type HashXOF, type Input\n} from './utils.ts';\n\n// No __PURE__ annotations in sha3 header:\n// EVERYTHING is in fact used on every export.\n// Various per round constants calculations\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\nconst _2n = BigInt(2);\nconst _7n = BigInt(7);\nconst _256n = BigInt(256);\nconst _0x71n = BigInt(0x71);\nconst SHA3_PI: number[] = [];\nconst SHA3_ROTL: number[] = [];\nconst _SHA3_IOTA: bigint[] = [];\nfor (let round = 0, R = _1n, x = 1, y = 0; round < 24; round++) {\n  // Pi\n  [x, y] = [y, (2 * x + 3 * y) % 5];\n  SHA3_PI.push(2 * (5 * y + x));\n  // Rotational\n  SHA3_ROTL.push((((round + 1) * (round + 2)) / 2) % 64);\n  // Iota\n  let t = _0n;\n  for (let j = 0; j < 7; j++) {\n    R = ((R << _1n) ^ ((R >> _7n) * _0x71n)) % _256n;\n    if (R & _2n) t ^= _1n << ((_1n << /* @__PURE__ */ BigInt(j)) - _1n);\n  }\n  _SHA3_IOTA.push(t);\n}\nconst IOTAS = split(_SHA3_IOTA, true);\nconst SHA3_IOTA_H = IOTAS[0];\nconst SHA3_IOTA_L = IOTAS[1];\n\n// Left rotation (without 0, 32, 64)\nconst rotlH = (h: number, l: number, s: number) => (s > 32 ? rotlBH(h, l, s) : rotlSH(h, l, s));\nconst rotlL = (h: number, l: number, s: number) => (s > 32 ? rotlBL(h, l, s) : rotlSL(h, l, s));\n\n/** `keccakf1600` internal function, additionally allows to adjust round count. */\nexport function keccakP(s: Uint32Array, rounds: number = 24): void {\n  const B = new Uint32Array(5 * 2);\n  // NOTE: all indices are x2 since we store state as u32 instead of u64 (bigints to slow in js)\n  for (let round = 24 - rounds; round < 24; round++) {\n    // Theta \u03B8\n    for (let x = 0; x < 10; x++) B[x] = s[x] ^ s[x + 10] ^ s[x + 20] ^ s[x + 30] ^ s[x + 40];\n    for (let x = 0; x < 10; x += 2) {\n      const idx1 = (x + 8) % 10;\n      const idx0 = (x + 2) % 10;\n      const B0 = B[idx0];\n      const B1 = B[idx0 + 1];\n      const Th = rotlH(B0, B1, 1) ^ B[idx1];\n      const Tl = rotlL(B0, B1, 1) ^ B[idx1 + 1];\n      for (let y = 0; y < 50; y += 10) {\n        s[x + y] ^= Th;\n        s[x + y + 1] ^= Tl;\n      }\n    }\n    // Rho (\u03C1) and Pi (\u03C0)\n    let curH = s[2];\n    let curL = s[3];\n    for (let t = 0; t < 24; t++) {\n      const shift = SHA3_ROTL[t];\n      const Th = rotlH(curH, curL, shift);\n      const Tl = rotlL(curH, curL, shift);\n      const PI = SHA3_PI[t];\n      curH = s[PI];\n      curL = s[PI + 1];\n      s[PI] = Th;\n      s[PI + 1] = Tl;\n    }\n    // Chi (\u03C7)\n    for (let y = 0; y < 50; y += 10) {\n      for (let x = 0; x < 10; x++) B[x] = s[y + x];\n      for (let x = 0; x < 10; x++) s[y + x] ^= ~B[(x + 2) % 10] & B[(x + 4) % 10];\n    }\n    // Iota (\u03B9)\n    s[0] ^= SHA3_IOTA_H[round];\n    s[1] ^= SHA3_IOTA_L[round];\n  }\n  clean(B);\n}\n\n/** Keccak sponge function. */\nexport class Keccak extends Hash<Keccak> implements HashXOF<Keccak> {\n  protected state: Uint8Array;\n  protected pos = 0;\n  protected posOut = 0;\n  protected finished = false;\n  protected state32: Uint32Array;\n  protected destroyed = false;\n\n  public blockLen: number;\n  public suffix: number;\n  public outputLen: number;\n  protected enableXOF = false;\n  protected rounds: number;\n\n  // NOTE: we accept arguments in bytes instead of bits here.\n  constructor(\n    blockLen: number,\n    suffix: number,\n    outputLen: number,\n    enableXOF = false,\n    rounds: number = 24\n  ) {\n    super();\n    this.blockLen = blockLen;\n    this.suffix = suffix;\n    this.outputLen = outputLen;\n    this.enableXOF = enableXOF;\n    this.rounds = rounds;\n    // Can be passed from user as dkLen\n    anumber(outputLen);\n    // 1600 = 5x5 matrix of 64bit.  1600 bits === 200 bytes\n    // 0 < blockLen < 200\n    if (!(0 < blockLen && blockLen < 200))\n      throw new Error('only keccak-f1600 function is supported');\n    this.state = new Uint8Array(200);\n    this.state32 = u32(this.state);\n  }\n  clone(): Keccak {\n    return this._cloneInto();\n  }\n  protected keccak(): void {\n    swap32IfBE(this.state32);\n    keccakP(this.state32, this.rounds);\n    swap32IfBE(this.state32);\n    this.posOut = 0;\n    this.pos = 0;\n  }\n  update(data: Input): this {\n    aexists(this);\n    data = toBytes(data);\n    abytes(data);\n    const { blockLen, state } = this;\n    const len = data.length;\n    for (let pos = 0; pos < len; ) {\n      const take = Math.min(blockLen - this.pos, len - pos);\n      for (let i = 0; i < take; i++) state[this.pos++] ^= data[pos++];\n      if (this.pos === blockLen) this.keccak();\n    }\n    return this;\n  }\n  protected finish(): void {\n    if (this.finished) return;\n    this.finished = true;\n    const { state, suffix, pos, blockLen } = this;\n    // Do the padding\n    state[pos] ^= suffix;\n    if ((suffix & 0x80) !== 0 && pos === blockLen - 1) this.keccak();\n    state[blockLen - 1] ^= 0x80;\n    this.keccak();\n  }\n  protected writeInto(out: Uint8Array): Uint8Array {\n    aexists(this, false);\n    abytes(out);\n    this.finish();\n    const bufferOut = this.state;\n    const { blockLen } = this;\n    for (let pos = 0, len = out.length; pos < len; ) {\n      if (this.posOut >= blockLen) this.keccak();\n      const take = Math.min(blockLen - this.posOut, len - pos);\n      out.set(bufferOut.subarray(this.posOut, this.posOut + take), pos);\n      this.posOut += take;\n      pos += take;\n    }\n    return out;\n  }\n  xofInto(out: Uint8Array): Uint8Array {\n    // Sha3/Keccak usage with XOF is probably mistake, only SHAKE instances can do XOF\n    if (!this.enableXOF) throw new Error('XOF is not possible for this instance');\n    return this.writeInto(out);\n  }\n  xof(bytes: number): Uint8Array {\n    anumber(bytes);\n    return this.xofInto(new Uint8Array(bytes));\n  }\n  digestInto(out: Uint8Array): Uint8Array {\n    aoutput(out, this);\n    if (this.finished) throw new Error('digest() was already called');\n    this.writeInto(out);\n    this.destroy();\n    return out;\n  }\n  digest(): Uint8Array {\n    return this.digestInto(new Uint8Array(this.outputLen));\n  }\n  destroy(): void {\n    this.destroyed = true;\n    clean(this.state);\n  }\n  _cloneInto(to?: Keccak): Keccak {\n    const { blockLen, suffix, outputLen, rounds, enableXOF } = this;\n    to ||= new Keccak(blockLen, suffix, outputLen, enableXOF, rounds);\n    to.state32.set(this.state32);\n    to.pos = this.pos;\n    to.posOut = this.posOut;\n    to.finished = this.finished;\n    to.rounds = rounds;\n    // Suffix can change in cSHAKE\n    to.suffix = suffix;\n    to.outputLen = outputLen;\n    to.enableXOF = enableXOF;\n    to.destroyed = this.destroyed;\n    return to;\n  }\n}\n\nconst gen = (suffix: number, blockLen: number, outputLen: number) =>\n  createHasher(() => new Keccak(blockLen, suffix, outputLen));\n\n/** SHA3-224 hash function. */\nexport const sha3_224: CHash = /* @__PURE__ */ (() => gen(0x06, 144, 224 / 8))();\n/** SHA3-256 hash function. Different from keccak-256. */\nexport const sha3_256: CHash = /* @__PURE__ */ (() => gen(0x06, 136, 256 / 8))();\n/** SHA3-384 hash function. */\nexport const sha3_384: CHash = /* @__PURE__ */ (() => gen(0x06, 104, 384 / 8))();\n/** SHA3-512 hash function. */\nexport const sha3_512: CHash = /* @__PURE__ */ (() => gen(0x06, 72, 512 / 8))();\n\n/** keccak-224 hash function. */\nexport const keccak_224: CHash = /* @__PURE__ */ (() => gen(0x01, 144, 224 / 8))();\n/** keccak-256 hash function. Different from SHA3-256. */\nexport const keccak_256: CHash = /* @__PURE__ */ (() => gen(0x01, 136, 256 / 8))();\n/** keccak-384 hash function. */\nexport const keccak_384: CHash = /* @__PURE__ */ (() => gen(0x01, 104, 384 / 8))();\n/** keccak-512 hash function. */\nexport const keccak_512: CHash = /* @__PURE__ */ (() => gen(0x01, 72, 512 / 8))();\n\nexport type ShakeOpts = { dkLen?: number };\n\nconst genShake = (suffix: number, blockLen: number, outputLen: number) =>\n  createXOFer<HashXOF<Keccak>, ShakeOpts>(\n    (opts: ShakeOpts = {}) =>\n      new Keccak(blockLen, suffix, opts.dkLen === undefined ? outputLen : opts.dkLen, true)\n  );\n\n/** SHAKE128 XOF with 128-bit security. */\nexport const shake128: CHashXO = /* @__PURE__ */ (() => genShake(0x1f, 168, 128 / 8))();\n/** SHAKE256 XOF with 256-bit security. */\nexport const shake256: CHashXO = /* @__PURE__ */ (() => genShake(0x1f, 136, 256 / 8))();\n", "\"use strict\";\nvar __createBinding = (this && this.__createBinding) || (Object.create ? (function(o, m, k, k2) {\n    if (k2 === undefined) k2 = k;\n    var desc = Object.getOwnPropertyDescriptor(m, k);\n    if (!desc || (\"get\" in desc ? !m.__esModule : desc.writable || desc.configurable)) {\n      desc = { enumerable: true, get: function() { return m[k]; } };\n    }\n    Object.defineProperty(o, k2, desc);\n}) : (function(o, m, k, k2) {\n    if (k2 === undefined) k2 = k;\n    o[k2] = m[k];\n}));\nvar __setModuleDefault = (this && this.__setModuleDefault) || (Object.create ? (function(o, v) {\n    Object.defineProperty(o, \"default\", { enumerable: true, value: v });\n}) : function(o, v) {\n    o[\"default\"] = v;\n});\nvar __importStar = (this && this.__importStar) || function (mod) {\n    if (mod && mod.__esModule) return mod;\n    var result = {};\n    if (mod != null) for (var k in mod) if (k !== \"default\" && Object.prototype.hasOwnProperty.call(mod, k)) __createBinding(result, mod, k);\n    __setModuleDefault(result, mod);\n    return result;\n};\nObject.defineProperty(exports, \"__esModule\", { value: true });\nexports.bn254 = void 0;\nexports.mapToCurveSVDW = mapToCurveSVDW;\nconst utils_1 = require(\"@noble/hashes/utils\");\nconst bls_1 = require(\"@noble/curves/abstract/bls\");\nconst modular_1 = require(\"@noble/curves/abstract/modular\");\nconst utils_2 = require(\"@noble/curves/abstract/utils\");\nconst tower_1 = require(\"@noble/curves/abstract/tower\");\nconst mod = __importStar(require(\"@noble/curves/abstract/modular\"));\nconst sha3_1 = require(\"@noble/hashes/sha3\");\nconst utils_3 = require(\"@noble/curves/abstract/utils\");\n/*\nbn254, previously known as alt_bn_128, when it had 128-bit security.\nBarbulescu-Duquesne 2017 shown it's weaker: just about 100 bits,\nso the naming has been adjusted to its prime bit count:\nhttps://hal.science/hal-01534101/file/main.pdf\n\nThere are huge compatibility issues in the ecosystem:\n\n1. Different libraries call it in different ways: \"bn254\", \"bn256\", \"alt_bn128\", \"bn128\".\n2. libff has bn128, but it's a different curve with different G2:\n   https://github.com/scipr-lab/libff/blob/a44f482e18b8ac04d034c193bd9d7df7817ad73f/libff/algebra/curves/bn128/bn128_init.cpp#L166-L169\n3. halo2curves bn256 is also incompatible and returns different outputs\n\nThe goal of our implementation is to support \"Ethereum\" variant of the curve,\nbecause it at least has specs:\n\n- EIP196 (https://eips.ethereum.org/EIPS/eip-196) describes bn254 ECADD and ECMUL opcodes for EVM\n- EIP197 (https://eips.ethereum.org/EIPS/eip-197) describes bn254 pairings\n- It's hard: EIPs don't have proper tests. EIP-197 returns boolean output instead of Fp12\n- The existing implementations are bad. Some are deprecated:\n    - https://github.com/paritytech/bn (old version)\n    - https://github.com/ewasm/ethereum-bn128.rs (uses paritytech/bn)\n    - https://github.com/zcash-hackworks/bn\n    - https://github.com/arkworks-rs/curves/blob/master/bn254/src/lib.rs\n- Python implementations use different towers and produce different Fp12 outputs:\n    - https://github.com/ethereum/py_pairing\n    - https://github.com/ethereum/execution-specs/blob/master/src/ethereum/crypto/alt_bn128.py\n- Points are encoded differently in different implementations\n*/\n// prettier-ignore\nconst _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n// prettier-ignore\nconst _6n = BigInt(6);\n/*\nSeed (X): 4965661367192848881\nFr: (36x\u2074+36x\u00B3+18x\u00B2+6x+1)\nFp: (36x\u2074+36x\u00B3+24x\u00B2+6x+1)\n(E  / Fp ): Y\u00B2 = X\u00B3+3\n(Et / Fp\u00B2): Y\u00B2 = X\u00B3+3/(u+9) (D-type twist)\nAte loop size: 6x+2\n\nTowers:\n- Fp\u00B2[u] = Fp/u\u00B2+1\n- Fp\u2076[v] = Fp\u00B2/v\u00B3-9-u\n- Fp\u00B9\u00B2[w] = Fp\u2076/w\u00B2-v\n*/\nconst BN_X = BigInt('4965661367192848881');\nconst BN_X_LEN = (0, utils_2.bitLen)(BN_X);\nconst SIX_X_SQUARED = _6n * BN_X ** _2n;\n// Finite field over r. It's for convenience and is not used in the code below.\nconst Fr = (0, modular_1.Field)(BigInt('21888242871839275222246405745257275088548364400416034343698204186575808495617'));\n// Fp2.div(Fp2.mul(Fp2.ONE, _3n), Fp2.NONRESIDUE)\nconst Fp2B = {\n    c0: BigInt('19485874751759354771024239261021720505790618469301721065564631296452457478373'),\n    c1: BigInt('266929791119991161246907387137283842545076965332900288569378510910307636690'),\n};\nconst { Fp, Fp2, Fp6, Fp4Square, Fp12 } = (0, tower_1.tower12)({\n    ORDER: BigInt('21888242871839275222246405745257275088696311157297823662689037894645226208583'),\n    FP2_NONRESIDUE: [BigInt(9), _1n],\n    Fp2mulByB: (num) => Fp2.mul(num, Fp2B),\n    // The result of any pairing is in a cyclotomic subgroup\n    // https://eprint.iacr.org/2009/565.pdf\n    Fp12cyclotomicSquare: ({ c0, c1 }) => {\n        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;\n        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;\n        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);\n        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);\n        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);\n        let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)\n        return {\n            c0: Fp6.create({\n                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3\n                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5\n                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),\n            }), // 2 * (T7 - c0c2)  + T7\n            c1: Fp6.create({\n                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9\n                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4\n                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),\n            }),\n        }; // 2 * (T6 + c1c2) + T6\n    },\n    Fp12cyclotomicExp(num, n) {\n        let z = Fp12.ONE;\n        for (let i = BN_X_LEN - 1; i >= 0; i--) {\n            z = Fp12._cyclotomicSquare(z);\n            if ((0, utils_2.bitGet)(n, i))\n                z = Fp12.mul(z, num);\n        }\n        return z;\n    },\n    // https://eprint.iacr.org/2010/354.pdf\n    // https://eprint.iacr.org/2009/565.pdf\n    Fp12finalExponentiate: (num) => {\n        const powMinusX = (num) => Fp12.conjugate(Fp12._cyclotomicExp(num, BN_X));\n        const r0 = Fp12.mul(Fp12.conjugate(num), Fp12.inv(num));\n        const r = Fp12.mul(Fp12.frobeniusMap(r0, 2), r0);\n        const y1 = Fp12._cyclotomicSquare(powMinusX(r));\n        const y2 = Fp12.mul(Fp12._cyclotomicSquare(y1), y1);\n        const y4 = powMinusX(y2);\n        const y6 = powMinusX(Fp12._cyclotomicSquare(y4));\n        const y8 = Fp12.mul(Fp12.mul(Fp12.conjugate(y6), y4), Fp12.conjugate(y2));\n        const y9 = Fp12.mul(y8, y1);\n        return Fp12.mul(Fp12.frobeniusMap(Fp12.mul(Fp12.conjugate(r), y9), 3), Fp12.mul(Fp12.frobeniusMap(y8, 2), Fp12.mul(Fp12.frobeniusMap(y9, 1), Fp12.mul(Fp12.mul(y8, y4), r))));\n    },\n});\n// END OF CURVE FIELDS\nconst { G2psi, psi } = (0, tower_1.psiFrobenius)(Fp, Fp2, Fp2.NONRESIDUE);\n///////////////////////////////////////////////////////////////////////////////\n/// BEGIN DRAND MODIFICATIONS /////////////////////////////////////////////////\n///////////////////////////////////////////////////////////////////////////////\nfunction SVDWFpIsSquare(Fp) {\n    // Compute the Legendre symbol to determine if `u` is a quadratic residue\n    return (u) => {\n        const x = Fp.pow(u, (Fp.ORDER - 1n) / 2n);\n        let legendre;\n        if (Fp.eql(x, Fp.neg(Fp.ONE))) {\n            legendre = -1n;\n        }\n        else if (Fp.eql(x, Fp.ZERO)) {\n            legendre = 0n;\n        }\n        else if (Fp.eql(x, Fp.ONE)) {\n            legendre = 1n;\n        }\n        else {\n            throw new Error('Legendre failed');\n        }\n        return legendre === 1n;\n    };\n}\n/**\n * Shallue-van de Woestijne (SVDW) map-to-curve (\"straight-line\" implementation)\n * https://datatracker.ietf.org/doc/html/rfc9380/#appendix-F.1\n */\nfunction mapToCurveSVDW(Fp, opts) {\n    mod.validateField(Fp);\n    if (!Fp.isValid(opts.A) || !Fp.isValid(opts.B) || !Fp.isValid(opts.Z))\n        throw new Error('mapToCurveSimpleSVDW: invalid opts');\n    const isSquare = SVDWFpIsSquare(Fp);\n    if (!Fp.isOdd)\n        throw new Error('Fp.isOdd is not implemented!');\n    // g(x) is the short Weierstrass equation of the curve g(x) = x^3 + A*x + B\n    const g = (x) => Fp.add(Fp.add(Fp.mul(Fp.mul(x, x), x), Fp.mul(opts.A, x)), opts.B);\n    const two = Fp.add(Fp.ONE, Fp.ONE);\n    const three = Fp.add(two, Fp.ONE);\n    const four = Fp.add(three, Fp.ONE);\n    // C1 = g(Z) where g(x) = x^3 + A*x + B\n    const c1 = g(opts.Z);\n    // C2 = -Z / 2\n    const c2 = Fp.mul(Fp.neg(opts.Z), Fp.inv(Fp.add(Fp.ONE, Fp.ONE)));\n    // C3 = sqrt(-g(Z) * (3 * Z^2 + 4 * A))\n    const c3 = Fp.sqrt(Fp.mul(Fp.neg(c1), Fp.add(Fp.mul(three, Fp.mul(opts.Z, opts.Z)), Fp.mul(four, opts.A))));\n    // C4 = 4 * -g(Z) / (3 * Z^2 + 4 * A)\n    const c4 = Fp.mul(Fp.mul(four, Fp.neg(c1)), Fp.inv(Fp.add(Fp.mul(three, Fp.mul(opts.Z, opts.Z)), Fp.mul(four, opts.A))));\n    // Input: u, an element of F.\n    // Output: (x, y), a point on E.\n    return (u) => {\n        // prettier-ignore\n        let tv1, tv2, tv3, tv4, x1, gx1, e1, x2, gx2, e2, x3, x, gx, y, e3;\n        tv1 = Fp.mul(u, u);\n        tv1 = Fp.mul(tv1, c1);\n        tv2 = Fp.add(Fp.ONE, tv1);\n        tv1 = Fp.sub(Fp.ONE, tv1);\n        tv3 = Fp.mul(tv1, tv2);\n        tv3 = Fp.inv(tv3);\n        tv4 = Fp.mul(u, tv1);\n        tv4 = Fp.mul(tv4, tv3);\n        tv4 = Fp.mul(tv4, c3);\n        x1 = Fp.sub(c2, tv4);\n        gx1 = Fp.mul(x1, x1);\n        gx1 = Fp.add(gx1, opts.A);\n        gx1 = Fp.mul(gx1, x1);\n        gx1 = Fp.add(gx1, opts.B);\n        e1 = isSquare(gx1);\n        x2 = Fp.add(c2, tv4);\n        gx2 = Fp.mul(x2, x2);\n        gx2 = Fp.add(gx2, opts.A);\n        gx2 = Fp.mul(gx2, x2);\n        gx2 = Fp.add(gx2, opts.B);\n        e2 = isSquare(gx2) && !e1;\n        x3 = Fp.mul(tv2, tv2);\n        x3 = Fp.mul(x3, tv3);\n        x3 = Fp.mul(x3, x3);\n        x3 = Fp.mul(x3, c4);\n        x3 = Fp.add(x3, opts.Z);\n        x = Fp.cmov(x3, x1, !!e1);\n        x = Fp.cmov(x, x2, !!e2);\n        gx = Fp.mul(x, x);\n        gx = Fp.add(gx, opts.A);\n        gx = Fp.mul(gx, x);\n        gx = Fp.add(gx, opts.B);\n        y = Fp.sqrt(gx);\n        e3 = Fp.isOdd(u) === Fp.isOdd(y);\n        y = Fp.cmov(Fp.neg(y), y, e3);\n        return { x, y };\n    };\n}\nconst G1_SVDW = mapToCurveSVDW(Fp, {\n    A: Fp.ZERO,\n    B: _3n,\n    Z: Fp.ONE,\n});\nconst mapToCurveG1 = (scalars) => G1_SVDW(scalars[0]);\n/*\nHash-to-curve & signatures implemented to drand evmnet specs.\n- Uses SVDW, test vectors generated using Sage reference implementation\n- Signatures on G1 only\n- No support for compressed points\n- Uses keccak256 for hashing\n*/\nconst drandHtf = Object.freeze({\n    // DST: a domain separation tag\n    // defined in section 2.2.5\n    // Use utils.getDSTLabel(), utils.setDSTLabel(value)\n    DST: 'BLS_SIG_BN254G1_XMD:KECCAK-256_SVDW_RO_NUL_',\n    encodeDST: 'BLS_SIG_BN254G1_XMD:KECCAK-256_SVDW_RO_NUL_',\n    // p: the characteristic of F\n    //    where F is a finite field of characteristic p and order q = p^m\n    p: Fp.ORDER,\n    // m: the extension degree of F, m >= 1\n    //     where F is a finite field of characteristic p and order q = p^m\n    m: 1,\n    // k: the target security level for the suite in bits\n    // defined in section 5.1\n    k: 128,\n    // option to use a message that has already been processed by\n    // expand_message_xmd\n    expand: 'xmd',\n    // NB: We use keccak_256 to hash-to-curve for bn254 drand, as it is the\n    // cheapest hash function in the EVM.\n    hash: sha3_1.keccak_256,\n});\n/**\n * bn254 (a.k.a. alt_bn128) pairing-friendly curve.\n * Contains G1 / G2 operations and pairings.\n */\nexports.bn254 = (0, bls_1.bls)({\n    // Fields\n    fields: { Fp, Fp2, Fp6, Fp12, Fr },\n    G1: {\n        Fp,\n        h: BigInt(1),\n        Gx: BigInt(1),\n        Gy: BigInt(2),\n        a: Fp.ZERO,\n        b: _3n,\n        htfDefaults: { ...drandHtf, m: 1 },\n        wrapPrivateKey: true,\n        allowInfinityPoint: true,\n        mapToCurve: mapToCurveG1,\n        fromBytes: (bytes) => {\n            // Deserialise from Kyber format\n            const p = [bytes.slice(0, 32), bytes.slice(32, 64)].map((buf) => (0, utils_3.bytesToNumberBE)(buf));\n            const point = { x: Fp.create(p[0]), y: Fp.create(p[1]) };\n            exports.bn254.G1.ProjectivePoint.fromAffine(point).assertValidity();\n            return point;\n        },\n        toBytes: (c, point, _isCompressed) => {\n            // Serialise to Kyber format\n            const isZero = point.equals(c.ZERO);\n            const { x, y } = point.toAffine();\n            const { BYTES: len } = Fp;\n            if (isZero) {\n                return new Uint8Array(len);\n            }\n            return (0, utils_2.concatBytes)((0, utils_3.numberToBytesBE)(x, len), (0, utils_3.numberToBytesBE)(y, len));\n        },\n        ShortSignature: {\n            fromHex(hex) {\n                return exports.bn254.G1.ProjectivePoint.fromHex(hex);\n            },\n            toRawBytes(point) {\n                return point.toRawBytes();\n            },\n            toHex(point) {\n                return point.toHex();\n            },\n        },\n    },\n    G2: {\n        Fp: Fp2,\n        // cofactor: (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1\n        h: BigInt('21888242871839275222246405745257275088844257914179612981679871602714643921549'),\n        Gx: Fp2.fromBigTuple([\n            BigInt('10857046999023057135944570762232829481370756359578518086990519993285655852781'),\n            BigInt('11559732032986387107991004021392285783925812861821192530917403151452391805634'),\n        ]),\n        Gy: Fp2.fromBigTuple([\n            BigInt('8495653923123431417604973247489272438418190587263600148770280649306958101930'),\n            BigInt('4082367875863433681332203403145435568316851327593401208105741076214120093531'),\n        ]),\n        a: Fp2.ZERO,\n        b: Fp2B,\n        hEff: BigInt('21888242871839275222246405745257275088844257914179612981679871602714643921549'),\n        htfDefaults: { ...drandHtf, m: 2 },\n        wrapPrivateKey: true,\n        allowInfinityPoint: true,\n        isTorsionFree: (c, P) => P.multiplyUnsafe(SIX_X_SQUARED).equals(G2psi(c, P)), // [p]P = [6X^2]P\n        mapToCurve: utils_2.notImplemented,\n        fromBytes: (bytes) => {\n            // Deserialise from Kyber format\n            const p = [\n                bytes.slice(32, 64),\n                bytes.slice(0, 32),\n                bytes.slice(96, 128),\n                bytes.slice(64, 96),\n            ].map((buf) => (0, utils_3.bytesToNumberBE)(buf));\n            const x = Fp2.create({ c0: p[0], c1: p[1] });\n            const y = Fp2.create({ c0: p[2], c1: p[3] });\n            exports.bn254.G2.ProjectivePoint.fromAffine({ x, y }).assertValidity();\n            return { x, y };\n        },\n        toBytes: (c, point, _isCompressed) => {\n            // Serialise to Kyber format. No point compression.\n            // https://github.com/drand/kyber/blob/master/pairing/bn254/point.go#L415\n            const { BYTES: len } = Fp;\n            const isZero = point.equals(c.ZERO);\n            const { x, y } = point.toAffine();\n            const marshalSize = 4 * len;\n            if (isZero) {\n                // Kyber returns zero bytes for point at infinity\n                return new Uint8Array(marshalSize);\n            }\n            // Kyber format is x = b + ai\n            const { re: x0, im: x1 } = Fp2.reim(x);\n            const { re: y0, im: y1 } = Fp2.reim(y);\n            return (0, utils_2.concatBytes)((0, utils_3.numberToBytesBE)(x1, len), (0, utils_3.numberToBytesBE)(x0, len), (0, utils_3.numberToBytesBE)(y1, len), (0, utils_3.numberToBytesBE)(y0, len));\n        },\n        Signature: {\n            fromHex(hex) {\n                return exports.bn254.G2.ProjectivePoint.fromHex(hex);\n            },\n            toRawBytes(point) {\n                return point.toRawBytes();\n            },\n            toHex(point) {\n                return point.toHex();\n            },\n        },\n    },\n    params: {\n        ateLoopSize: BN_X * _6n + _2n,\n        r: Fr.ORDER,\n        xNegative: false,\n        twistType: 'divisive',\n    },\n    htfDefaults: drandHtf,\n    hash: sha3_1.keccak_256,\n    randomBytes: utils_1.randomBytes,\n    postPrecompute: (Rx, Ry, Rz, Qx, Qy, pointAdd) => {\n        const q = psi(Qx, Qy);\n        ({ Rx, Ry, Rz } = pointAdd(Rx, Ry, Rz, q[0], q[1]));\n        const q2 = psi(q[0], q[1]);\n        pointAdd(Rx, Ry, Rz, q2[0], Fp2.neg(q2[1]));\n    },\n});\n", "\"use strict\";\nvar __createBinding = (this && this.__createBinding) || (Object.create ? (function(o, m, k, k2) {\n    if (k2 === undefined) k2 = k;\n    var desc = Object.getOwnPropertyDescriptor(m, k);\n    if (!desc || (\"get\" in desc ? !m.__esModule : desc.writable || desc.configurable)) {\n      desc = { enumerable: true, get: function() { return m[k]; } };\n    }\n    Object.defineProperty(o, k2, desc);\n}) : (function(o, m, k, k2) {\n    if (k2 === undefined) k2 = k;\n    o[k2] = m[k];\n}));\nvar __exportStar = (this && this.__exportStar) || function(m, exports) {\n    for (var p in m) if (p !== \"default\" && !Object.prototype.hasOwnProperty.call(exports, p)) __createBinding(exports, m, p);\n};\nObject.defineProperty(exports, \"__esModule\", { value: true });\n__exportStar(require(\"./bn254\"), exports);\n", "'use strict'\n\nexports.byteLength = byteLength\nexports.toByteArray = toByteArray\nexports.fromByteArray = fromByteArray\n\nvar lookup = []\nvar revLookup = []\nvar Arr = typeof Uint8Array !== 'undefined' ? Uint8Array : Array\n\nvar code = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'\nfor (var i = 0, len = code.length; i < len; ++i) {\n  lookup[i] = code[i]\n  revLookup[code.charCodeAt(i)] = i\n}\n\n// Support decoding URL-safe base64 strings, as Node.js does.\n// See: https://en.wikipedia.org/wiki/Base64#URL_applications\nrevLookup['-'.charCodeAt(0)] = 62\nrevLookup['_'.charCodeAt(0)] = 63\n\nfunction getLens (b64) {\n  var len = b64.length\n\n  if (len % 4 > 0) {\n    throw new Error('Invalid string. Length must be a multiple of 4')\n  }\n\n  // Trim off extra bytes after placeholder bytes are found\n  // See: https://github.com/beatgammit/base64-js/issues/42\n  var validLen = b64.indexOf('=')\n  if (validLen === -1) validLen = len\n\n  var placeHoldersLen = validLen === len\n    ? 0\n    : 4 - (validLen % 4)\n\n  return [validLen, placeHoldersLen]\n}\n\n// base64 is 4/3 + up to two characters of the original data\nfunction byteLength (b64) {\n  var lens = getLens(b64)\n  var validLen = lens[0]\n  var placeHoldersLen = lens[1]\n  return ((validLen + placeHoldersLen) * 3 / 4) - placeHoldersLen\n}\n\nfunction _byteLength (b64, validLen, placeHoldersLen) {\n  return ((validLen + placeHoldersLen) * 3 / 4) - placeHoldersLen\n}\n\nfunction toByteArray (b64) {\n  var tmp\n  var lens = getLens(b64)\n  var validLen = lens[0]\n  var placeHoldersLen = lens[1]\n\n  var arr = new Arr(_byteLength(b64, validLen, placeHoldersLen))\n\n  var curByte = 0\n\n  // if there are placeholders, only get up to the last complete 4 chars\n  var len = placeHoldersLen > 0\n    ? validLen - 4\n    : validLen\n\n  var i\n  for (i = 0; i < len; i += 4) {\n    tmp =\n      (revLookup[b64.charCodeAt(i)] << 18) |\n      (revLookup[b64.charCodeAt(i + 1)] << 12) |\n      (revLookup[b64.charCodeAt(i + 2)] << 6) |\n      revLookup[b64.charCodeAt(i + 3)]\n    arr[curByte++] = (tmp >> 16) & 0xFF\n    arr[curByte++] = (tmp >> 8) & 0xFF\n    arr[curByte++] = tmp & 0xFF\n  }\n\n  if (placeHoldersLen === 2) {\n    tmp =\n      (revLookup[b64.charCodeAt(i)] << 2) |\n      (revLookup[b64.charCodeAt(i + 1)] >> 4)\n    arr[curByte++] = tmp & 0xFF\n  }\n\n  if (placeHoldersLen === 1) {\n    tmp =\n      (revLookup[b64.charCodeAt(i)] << 10) |\n      (revLookup[b64.charCodeAt(i + 1)] << 4) |\n      (revLookup[b64.charCodeAt(i + 2)] >> 2)\n    arr[curByte++] = (tmp >> 8) & 0xFF\n    arr[curByte++] = tmp & 0xFF\n  }\n\n  return arr\n}\n\nfunction tripletToBase64 (num) {\n  return lookup[num >> 18 & 0x3F] +\n    lookup[num >> 12 & 0x3F] +\n    lookup[num >> 6 & 0x3F] +\n    lookup[num & 0x3F]\n}\n\nfunction encodeChunk (uint8, start, end) {\n  var tmp\n  var output = []\n  for (var i = start; i < end; i += 3) {\n    tmp =\n      ((uint8[i] << 16) & 0xFF0000) +\n      ((uint8[i + 1] << 8) & 0xFF00) +\n      (uint8[i + 2] & 0xFF)\n    output.push(tripletToBase64(tmp))\n  }\n  return output.join('')\n}\n\nfunction fromByteArray (uint8) {\n  var tmp\n  var len = uint8.length\n  var extraBytes = len % 3 // if we have 1 byte left, pad 2 bytes\n  var parts = []\n  var maxChunkLength = 16383 // must be multiple of 3\n\n  // go through the array every three bytes, we'll deal with trailing stuff later\n  for (var i = 0, len2 = len - extraBytes; i < len2; i += maxChunkLength) {\n    parts.push(encodeChunk(uint8, i, (i + maxChunkLength) > len2 ? len2 : (i + maxChunkLength)))\n  }\n\n  // pad the end with zeros, but make sure to not forget the extra bytes\n  if (extraBytes === 1) {\n    tmp = uint8[len - 1]\n    parts.push(\n      lookup[tmp >> 2] +\n      lookup[(tmp << 4) & 0x3F] +\n      '=='\n    )\n  } else if (extraBytes === 2) {\n    tmp = (uint8[len - 2] << 8) + uint8[len - 1]\n    parts.push(\n      lookup[tmp >> 10] +\n      lookup[(tmp >> 4) & 0x3F] +\n      lookup[(tmp << 2) & 0x3F] +\n      '='\n    )\n  }\n\n  return parts.join('')\n}\n", "/*! ieee754. BSD-3-Clause License. Feross Aboukhadijeh <https://feross.org/opensource> */\nexports.read = function (buffer, offset, isLE, mLen, nBytes) {\n  var e, m\n  var eLen = (nBytes * 8) - mLen - 1\n  var eMax = (1 << eLen) - 1\n  var eBias = eMax >> 1\n  var nBits = -7\n  var i = isLE ? (nBytes - 1) : 0\n  var d = isLE ? -1 : 1\n  var s = buffer[offset + i]\n\n  i += d\n\n  e = s & ((1 << (-nBits)) - 1)\n  s >>= (-nBits)\n  nBits += eLen\n  for (; nBits > 0; e = (e * 256) + buffer[offset + i], i += d, nBits -= 8) {}\n\n  m = e & ((1 << (-nBits)) - 1)\n  e >>= (-nBits)\n  nBits += mLen\n  for (; nBits > 0; m = (m * 256) + buffer[offset + i], i += d, nBits -= 8) {}\n\n  if (e === 0) {\n    e = 1 - eBias\n  } else if (e === eMax) {\n    return m ? NaN : ((s ? -1 : 1) * Infinity)\n  } else {\n    m = m + Math.pow(2, mLen)\n    e = e - eBias\n  }\n  return (s ? -1 : 1) * m * Math.pow(2, e - mLen)\n}\n\nexports.write = function (buffer, value, offset, isLE, mLen, nBytes) {\n  var e, m, c\n  var eLen = (nBytes * 8) - mLen - 1\n  var eMax = (1 << eLen) - 1\n  var eBias = eMax >> 1\n  var rt = (mLen === 23 ? Math.pow(2, -24) - Math.pow(2, -77) : 0)\n  var i = isLE ? 0 : (nBytes - 1)\n  var d = isLE ? 1 : -1\n  var s = value < 0 || (value === 0 && 1 / value < 0) ? 1 : 0\n\n  value = Math.abs(value)\n\n  if (isNaN(value) || value === Infinity) {\n    m = isNaN(value) ? 1 : 0\n    e = eMax\n  } else {\n    e = Math.floor(Math.log(value) / Math.LN2)\n    if (value * (c = Math.pow(2, -e)) < 1) {\n      e--\n      c *= 2\n    }\n    if (e + eBias >= 1) {\n      value += rt / c\n    } else {\n      value += rt * Math.pow(2, 1 - eBias)\n    }\n    if (value * c >= 2) {\n      e++\n      c /= 2\n    }\n\n    if (e + eBias >= eMax) {\n      m = 0\n      e = eMax\n    } else if (e + eBias >= 1) {\n      m = ((value * c) - 1) * Math.pow(2, mLen)\n      e = e + eBias\n    } else {\n      m = value * Math.pow(2, eBias - 1) * Math.pow(2, mLen)\n      e = 0\n    }\n  }\n\n  for (; mLen >= 8; buffer[offset + i] = m & 0xff, i += d, m /= 256, mLen -= 8) {}\n\n  e = (e << mLen) | m\n  eLen += mLen\n  for (; eLen > 0; buffer[offset + i] = e & 0xff, i += d, e /= 256, eLen -= 8) {}\n\n  buffer[offset + i - d] |= s * 128\n}\n", "/*!\n * The buffer module from node.js, for the browser.\n *\n * @author   Feross Aboukhadijeh <https://feross.org>\n * @license  MIT\n */\n/* eslint-disable no-proto */\n\n'use strict'\n\nconst base64 = require('base64-js')\nconst ieee754 = require('ieee754')\nconst customInspectSymbol =\n  (typeof Symbol === 'function' && typeof Symbol['for'] === 'function') // eslint-disable-line dot-notation\n    ? Symbol['for']('nodejs.util.inspect.custom') // eslint-disable-line dot-notation\n    : null\n\nexports.Buffer = Buffer\nexports.SlowBuffer = SlowBuffer\nexports.INSPECT_MAX_BYTES = 50\n\nconst K_MAX_LENGTH = 0x7fffffff\nexports.kMaxLength = K_MAX_LENGTH\n\n/**\n * If `Buffer.TYPED_ARRAY_SUPPORT`:\n *   === true    Use Uint8Array implementation (fastest)\n *   === false   Print warning and recommend using `buffer` v4.x which has an Object\n *               implementation (most compatible, even IE6)\n *\n * Browsers that support typed arrays are IE 10+, Firefox 4+, Chrome 7+, Safari 5.1+,\n * Opera 11.6+, iOS 4.2+.\n *\n * We report that the browser does not support typed arrays if the are not subclassable\n * using __proto__. Firefox 4-29 lacks support for adding new properties to `Uint8Array`\n * (See: https://bugzilla.mozilla.org/show_bug.cgi?id=695438). IE 10 lacks support\n * for __proto__ and has a buggy typed array implementation.\n */\nBuffer.TYPED_ARRAY_SUPPORT = typedArraySupport()\n\nif (!Buffer.TYPED_ARRAY_SUPPORT && typeof console !== 'undefined' &&\n    typeof console.error === 'function') {\n  console.error(\n    'This browser lacks typed array (Uint8Array) support which is required by ' +\n    '`buffer` v5.x. Use `buffer` v4.x if you require old browser support.'\n  )\n}\n\nfunction typedArraySupport () {\n  // Can typed array instances can be augmented?\n  try {\n    const arr = new Uint8Array(1)\n    const proto = { foo: function () { return 42 } }\n    Object.setPrototypeOf(proto, Uint8Array.prototype)\n    Object.setPrototypeOf(arr, proto)\n    return arr.foo() === 42\n  } catch (e) {\n    return false\n  }\n}\n\nObject.defineProperty(Buffer.prototype, 'parent', {\n  enumerable: true,\n  get: function () {\n    if (!Buffer.isBuffer(this)) return undefined\n    return this.buffer\n  }\n})\n\nObject.defineProperty(Buffer.prototype, 'offset', {\n  enumerable: true,\n  get: function () {\n    if (!Buffer.isBuffer(this)) return undefined\n    return this.byteOffset\n  }\n})\n\nfunction createBuffer (length) {\n  if (length > K_MAX_LENGTH) {\n    throw new RangeError('The value \"' + length + '\" is invalid for option \"size\"')\n  }\n  // Return an augmented `Uint8Array` instance\n  const buf = new Uint8Array(length)\n  Object.setPrototypeOf(buf, Buffer.prototype)\n  return buf\n}\n\n/**\n * The Buffer constructor returns instances of `Uint8Array` that have their\n * prototype changed to `Buffer.prototype`. Furthermore, `Buffer` is a subclass of\n * `Uint8Array`, so the returned instances will have all the node `Buffer` methods\n * and the `Uint8Array` methods. Square bracket notation works as expected -- it\n * returns a single octet.\n *\n * The `Uint8Array` prototype remains unmodified.\n */\n\nfunction Buffer (arg, encodingOrOffset, length) {\n  // Common case.\n  if (typeof arg === 'number') {\n    if (typeof encodingOrOffset === 'string') {\n      throw new TypeError(\n        'The \"string\" argument must be of type string. Received type number'\n      )\n    }\n    return allocUnsafe(arg)\n  }\n  return from(arg, encodingOrOffset, length)\n}\n\nBuffer.poolSize = 8192 // not used by this implementation\n\nfunction from (value, encodingOrOffset, length) {\n  if (typeof value === 'string') {\n    return fromString(value, encodingOrOffset)\n  }\n\n  if (ArrayBuffer.isView(value)) {\n    return fromArrayView(value)\n  }\n\n  if (value == null) {\n    throw new TypeError(\n      'The first argument must be one of type string, Buffer, ArrayBuffer, Array, ' +\n      'or Array-like Object. Received type ' + (typeof value)\n    )\n  }\n\n  if (isInstance(value, ArrayBuffer) ||\n      (value && isInstance(value.buffer, ArrayBuffer))) {\n    return fromArrayBuffer(value, encodingOrOffset, length)\n  }\n\n  if (typeof SharedArrayBuffer !== 'undefined' &&\n      (isInstance(value, SharedArrayBuffer) ||\n      (value && isInstance(value.buffer, SharedArrayBuffer)))) {\n    return fromArrayBuffer(value, encodingOrOffset, length)\n  }\n\n  if (typeof value === 'number') {\n    throw new TypeError(\n      'The \"value\" argument must not be of type number. Received type number'\n    )\n  }\n\n  const valueOf = value.valueOf && value.valueOf()\n  if (valueOf != null && valueOf !== value) {\n    return Buffer.from(valueOf, encodingOrOffset, length)\n  }\n\n  const b = fromObject(value)\n  if (b) return b\n\n  if (typeof Symbol !== 'undefined' && Symbol.toPrimitive != null &&\n      typeof value[Symbol.toPrimitive] === 'function') {\n    return Buffer.from(value[Symbol.toPrimitive]('string'), encodingOrOffset, length)\n  }\n\n  throw new TypeError(\n    'The first argument must be one of type string, Buffer, ArrayBuffer, Array, ' +\n    'or Array-like Object. Received type ' + (typeof value)\n  )\n}\n\n/**\n * Functionally equivalent to Buffer(arg, encoding) but throws a TypeError\n * if value is a number.\n * Buffer.from(str[, encoding])\n * Buffer.from(array)\n * Buffer.from(buffer)\n * Buffer.from(arrayBuffer[, byteOffset[, length]])\n **/\nBuffer.from = function (value, encodingOrOffset, length) {\n  return from(value, encodingOrOffset, length)\n}\n\n// Note: Change prototype *after* Buffer.from is defined to workaround Chrome bug:\n// https://github.com/feross/buffer/pull/148\nObject.setPrototypeOf(Buffer.prototype, Uint8Array.prototype)\nObject.setPrototypeOf(Buffer, Uint8Array)\n\nfunction assertSize (size) {\n  if (typeof size !== 'number') {\n    throw new TypeError('\"size\" argument must be of type number')\n  } else if (size < 0) {\n    throw new RangeError('The value \"' + size + '\" is invalid for option \"size\"')\n  }\n}\n\nfunction alloc (size, fill, encoding) {\n  assertSize(size)\n  if (size <= 0) {\n    return createBuffer(size)\n  }\n  if (fill !== undefined) {\n    // Only pay attention to encoding if it's a string. This\n    // prevents accidentally sending in a number that would\n    // be interpreted as a start offset.\n    return typeof encoding === 'string'\n      ? createBuffer(size).fill(fill, encoding)\n      : createBuffer(size).fill(fill)\n  }\n  return createBuffer(size)\n}\n\n/**\n * Creates a new filled Buffer instance.\n * alloc(size[, fill[, encoding]])\n **/\nBuffer.alloc = function (size, fill, encoding) {\n  return alloc(size, fill, encoding)\n}\n\nfunction allocUnsafe (size) {\n  assertSize(size)\n  return createBuffer(size < 0 ? 0 : checked(size) | 0)\n}\n\n/**\n * Equivalent to Buffer(num), by default creates a non-zero-filled Buffer instance.\n * */\nBuffer.allocUnsafe = function (size) {\n  return allocUnsafe(size)\n}\n/**\n * Equivalent to SlowBuffer(num), by default creates a non-zero-filled Buffer instance.\n */\nBuffer.allocUnsafeSlow = function (size) {\n  return allocUnsafe(size)\n}\n\nfunction fromString (string, encoding) {\n  if (typeof encoding !== 'string' || encoding === '') {\n    encoding = 'utf8'\n  }\n\n  if (!Buffer.isEncoding(encoding)) {\n    throw new TypeError('Unknown encoding: ' + encoding)\n  }\n\n  const length = byteLength(string, encoding) | 0\n  let buf = createBuffer(length)\n\n  const actual = buf.write(string, encoding)\n\n  if (actual !== length) {\n    // Writing a hex string, for example, that contains invalid characters will\n    // cause everything after the first invalid character to be ignored. (e.g.\n    // 'abxxcd' will be treated as 'ab')\n    buf = buf.slice(0, actual)\n  }\n\n  return buf\n}\n\nfunction fromArrayLike (array) {\n  const length = array.length < 0 ? 0 : checked(array.length) | 0\n  const buf = createBuffer(length)\n  for (let i = 0; i < length; i += 1) {\n    buf[i] = array[i] & 255\n  }\n  return buf\n}\n\nfunction fromArrayView (arrayView) {\n  if (isInstance(arrayView, Uint8Array)) {\n    const copy = new Uint8Array(arrayView)\n    return fromArrayBuffer(copy.buffer, copy.byteOffset, copy.byteLength)\n  }\n  return fromArrayLike(arrayView)\n}\n\nfunction fromArrayBuffer (array, byteOffset, length) {\n  if (byteOffset < 0 || array.byteLength < byteOffset) {\n    throw new RangeError('\"offset\" is outside of buffer bounds')\n  }\n\n  if (array.byteLength < byteOffset + (length || 0)) {\n    throw new RangeError('\"length\" is outside of buffer bounds')\n  }\n\n  let buf\n  if (byteOffset === undefined && length === undefined) {\n    buf = new Uint8Array(array)\n  } else if (length === undefined) {\n    buf = new Uint8Array(array, byteOffset)\n  } else {\n    buf = new Uint8Array(array, byteOffset, length)\n  }\n\n  // Return an augmented `Uint8Array` instance\n  Object.setPrototypeOf(buf, Buffer.prototype)\n\n  return buf\n}\n\nfunction fromObject (obj) {\n  if (Buffer.isBuffer(obj)) {\n    const len = checked(obj.length) | 0\n    const buf = createBuffer(len)\n\n    if (buf.length === 0) {\n      return buf\n    }\n\n    obj.copy(buf, 0, 0, len)\n    return buf\n  }\n\n  if (obj.length !== undefined) {\n    if (typeof obj.length !== 'number' || numberIsNaN(obj.length)) {\n      return createBuffer(0)\n    }\n    return fromArrayLike(obj)\n  }\n\n  if (obj.type === 'Buffer' && Array.isArray(obj.data)) {\n    return fromArrayLike(obj.data)\n  }\n}\n\nfunction checked (length) {\n  // Note: cannot use `length < K_MAX_LENGTH` here because that fails when\n  // length is NaN (which is otherwise coerced to zero.)\n  if (length >= K_MAX_LENGTH) {\n    throw new RangeError('Attempt to allocate Buffer larger than maximum ' +\n                         'size: 0x' + K_MAX_LENGTH.toString(16) + ' bytes')\n  }\n  return length | 0\n}\n\nfunction SlowBuffer (length) {\n  if (+length != length) { // eslint-disable-line eqeqeq\n    length = 0\n  }\n  return Buffer.alloc(+length)\n}\n\nBuffer.isBuffer = function isBuffer (b) {\n  return b != null && b._isBuffer === true &&\n    b !== Buffer.prototype // so Buffer.isBuffer(Buffer.prototype) will be false\n}\n\nBuffer.compare = function compare (a, b) {\n  if (isInstance(a, Uint8Array)) a = Buffer.from(a, a.offset, a.byteLength)\n  if (isInstance(b, Uint8Array)) b = Buffer.from(b, b.offset, b.byteLength)\n  if (!Buffer.isBuffer(a) || !Buffer.isBuffer(b)) {\n    throw new TypeError(\n      'The \"buf1\", \"buf2\" arguments must be one of type Buffer or Uint8Array'\n    )\n  }\n\n  if (a === b) return 0\n\n  let x = a.length\n  let y = b.length\n\n  for (let i = 0, len = Math.min(x, y); i < len; ++i) {\n    if (a[i] !== b[i]) {\n      x = a[i]\n      y = b[i]\n      break\n    }\n  }\n\n  if (x < y) return -1\n  if (y < x) return 1\n  return 0\n}\n\nBuffer.isEncoding = function isEncoding (encoding) {\n  switch (String(encoding).toLowerCase()) {\n    case 'hex':\n    case 'utf8':\n    case 'utf-8':\n    case 'ascii':\n    case 'latin1':\n    case 'binary':\n    case 'base64':\n    case 'ucs2':\n    case 'ucs-2':\n    case 'utf16le':\n    case 'utf-16le':\n      return true\n    default:\n      return false\n  }\n}\n\nBuffer.concat = function concat (list, length) {\n  if (!Array.isArray(list)) {\n    throw new TypeError('\"list\" argument must be an Array of Buffers')\n  }\n\n  if (list.length === 0) {\n    return Buffer.alloc(0)\n  }\n\n  let i\n  if (length === undefined) {\n    length = 0\n    for (i = 0; i < list.length; ++i) {\n      length += list[i].length\n    }\n  }\n\n  const buffer = Buffer.allocUnsafe(length)\n  let pos = 0\n  for (i = 0; i < list.length; ++i) {\n    let buf = list[i]\n    if (isInstance(buf, Uint8Array)) {\n      if (pos + buf.length > buffer.length) {\n        if (!Buffer.isBuffer(buf)) buf = Buffer.from(buf)\n        buf.copy(buffer, pos)\n      } else {\n        Uint8Array.prototype.set.call(\n          buffer,\n          buf,\n          pos\n        )\n      }\n    } else if (!Buffer.isBuffer(buf)) {\n      throw new TypeError('\"list\" argument must be an Array of Buffers')\n    } else {\n      buf.copy(buffer, pos)\n    }\n    pos += buf.length\n  }\n  return buffer\n}\n\nfunction byteLength (string, encoding) {\n  if (Buffer.isBuffer(string)) {\n    return string.length\n  }\n  if (ArrayBuffer.isView(string) || isInstance(string, ArrayBuffer)) {\n    return string.byteLength\n  }\n  if (typeof string !== 'string') {\n    throw new TypeError(\n      'The \"string\" argument must be one of type string, Buffer, or ArrayBuffer. ' +\n      'Received type ' + typeof string\n    )\n  }\n\n  const len = string.length\n  const mustMatch = (arguments.length > 2 && arguments[2] === true)\n  if (!mustMatch && len === 0) return 0\n\n  // Use a for loop to avoid recursion\n  let loweredCase = false\n  for (;;) {\n    switch (encoding) {\n      case 'ascii':\n      case 'latin1':\n      case 'binary':\n        return len\n      case 'utf8':\n      case 'utf-8':\n        return utf8ToBytes(string).length\n      case 'ucs2':\n      case 'ucs-2':\n      case 'utf16le':\n      case 'utf-16le':\n        return len * 2\n      case 'hex':\n        return len >>> 1\n      case 'base64':\n        return base64ToBytes(string).length\n      default:\n        if (loweredCase) {\n          return mustMatch ? -1 : utf8ToBytes(string).length // assume utf8\n        }\n        encoding = ('' + encoding).toLowerCase()\n        loweredCase = true\n    }\n  }\n}\nBuffer.byteLength = byteLength\n\nfunction slowToString (encoding, start, end) {\n  let loweredCase = false\n\n  // No need to verify that \"this.length <= MAX_UINT32\" since it's a read-only\n  // property of a typed array.\n\n  // This behaves neither like String nor Uint8Array in that we set start/end\n  // to their upper/lower bounds if the value passed is out of range.\n  // undefined is handled specially as per ECMA-262 6th Edition,\n  // Section 13.3.3.7 Runtime Semantics: KeyedBindingInitialization.\n  if (start === undefined || start < 0) {\n    start = 0\n  }\n  // Return early if start > this.length. Done here to prevent potential uint32\n  // coercion fail below.\n  if (start > this.length) {\n    return ''\n  }\n\n  if (end === undefined || end > this.length) {\n    end = this.length\n  }\n\n  if (end <= 0) {\n    return ''\n  }\n\n  // Force coercion to uint32. This will also coerce falsey/NaN values to 0.\n  end >>>= 0\n  start >>>= 0\n\n  if (end <= start) {\n    return ''\n  }\n\n  if (!encoding) encoding = 'utf8'\n\n  while (true) {\n    switch (encoding) {\n      case 'hex':\n        return hexSlice(this, start, end)\n\n      case 'utf8':\n      case 'utf-8':\n        return utf8Slice(this, start, end)\n\n      case 'ascii':\n        return asciiSlice(this, start, end)\n\n      case 'latin1':\n      case 'binary':\n        return latin1Slice(this, start, end)\n\n      case 'base64':\n        return base64Slice(this, start, end)\n\n      case 'ucs2':\n      case 'ucs-2':\n      case 'utf16le':\n      case 'utf-16le':\n        return utf16leSlice(this, start, end)\n\n      default:\n        if (loweredCase) throw new TypeError('Unknown encoding: ' + encoding)\n        encoding = (encoding + '').toLowerCase()\n        loweredCase = true\n    }\n  }\n}\n\n// This property is used by `Buffer.isBuffer` (and the `is-buffer` npm package)\n// to detect a Buffer instance. It's not possible to use `instanceof Buffer`\n// reliably in a browserify context because there could be multiple different\n// copies of the 'buffer' package in use. This method works even for Buffer\n// instances that were created from another copy of the `buffer` package.\n// See: https://github.com/feross/buffer/issues/154\nBuffer.prototype._isBuffer = true\n\nfunction swap (b, n, m) {\n  const i = b[n]\n  b[n] = b[m]\n  b[m] = i\n}\n\nBuffer.prototype.swap16 = function swap16 () {\n  const len = this.length\n  if (len % 2 !== 0) {\n    throw new RangeError('Buffer size must be a multiple of 16-bits')\n  }\n  for (let i = 0; i < len; i += 2) {\n    swap(this, i, i + 1)\n  }\n  return this\n}\n\nBuffer.prototype.swap32 = function swap32 () {\n  const len = this.length\n  if (len % 4 !== 0) {\n    throw new RangeError('Buffer size must be a multiple of 32-bits')\n  }\n  for (let i = 0; i < len; i += 4) {\n    swap(this, i, i + 3)\n    swap(this, i + 1, i + 2)\n  }\n  return this\n}\n\nBuffer.prototype.swap64 = function swap64 () {\n  const len = this.length\n  if (len % 8 !== 0) {\n    throw new RangeError('Buffer size must be a multiple of 64-bits')\n  }\n  for (let i = 0; i < len; i += 8) {\n    swap(this, i, i + 7)\n    swap(this, i + 1, i + 6)\n    swap(this, i + 2, i + 5)\n    swap(this, i + 3, i + 4)\n  }\n  return this\n}\n\nBuffer.prototype.toString = function toString () {\n  const length = this.length\n  if (length === 0) return ''\n  if (arguments.length === 0) return utf8Slice(this, 0, length)\n  return slowToString.apply(this, arguments)\n}\n\nBuffer.prototype.toLocaleString = Buffer.prototype.toString\n\nBuffer.prototype.equals = function equals (b) {\n  if (!Buffer.isBuffer(b)) throw new TypeError('Argument must be a Buffer')\n  if (this === b) return true\n  return Buffer.compare(this, b) === 0\n}\n\nBuffer.prototype.inspect = function inspect () {\n  let str = ''\n  const max = exports.INSPECT_MAX_BYTES\n  str = this.toString('hex', 0, max).replace(/(.{2})/g, '$1 ').trim()\n  if (this.length > max) str += ' ... '\n  return '<Buffer ' + str + '>'\n}\nif (customInspectSymbol) {\n  Buffer.prototype[customInspectSymbol] = Buffer.prototype.inspect\n}\n\nBuffer.prototype.compare = function compare (target, start, end, thisStart, thisEnd) {\n  if (isInstance(target, Uint8Array)) {\n    target = Buffer.from(target, target.offset, target.byteLength)\n  }\n  if (!Buffer.isBuffer(target)) {\n    throw new TypeError(\n      'The \"target\" argument must be one of type Buffer or Uint8Array. ' +\n      'Received type ' + (typeof target)\n    )\n  }\n\n  if (start === undefined) {\n    start = 0\n  }\n  if (end === undefined) {\n    end = target ? target.length : 0\n  }\n  if (thisStart === undefined) {\n    thisStart = 0\n  }\n  if (thisEnd === undefined) {\n    thisEnd = this.length\n  }\n\n  if (start < 0 || end > target.length || thisStart < 0 || thisEnd > this.length) {\n    throw new RangeError('out of range index')\n  }\n\n  if (thisStart >= thisEnd && start >= end) {\n    return 0\n  }\n  if (thisStart >= thisEnd) {\n    return -1\n  }\n  if (start >= end) {\n    return 1\n  }\n\n  start >>>= 0\n  end >>>= 0\n  thisStart >>>= 0\n  thisEnd >>>= 0\n\n  if (this === target) return 0\n\n  let x = thisEnd - thisStart\n  let y = end - start\n  const len = Math.min(x, y)\n\n  const thisCopy = this.slice(thisStart, thisEnd)\n  const targetCopy = target.slice(start, end)\n\n  for (let i = 0; i < len; ++i) {\n    if (thisCopy[i] !== targetCopy[i]) {\n      x = thisCopy[i]\n      y = targetCopy[i]\n      break\n    }\n  }\n\n  if (x < y) return -1\n  if (y < x) return 1\n  return 0\n}\n\n// Finds either the first index of `val` in `buffer` at offset >= `byteOffset`,\n// OR the last index of `val` in `buffer` at offset <= `byteOffset`.\n//\n// Arguments:\n// - buffer - a Buffer to search\n// - val - a string, Buffer, or number\n// - byteOffset - an index into `buffer`; will be clamped to an int32\n// - encoding - an optional encoding, relevant is val is a string\n// - dir - true for indexOf, false for lastIndexOf\nfunction bidirectionalIndexOf (buffer, val, byteOffset, encoding, dir) {\n  // Empty buffer means no match\n  if (buffer.length === 0) return -1\n\n  // Normalize byteOffset\n  if (typeof byteOffset === 'string') {\n    encoding = byteOffset\n    byteOffset = 0\n  } else if (byteOffset > 0x7fffffff) {\n    byteOffset = 0x7fffffff\n  } else if (byteOffset < -0x80000000) {\n    byteOffset = -0x80000000\n  }\n  byteOffset = +byteOffset // Coerce to Number.\n  if (numberIsNaN(byteOffset)) {\n    // byteOffset: it it's undefined, null, NaN, \"foo\", etc, search whole buffer\n    byteOffset = dir ? 0 : (buffer.length - 1)\n  }\n\n  // Normalize byteOffset: negative offsets start from the end of the buffer\n  if (byteOffset < 0) byteOffset = buffer.length + byteOffset\n  if (byteOffset >= buffer.length) {\n    if (dir) return -1\n    else byteOffset = buffer.length - 1\n  } else if (byteOffset < 0) {\n    if (dir) byteOffset = 0\n    else return -1\n  }\n\n  // Normalize val\n  if (typeof val === 'string') {\n    val = Buffer.from(val, encoding)\n  }\n\n  // Finally, search either indexOf (if dir is true) or lastIndexOf\n  if (Buffer.isBuffer(val)) {\n    // Special case: looking for empty string/buffer always fails\n    if (val.length === 0) {\n      return -1\n    }\n    return arrayIndexOf(buffer, val, byteOffset, encoding, dir)\n  } else if (typeof val === 'number') {\n    val = val & 0xFF // Search for a byte value [0-255]\n    if (typeof Uint8Array.prototype.indexOf === 'function') {\n      if (dir) {\n        return Uint8Array.prototype.indexOf.call(buffer, val, byteOffset)\n      } else {\n        return Uint8Array.prototype.lastIndexOf.call(buffer, val, byteOffset)\n      }\n    }\n    return arrayIndexOf(buffer, [val], byteOffset, encoding, dir)\n  }\n\n  throw new TypeError('val must be string, number or Buffer')\n}\n\nfunction arrayIndexOf (arr, val, byteOffset, encoding, dir) {\n  let indexSize = 1\n  let arrLength = arr.length\n  let valLength = val.length\n\n  if (encoding !== undefined) {\n    encoding = String(encoding).toLowerCase()\n    if (encoding === 'ucs2' || encoding === 'ucs-2' ||\n        encoding === 'utf16le' || encoding === 'utf-16le') {\n      if (arr.length < 2 || val.length < 2) {\n        return -1\n      }\n      indexSize = 2\n      arrLength /= 2\n      valLength /= 2\n      byteOffset /= 2\n    }\n  }\n\n  function read (buf, i) {\n    if (indexSize === 1) {\n      return buf[i]\n    } else {\n      return buf.readUInt16BE(i * indexSize)\n    }\n  }\n\n  let i\n  if (dir) {\n    let foundIndex = -1\n    for (i = byteOffset; i < arrLength; i++) {\n      if (read(arr, i) === read(val, foundIndex === -1 ? 0 : i - foundIndex)) {\n        if (foundIndex === -1) foundIndex = i\n        if (i - foundIndex + 1 === valLength) return foundIndex * indexSize\n      } else {\n        if (foundIndex !== -1) i -= i - foundIndex\n        foundIndex = -1\n      }\n    }\n  } else {\n    if (byteOffset + valLength > arrLength) byteOffset = arrLength - valLength\n    for (i = byteOffset; i >= 0; i--) {\n      let found = true\n      for (let j = 0; j < valLength; j++) {\n        if (read(arr, i + j) !== read(val, j)) {\n          found = false\n          break\n        }\n      }\n      if (found) return i\n    }\n  }\n\n  return -1\n}\n\nBuffer.prototype.includes = function includes (val, byteOffset, encoding) {\n  return this.indexOf(val, byteOffset, encoding) !== -1\n}\n\nBuffer.prototype.indexOf = function indexOf (val, byteOffset, encoding) {\n  return bidirectionalIndexOf(this, val, byteOffset, encoding, true)\n}\n\nBuffer.prototype.lastIndexOf = function lastIndexOf (val, byteOffset, encoding) {\n  return bidirectionalIndexOf(this, val, byteOffset, encoding, false)\n}\n\nfunction hexWrite (buf, string, offset, length) {\n  offset = Number(offset) || 0\n  const remaining = buf.length - offset\n  if (!length) {\n    length = remaining\n  } else {\n    length = Number(length)\n    if (length > remaining) {\n      length = remaining\n    }\n  }\n\n  const strLen = string.length\n\n  if (length > strLen / 2) {\n    length = strLen / 2\n  }\n  let i\n  for (i = 0; i < length; ++i) {\n    const parsed = parseInt(string.substr(i * 2, 2), 16)\n    if (numberIsNaN(parsed)) return i\n    buf[offset + i] = parsed\n  }\n  return i\n}\n\nfunction utf8Write (buf, string, offset, length) {\n  return blitBuffer(utf8ToBytes(string, buf.length - offset), buf, offset, length)\n}\n\nfunction asciiWrite (buf, string, offset, length) {\n  return blitBuffer(asciiToBytes(string), buf, offset, length)\n}\n\nfunction base64Write (buf, string, offset, length) {\n  return blitBuffer(base64ToBytes(string), buf, offset, length)\n}\n\nfunction ucs2Write (buf, string, offset, length) {\n  return blitBuffer(utf16leToBytes(string, buf.length - offset), buf, offset, length)\n}\n\nBuffer.prototype.write = function write (string, offset, length, encoding) {\n  // Buffer#write(string)\n  if (offset === undefined) {\n    encoding = 'utf8'\n    length = this.length\n    offset = 0\n  // Buffer#write(string, encoding)\n  } else if (length === undefined && typeof offset === 'string') {\n    encoding = offset\n    length = this.length\n    offset = 0\n  // Buffer#write(string, offset[, length][, encoding])\n  } else if (isFinite(offset)) {\n    offset = offset >>> 0\n    if (isFinite(length)) {\n      length = length >>> 0\n      if (encoding === undefined) encoding = 'utf8'\n    } else {\n      encoding = length\n      length = undefined\n    }\n  } else {\n    throw new Error(\n      'Buffer.write(string, encoding, offset[, length]) is no longer supported'\n    )\n  }\n\n  const remaining = this.length - offset\n  if (length === undefined || length > remaining) length = remaining\n\n  if ((string.length > 0 && (length < 0 || offset < 0)) || offset > this.length) {\n    throw new RangeError('Attempt to write outside buffer bounds')\n  }\n\n  if (!encoding) encoding = 'utf8'\n\n  let loweredCase = false\n  for (;;) {\n    switch (encoding) {\n      case 'hex':\n        return hexWrite(this, string, offset, length)\n\n      case 'utf8':\n      case 'utf-8':\n        return utf8Write(this, string, offset, length)\n\n      case 'ascii':\n      case 'latin1':\n      case 'binary':\n        return asciiWrite(this, string, offset, length)\n\n      case 'base64':\n        // Warning: maxLength not taken into account in base64Write\n        return base64Write(this, string, offset, length)\n\n      case 'ucs2':\n      case 'ucs-2':\n      case 'utf16le':\n      case 'utf-16le':\n        return ucs2Write(this, string, offset, length)\n\n      default:\n        if (loweredCase) throw new TypeError('Unknown encoding: ' + encoding)\n        encoding = ('' + encoding).toLowerCase()\n        loweredCase = true\n    }\n  }\n}\n\nBuffer.prototype.toJSON = function toJSON () {\n  return {\n    type: 'Buffer',\n    data: Array.prototype.slice.call(this._arr || this, 0)\n  }\n}\n\nfunction base64Slice (buf, start, end) {\n  if (start === 0 && end === buf.length) {\n    return base64.fromByteArray(buf)\n  } else {\n    return base64.fromByteArray(buf.slice(start, end))\n  }\n}\n\nfunction utf8Slice (buf, start, end) {\n  end = Math.min(buf.length, end)\n  const res = []\n\n  let i = start\n  while (i < end) {\n    const firstByte = buf[i]\n    let codePoint = null\n    let bytesPerSequence = (firstByte > 0xEF)\n      ? 4\n      : (firstByte > 0xDF)\n          ? 3\n          : (firstByte > 0xBF)\n              ? 2\n              : 1\n\n    if (i + bytesPerSequence <= end) {\n      let secondByte, thirdByte, fourthByte, tempCodePoint\n\n      switch (bytesPerSequence) {\n        case 1:\n          if (firstByte < 0x80) {\n            codePoint = firstByte\n          }\n          break\n        case 2:\n          secondByte = buf[i + 1]\n          if ((secondByte & 0xC0) === 0x80) {\n            tempCodePoint = (firstByte & 0x1F) << 0x6 | (secondByte & 0x3F)\n            if (tempCodePoint > 0x7F) {\n              codePoint = tempCodePoint\n            }\n          }\n          break\n        case 3:\n          secondByte = buf[i + 1]\n          thirdByte = buf[i + 2]\n          if ((secondByte & 0xC0) === 0x80 && (thirdByte & 0xC0) === 0x80) {\n            tempCodePoint = (firstByte & 0xF) << 0xC | (secondByte & 0x3F) << 0x6 | (thirdByte & 0x3F)\n            if (tempCodePoint > 0x7FF && (tempCodePoint < 0xD800 || tempCodePoint > 0xDFFF)) {\n              codePoint = tempCodePoint\n            }\n          }\n          break\n        case 4:\n          secondByte = buf[i + 1]\n          thirdByte = buf[i + 2]\n          fourthByte = buf[i + 3]\n          if ((secondByte & 0xC0) === 0x80 && (thirdByte & 0xC0) === 0x80 && (fourthByte & 0xC0) === 0x80) {\n            tempCodePoint = (firstByte & 0xF) << 0x12 | (secondByte & 0x3F) << 0xC | (thirdByte & 0x3F) << 0x6 | (fourthByte & 0x3F)\n            if (tempCodePoint > 0xFFFF && tempCodePoint < 0x110000) {\n              codePoint = tempCodePoint\n            }\n          }\n      }\n    }\n\n    if (codePoint === null) {\n      // we did not generate a valid codePoint so insert a\n      // replacement char (U+FFFD) and advance only 1 byte\n      codePoint = 0xFFFD\n      bytesPerSequence = 1\n    } else if (codePoint > 0xFFFF) {\n      // encode to utf16 (surrogate pair dance)\n      codePoint -= 0x10000\n      res.push(codePoint >>> 10 & 0x3FF | 0xD800)\n      codePoint = 0xDC00 | codePoint & 0x3FF\n    }\n\n    res.push(codePoint)\n    i += bytesPerSequence\n  }\n\n  return decodeCodePointsArray(res)\n}\n\n// Based on http://stackoverflow.com/a/22747272/680742, the browser with\n// the lowest limit is Chrome, with 0x10000 args.\n// We go 1 magnitude less, for safety\nconst MAX_ARGUMENTS_LENGTH = 0x1000\n\nfunction decodeCodePointsArray (codePoints) {\n  const len = codePoints.length\n  if (len <= MAX_ARGUMENTS_LENGTH) {\n    return String.fromCharCode.apply(String, codePoints) // avoid extra slice()\n  }\n\n  // Decode in chunks to avoid \"call stack size exceeded\".\n  let res = ''\n  let i = 0\n  while (i < len) {\n    res += String.fromCharCode.apply(\n      String,\n      codePoints.slice(i, i += MAX_ARGUMENTS_LENGTH)\n    )\n  }\n  return res\n}\n\nfunction asciiSlice (buf, start, end) {\n  let ret = ''\n  end = Math.min(buf.length, end)\n\n  for (let i = start; i < end; ++i) {\n    ret += String.fromCharCode(buf[i] & 0x7F)\n  }\n  return ret\n}\n\nfunction latin1Slice (buf, start, end) {\n  let ret = ''\n  end = Math.min(buf.length, end)\n\n  for (let i = start; i < end; ++i) {\n    ret += String.fromCharCode(buf[i])\n  }\n  return ret\n}\n\nfunction hexSlice (buf, start, end) {\n  const len = buf.length\n\n  if (!start || start < 0) start = 0\n  if (!end || end < 0 || end > len) end = len\n\n  let out = ''\n  for (let i = start; i < end; ++i) {\n    out += hexSliceLookupTable[buf[i]]\n  }\n  return out\n}\n\nfunction utf16leSlice (buf, start, end) {\n  const bytes = buf.slice(start, end)\n  let res = ''\n  // If bytes.length is odd, the last 8 bits must be ignored (same as node.js)\n  for (let i = 0; i < bytes.length - 1; i += 2) {\n    res += String.fromCharCode(bytes[i] + (bytes[i + 1] * 256))\n  }\n  return res\n}\n\nBuffer.prototype.slice = function slice (start, end) {\n  const len = this.length\n  start = ~~start\n  end = end === undefined ? len : ~~end\n\n  if (start < 0) {\n    start += len\n    if (start < 0) start = 0\n  } else if (start > len) {\n    start = len\n  }\n\n  if (end < 0) {\n    end += len\n    if (end < 0) end = 0\n  } else if (end > len) {\n    end = len\n  }\n\n  if (end < start) end = start\n\n  const newBuf = this.subarray(start, end)\n  // Return an augmented `Uint8Array` instance\n  Object.setPrototypeOf(newBuf, Buffer.prototype)\n\n  return newBuf\n}\n\n/*\n * Need to make sure that buffer isn't trying to write out of bounds.\n */\nfunction checkOffset (offset, ext, length) {\n  if ((offset % 1) !== 0 || offset < 0) throw new RangeError('offset is not uint')\n  if (offset + ext > length) throw new RangeError('Trying to access beyond buffer length')\n}\n\nBuffer.prototype.readUintLE =\nBuffer.prototype.readUIntLE = function readUIntLE (offset, byteLength, noAssert) {\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) checkOffset(offset, byteLength, this.length)\n\n  let val = this[offset]\n  let mul = 1\n  let i = 0\n  while (++i < byteLength && (mul *= 0x100)) {\n    val += this[offset + i] * mul\n  }\n\n  return val\n}\n\nBuffer.prototype.readUintBE =\nBuffer.prototype.readUIntBE = function readUIntBE (offset, byteLength, noAssert) {\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) {\n    checkOffset(offset, byteLength, this.length)\n  }\n\n  let val = this[offset + --byteLength]\n  let mul = 1\n  while (byteLength > 0 && (mul *= 0x100)) {\n    val += this[offset + --byteLength] * mul\n  }\n\n  return val\n}\n\nBuffer.prototype.readUint8 =\nBuffer.prototype.readUInt8 = function readUInt8 (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 1, this.length)\n  return this[offset]\n}\n\nBuffer.prototype.readUint16LE =\nBuffer.prototype.readUInt16LE = function readUInt16LE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 2, this.length)\n  return this[offset] | (this[offset + 1] << 8)\n}\n\nBuffer.prototype.readUint16BE =\nBuffer.prototype.readUInt16BE = function readUInt16BE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 2, this.length)\n  return (this[offset] << 8) | this[offset + 1]\n}\n\nBuffer.prototype.readUint32LE =\nBuffer.prototype.readUInt32LE = function readUInt32LE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n\n  return ((this[offset]) |\n      (this[offset + 1] << 8) |\n      (this[offset + 2] << 16)) +\n      (this[offset + 3] * 0x1000000)\n}\n\nBuffer.prototype.readUint32BE =\nBuffer.prototype.readUInt32BE = function readUInt32BE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n\n  return (this[offset] * 0x1000000) +\n    ((this[offset + 1] << 16) |\n    (this[offset + 2] << 8) |\n    this[offset + 3])\n}\n\nBuffer.prototype.readBigUInt64LE = defineBigIntMethod(function readBigUInt64LE (offset) {\n  offset = offset >>> 0\n  validateNumber(offset, 'offset')\n  const first = this[offset]\n  const last = this[offset + 7]\n  if (first === undefined || last === undefined) {\n    boundsError(offset, this.length - 8)\n  }\n\n  const lo = first +\n    this[++offset] * 2 ** 8 +\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 24\n\n  const hi = this[++offset] +\n    this[++offset] * 2 ** 8 +\n    this[++offset] * 2 ** 16 +\n    last * 2 ** 24\n\n  return BigInt(lo) + (BigInt(hi) << BigInt(32))\n})\n\nBuffer.prototype.readBigUInt64BE = defineBigIntMethod(function readBigUInt64BE (offset) {\n  offset = offset >>> 0\n  validateNumber(offset, 'offset')\n  const first = this[offset]\n  const last = this[offset + 7]\n  if (first === undefined || last === undefined) {\n    boundsError(offset, this.length - 8)\n  }\n\n  const hi = first * 2 ** 24 +\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 8 +\n    this[++offset]\n\n  const lo = this[++offset] * 2 ** 24 +\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 8 +\n    last\n\n  return (BigInt(hi) << BigInt(32)) + BigInt(lo)\n})\n\nBuffer.prototype.readIntLE = function readIntLE (offset, byteLength, noAssert) {\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) checkOffset(offset, byteLength, this.length)\n\n  let val = this[offset]\n  let mul = 1\n  let i = 0\n  while (++i < byteLength && (mul *= 0x100)) {\n    val += this[offset + i] * mul\n  }\n  mul *= 0x80\n\n  if (val >= mul) val -= Math.pow(2, 8 * byteLength)\n\n  return val\n}\n\nBuffer.prototype.readIntBE = function readIntBE (offset, byteLength, noAssert) {\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) checkOffset(offset, byteLength, this.length)\n\n  let i = byteLength\n  let mul = 1\n  let val = this[offset + --i]\n  while (i > 0 && (mul *= 0x100)) {\n    val += this[offset + --i] * mul\n  }\n  mul *= 0x80\n\n  if (val >= mul) val -= Math.pow(2, 8 * byteLength)\n\n  return val\n}\n\nBuffer.prototype.readInt8 = function readInt8 (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 1, this.length)\n  if (!(this[offset] & 0x80)) return (this[offset])\n  return ((0xff - this[offset] + 1) * -1)\n}\n\nBuffer.prototype.readInt16LE = function readInt16LE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 2, this.length)\n  const val = this[offset] | (this[offset + 1] << 8)\n  return (val & 0x8000) ? val | 0xFFFF0000 : val\n}\n\nBuffer.prototype.readInt16BE = function readInt16BE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 2, this.length)\n  const val = this[offset + 1] | (this[offset] << 8)\n  return (val & 0x8000) ? val | 0xFFFF0000 : val\n}\n\nBuffer.prototype.readInt32LE = function readInt32LE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n\n  return (this[offset]) |\n    (this[offset + 1] << 8) |\n    (this[offset + 2] << 16) |\n    (this[offset + 3] << 24)\n}\n\nBuffer.prototype.readInt32BE = function readInt32BE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n\n  return (this[offset] << 24) |\n    (this[offset + 1] << 16) |\n    (this[offset + 2] << 8) |\n    (this[offset + 3])\n}\n\nBuffer.prototype.readBigInt64LE = defineBigIntMethod(function readBigInt64LE (offset) {\n  offset = offset >>> 0\n  validateNumber(offset, 'offset')\n  const first = this[offset]\n  const last = this[offset + 7]\n  if (first === undefined || last === undefined) {\n    boundsError(offset, this.length - 8)\n  }\n\n  const val = this[offset + 4] +\n    this[offset + 5] * 2 ** 8 +\n    this[offset + 6] * 2 ** 16 +\n    (last << 24) // Overflow\n\n  return (BigInt(val) << BigInt(32)) +\n    BigInt(first +\n    this[++offset] * 2 ** 8 +\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 24)\n})\n\nBuffer.prototype.readBigInt64BE = defineBigIntMethod(function readBigInt64BE (offset) {\n  offset = offset >>> 0\n  validateNumber(offset, 'offset')\n  const first = this[offset]\n  const last = this[offset + 7]\n  if (first === undefined || last === undefined) {\n    boundsError(offset, this.length - 8)\n  }\n\n  const val = (first << 24) + // Overflow\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 8 +\n    this[++offset]\n\n  return (BigInt(val) << BigInt(32)) +\n    BigInt(this[++offset] * 2 ** 24 +\n    this[++offset] * 2 ** 16 +\n    this[++offset] * 2 ** 8 +\n    last)\n})\n\nBuffer.prototype.readFloatLE = function readFloatLE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n  return ieee754.read(this, offset, true, 23, 4)\n}\n\nBuffer.prototype.readFloatBE = function readFloatBE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 4, this.length)\n  return ieee754.read(this, offset, false, 23, 4)\n}\n\nBuffer.prototype.readDoubleLE = function readDoubleLE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 8, this.length)\n  return ieee754.read(this, offset, true, 52, 8)\n}\n\nBuffer.prototype.readDoubleBE = function readDoubleBE (offset, noAssert) {\n  offset = offset >>> 0\n  if (!noAssert) checkOffset(offset, 8, this.length)\n  return ieee754.read(this, offset, false, 52, 8)\n}\n\nfunction checkInt (buf, value, offset, ext, max, min) {\n  if (!Buffer.isBuffer(buf)) throw new TypeError('\"buffer\" argument must be a Buffer instance')\n  if (value > max || value < min) throw new RangeError('\"value\" argument is out of bounds')\n  if (offset + ext > buf.length) throw new RangeError('Index out of range')\n}\n\nBuffer.prototype.writeUintLE =\nBuffer.prototype.writeUIntLE = function writeUIntLE (value, offset, byteLength, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) {\n    const maxBytes = Math.pow(2, 8 * byteLength) - 1\n    checkInt(this, value, offset, byteLength, maxBytes, 0)\n  }\n\n  let mul = 1\n  let i = 0\n  this[offset] = value & 0xFF\n  while (++i < byteLength && (mul *= 0x100)) {\n    this[offset + i] = (value / mul) & 0xFF\n  }\n\n  return offset + byteLength\n}\n\nBuffer.prototype.writeUintBE =\nBuffer.prototype.writeUIntBE = function writeUIntBE (value, offset, byteLength, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  byteLength = byteLength >>> 0\n  if (!noAssert) {\n    const maxBytes = Math.pow(2, 8 * byteLength) - 1\n    checkInt(this, value, offset, byteLength, maxBytes, 0)\n  }\n\n  let i = byteLength - 1\n  let mul = 1\n  this[offset + i] = value & 0xFF\n  while (--i >= 0 && (mul *= 0x100)) {\n    this[offset + i] = (value / mul) & 0xFF\n  }\n\n  return offset + byteLength\n}\n\nBuffer.prototype.writeUint8 =\nBuffer.prototype.writeUInt8 = function writeUInt8 (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 1, 0xff, 0)\n  this[offset] = (value & 0xff)\n  return offset + 1\n}\n\nBuffer.prototype.writeUint16LE =\nBuffer.prototype.writeUInt16LE = function writeUInt16LE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 2, 0xffff, 0)\n  this[offset] = (value & 0xff)\n  this[offset + 1] = (value >>> 8)\n  return offset + 2\n}\n\nBuffer.prototype.writeUint16BE =\nBuffer.prototype.writeUInt16BE = function writeUInt16BE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 2, 0xffff, 0)\n  this[offset] = (value >>> 8)\n  this[offset + 1] = (value & 0xff)\n  return offset + 2\n}\n\nBuffer.prototype.writeUint32LE =\nBuffer.prototype.writeUInt32LE = function writeUInt32LE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 4, 0xffffffff, 0)\n  this[offset + 3] = (value >>> 24)\n  this[offset + 2] = (value >>> 16)\n  this[offset + 1] = (value >>> 8)\n  this[offset] = (value & 0xff)\n  return offset + 4\n}\n\nBuffer.prototype.writeUint32BE =\nBuffer.prototype.writeUInt32BE = function writeUInt32BE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 4, 0xffffffff, 0)\n  this[offset] = (value >>> 24)\n  this[offset + 1] = (value >>> 16)\n  this[offset + 2] = (value >>> 8)\n  this[offset + 3] = (value & 0xff)\n  return offset + 4\n}\n\nfunction wrtBigUInt64LE (buf, value, offset, min, max) {\n  checkIntBI(value, min, max, buf, offset, 7)\n\n  let lo = Number(value & BigInt(0xffffffff))\n  buf[offset++] = lo\n  lo = lo >> 8\n  buf[offset++] = lo\n  lo = lo >> 8\n  buf[offset++] = lo\n  lo = lo >> 8\n  buf[offset++] = lo\n  let hi = Number(value >> BigInt(32) & BigInt(0xffffffff))\n  buf[offset++] = hi\n  hi = hi >> 8\n  buf[offset++] = hi\n  hi = hi >> 8\n  buf[offset++] = hi\n  hi = hi >> 8\n  buf[offset++] = hi\n  return offset\n}\n\nfunction wrtBigUInt64BE (buf, value, offset, min, max) {\n  checkIntBI(value, min, max, buf, offset, 7)\n\n  let lo = Number(value & BigInt(0xffffffff))\n  buf[offset + 7] = lo\n  lo = lo >> 8\n  buf[offset + 6] = lo\n  lo = lo >> 8\n  buf[offset + 5] = lo\n  lo = lo >> 8\n  buf[offset + 4] = lo\n  let hi = Number(value >> BigInt(32) & BigInt(0xffffffff))\n  buf[offset + 3] = hi\n  hi = hi >> 8\n  buf[offset + 2] = hi\n  hi = hi >> 8\n  buf[offset + 1] = hi\n  hi = hi >> 8\n  buf[offset] = hi\n  return offset + 8\n}\n\nBuffer.prototype.writeBigUInt64LE = defineBigIntMethod(function writeBigUInt64LE (value, offset = 0) {\n  return wrtBigUInt64LE(this, value, offset, BigInt(0), BigInt('0xffffffffffffffff'))\n})\n\nBuffer.prototype.writeBigUInt64BE = defineBigIntMethod(function writeBigUInt64BE (value, offset = 0) {\n  return wrtBigUInt64BE(this, value, offset, BigInt(0), BigInt('0xffffffffffffffff'))\n})\n\nBuffer.prototype.writeIntLE = function writeIntLE (value, offset, byteLength, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) {\n    const limit = Math.pow(2, (8 * byteLength) - 1)\n\n    checkInt(this, value, offset, byteLength, limit - 1, -limit)\n  }\n\n  let i = 0\n  let mul = 1\n  let sub = 0\n  this[offset] = value & 0xFF\n  while (++i < byteLength && (mul *= 0x100)) {\n    if (value < 0 && sub === 0 && this[offset + i - 1] !== 0) {\n      sub = 1\n    }\n    this[offset + i] = ((value / mul) >> 0) - sub & 0xFF\n  }\n\n  return offset + byteLength\n}\n\nBuffer.prototype.writeIntBE = function writeIntBE (value, offset, byteLength, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) {\n    const limit = Math.pow(2, (8 * byteLength) - 1)\n\n    checkInt(this, value, offset, byteLength, limit - 1, -limit)\n  }\n\n  let i = byteLength - 1\n  let mul = 1\n  let sub = 0\n  this[offset + i] = value & 0xFF\n  while (--i >= 0 && (mul *= 0x100)) {\n    if (value < 0 && sub === 0 && this[offset + i + 1] !== 0) {\n      sub = 1\n    }\n    this[offset + i] = ((value / mul) >> 0) - sub & 0xFF\n  }\n\n  return offset + byteLength\n}\n\nBuffer.prototype.writeInt8 = function writeInt8 (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 1, 0x7f, -0x80)\n  if (value < 0) value = 0xff + value + 1\n  this[offset] = (value & 0xff)\n  return offset + 1\n}\n\nBuffer.prototype.writeInt16LE = function writeInt16LE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 2, 0x7fff, -0x8000)\n  this[offset] = (value & 0xff)\n  this[offset + 1] = (value >>> 8)\n  return offset + 2\n}\n\nBuffer.prototype.writeInt16BE = function writeInt16BE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 2, 0x7fff, -0x8000)\n  this[offset] = (value >>> 8)\n  this[offset + 1] = (value & 0xff)\n  return offset + 2\n}\n\nBuffer.prototype.writeInt32LE = function writeInt32LE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 4, 0x7fffffff, -0x80000000)\n  this[offset] = (value & 0xff)\n  this[offset + 1] = (value >>> 8)\n  this[offset + 2] = (value >>> 16)\n  this[offset + 3] = (value >>> 24)\n  return offset + 4\n}\n\nBuffer.prototype.writeInt32BE = function writeInt32BE (value, offset, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) checkInt(this, value, offset, 4, 0x7fffffff, -0x80000000)\n  if (value < 0) value = 0xffffffff + value + 1\n  this[offset] = (value >>> 24)\n  this[offset + 1] = (value >>> 16)\n  this[offset + 2] = (value >>> 8)\n  this[offset + 3] = (value & 0xff)\n  return offset + 4\n}\n\nBuffer.prototype.writeBigInt64LE = defineBigIntMethod(function writeBigInt64LE (value, offset = 0) {\n  return wrtBigUInt64LE(this, value, offset, -BigInt('0x8000000000000000'), BigInt('0x7fffffffffffffff'))\n})\n\nBuffer.prototype.writeBigInt64BE = defineBigIntMethod(function writeBigInt64BE (value, offset = 0) {\n  return wrtBigUInt64BE(this, value, offset, -BigInt('0x8000000000000000'), BigInt('0x7fffffffffffffff'))\n})\n\nfunction checkIEEE754 (buf, value, offset, ext, max, min) {\n  if (offset + ext > buf.length) throw new RangeError('Index out of range')\n  if (offset < 0) throw new RangeError('Index out of range')\n}\n\nfunction writeFloat (buf, value, offset, littleEndian, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) {\n    checkIEEE754(buf, value, offset, 4, 3.4028234663852886e+38, -3.4028234663852886e+38)\n  }\n  ieee754.write(buf, value, offset, littleEndian, 23, 4)\n  return offset + 4\n}\n\nBuffer.prototype.writeFloatLE = function writeFloatLE (value, offset, noAssert) {\n  return writeFloat(this, value, offset, true, noAssert)\n}\n\nBuffer.prototype.writeFloatBE = function writeFloatBE (value, offset, noAssert) {\n  return writeFloat(this, value, offset, false, noAssert)\n}\n\nfunction writeDouble (buf, value, offset, littleEndian, noAssert) {\n  value = +value\n  offset = offset >>> 0\n  if (!noAssert) {\n    checkIEEE754(buf, value, offset, 8, 1.7976931348623157E+308, -1.7976931348623157E+308)\n  }\n  ieee754.write(buf, value, offset, littleEndian, 52, 8)\n  return offset + 8\n}\n\nBuffer.prototype.writeDoubleLE = function writeDoubleLE (value, offset, noAssert) {\n  return writeDouble(this, value, offset, true, noAssert)\n}\n\nBuffer.prototype.writeDoubleBE = function writeDoubleBE (value, offset, noAssert) {\n  return writeDouble(this, value, offset, false, noAssert)\n}\n\n// copy(targetBuffer, targetStart=0, sourceStart=0, sourceEnd=buffer.length)\nBuffer.prototype.copy = function copy (target, targetStart, start, end) {\n  if (!Buffer.isBuffer(target)) throw new TypeError('argument should be a Buffer')\n  if (!start) start = 0\n  if (!end && end !== 0) end = this.length\n  if (targetStart >= target.length) targetStart = target.length\n  if (!targetStart) targetStart = 0\n  if (end > 0 && end < start) end = start\n\n  // Copy 0 bytes; we're done\n  if (end === start) return 0\n  if (target.length === 0 || this.length === 0) return 0\n\n  // Fatal error conditions\n  if (targetStart < 0) {\n    throw new RangeError('targetStart out of bounds')\n  }\n  if (start < 0 || start >= this.length) throw new RangeError('Index out of range')\n  if (end < 0) throw new RangeError('sourceEnd out of bounds')\n\n  // Are we oob?\n  if (end > this.length) end = this.length\n  if (target.length - targetStart < end - start) {\n    end = target.length - targetStart + start\n  }\n\n  const len = end - start\n\n  if (this === target && typeof Uint8Array.prototype.copyWithin === 'function') {\n    // Use built-in when available, missing from IE11\n    this.copyWithin(targetStart, start, end)\n  } else {\n    Uint8Array.prototype.set.call(\n      target,\n      this.subarray(start, end),\n      targetStart\n    )\n  }\n\n  return len\n}\n\n// Usage:\n//    buffer.fill(number[, offset[, end]])\n//    buffer.fill(buffer[, offset[, end]])\n//    buffer.fill(string[, offset[, end]][, encoding])\nBuffer.prototype.fill = function fill (val, start, end, encoding) {\n  // Handle string cases:\n  if (typeof val === 'string') {\n    if (typeof start === 'string') {\n      encoding = start\n      start = 0\n      end = this.length\n    } else if (typeof end === 'string') {\n      encoding = end\n      end = this.length\n    }\n    if (encoding !== undefined && typeof encoding !== 'string') {\n      throw new TypeError('encoding must be a string')\n    }\n    if (typeof encoding === 'string' && !Buffer.isEncoding(encoding)) {\n      throw new TypeError('Unknown encoding: ' + encoding)\n    }\n    if (val.length === 1) {\n      const code = val.charCodeAt(0)\n      if ((encoding === 'utf8' && code < 128) ||\n          encoding === 'latin1') {\n        // Fast path: If `val` fits into a single byte, use that numeric value.\n        val = code\n      }\n    }\n  } else if (typeof val === 'number') {\n    val = val & 255\n  } else if (typeof val === 'boolean') {\n    val = Number(val)\n  }\n\n  // Invalid ranges are not set to a default, so can range check early.\n  if (start < 0 || this.length < start || this.length < end) {\n    throw new RangeError('Out of range index')\n  }\n\n  if (end <= start) {\n    return this\n  }\n\n  start = start >>> 0\n  end = end === undefined ? this.length : end >>> 0\n\n  if (!val) val = 0\n\n  let i\n  if (typeof val === 'number') {\n    for (i = start; i < end; ++i) {\n      this[i] = val\n    }\n  } else {\n    const bytes = Buffer.isBuffer(val)\n      ? val\n      : Buffer.from(val, encoding)\n    const len = bytes.length\n    if (len === 0) {\n      throw new TypeError('The value \"' + val +\n        '\" is invalid for argument \"value\"')\n    }\n    for (i = 0; i < end - start; ++i) {\n      this[i + start] = bytes[i % len]\n    }\n  }\n\n  return this\n}\n\n// CUSTOM ERRORS\n// =============\n\n// Simplified versions from Node, changed for Buffer-only usage\nconst errors = {}\nfunction E (sym, getMessage, Base) {\n  errors[sym] = class NodeError extends Base {\n    constructor () {\n      super()\n\n      Object.defineProperty(this, 'message', {\n        value: getMessage.apply(this, arguments),\n        writable: true,\n        configurable: true\n      })\n\n      // Add the error code to the name to include it in the stack trace.\n      this.name = `${this.name} [${sym}]`\n      // Access the stack to generate the error message including the error code\n      // from the name.\n      this.stack // eslint-disable-line no-unused-expressions\n      // Reset the name to the actual name.\n      delete this.name\n    }\n\n    get code () {\n      return sym\n    }\n\n    set code (value) {\n      Object.defineProperty(this, 'code', {\n        configurable: true,\n        enumerable: true,\n        value,\n        writable: true\n      })\n    }\n\n    toString () {\n      return `${this.name} [${sym}]: ${this.message}`\n    }\n  }\n}\n\nE('ERR_BUFFER_OUT_OF_BOUNDS',\n  function (name) {\n    if (name) {\n      return `${name} is outside of buffer bounds`\n    }\n\n    return 'Attempt to access memory outside buffer bounds'\n  }, RangeError)\nE('ERR_INVALID_ARG_TYPE',\n  function (name, actual) {\n    return `The \"${name}\" argument must be of type number. Received type ${typeof actual}`\n  }, TypeError)\nE('ERR_OUT_OF_RANGE',\n  function (str, range, input) {\n    let msg = `The value of \"${str}\" is out of range.`\n    let received = input\n    if (Number.isInteger(input) && Math.abs(input) > 2 ** 32) {\n      received = addNumericalSeparator(String(input))\n    } else if (typeof input === 'bigint') {\n      received = String(input)\n      if (input > BigInt(2) ** BigInt(32) || input < -(BigInt(2) ** BigInt(32))) {\n        received = addNumericalSeparator(received)\n      }\n      received += 'n'\n    }\n    msg += ` It must be ${range}. Received ${received}`\n    return msg\n  }, RangeError)\n\nfunction addNumericalSeparator (val) {\n  let res = ''\n  let i = val.length\n  const start = val[0] === '-' ? 1 : 0\n  for (; i >= start + 4; i -= 3) {\n    res = `_${val.slice(i - 3, i)}${res}`\n  }\n  return `${val.slice(0, i)}${res}`\n}\n\n// CHECK FUNCTIONS\n// ===============\n\nfunction checkBounds (buf, offset, byteLength) {\n  validateNumber(offset, 'offset')\n  if (buf[offset] === undefined || buf[offset + byteLength] === undefined) {\n    boundsError(offset, buf.length - (byteLength + 1))\n  }\n}\n\nfunction checkIntBI (value, min, max, buf, offset, byteLength) {\n  if (value > max || value < min) {\n    const n = typeof min === 'bigint' ? 'n' : ''\n    let range\n    if (byteLength > 3) {\n      if (min === 0 || min === BigInt(0)) {\n        range = `>= 0${n} and < 2${n} ** ${(byteLength + 1) * 8}${n}`\n      } else {\n        range = `>= -(2${n} ** ${(byteLength + 1) * 8 - 1}${n}) and < 2 ** ` +\n                `${(byteLength + 1) * 8 - 1}${n}`\n      }\n    } else {\n      range = `>= ${min}${n} and <= ${max}${n}`\n    }\n    throw new errors.ERR_OUT_OF_RANGE('value', range, value)\n  }\n  checkBounds(buf, offset, byteLength)\n}\n\nfunction validateNumber (value, name) {\n  if (typeof value !== 'number') {\n    throw new errors.ERR_INVALID_ARG_TYPE(name, 'number', value)\n  }\n}\n\nfunction boundsError (value, length, type) {\n  if (Math.floor(value) !== value) {\n    validateNumber(value, type)\n    throw new errors.ERR_OUT_OF_RANGE(type || 'offset', 'an integer', value)\n  }\n\n  if (length < 0) {\n    throw new errors.ERR_BUFFER_OUT_OF_BOUNDS()\n  }\n\n  throw new errors.ERR_OUT_OF_RANGE(type || 'offset',\n                                    `>= ${type ? 1 : 0} and <= ${length}`,\n                                    value)\n}\n\n// HELPER FUNCTIONS\n// ================\n\nconst INVALID_BASE64_RE = /[^+/0-9A-Za-z-_]/g\n\nfunction base64clean (str) {\n  // Node takes equal signs as end of the Base64 encoding\n  str = str.split('=')[0]\n  // Node strips out invalid characters like \\n and \\t from the string, base64-js does not\n  str = str.trim().replace(INVALID_BASE64_RE, '')\n  // Node converts strings with length < 2 to ''\n  if (str.length < 2) return ''\n  // Node allows for non-padded base64 strings (missing trailing ===), base64-js does not\n  while (str.length % 4 !== 0) {\n    str = str + '='\n  }\n  return str\n}\n\nfunction utf8ToBytes (string, units) {\n  units = units || Infinity\n  let codePoint\n  const length = string.length\n  let leadSurrogate = null\n  const bytes = []\n\n  for (let i = 0; i < length; ++i) {\n    codePoint = string.charCodeAt(i)\n\n    // is surrogate component\n    if (codePoint > 0xD7FF && codePoint < 0xE000) {\n      // last char was a lead\n      if (!leadSurrogate) {\n        // no lead yet\n        if (codePoint > 0xDBFF) {\n          // unexpected trail\n          if ((units -= 3) > -1) bytes.push(0xEF, 0xBF, 0xBD)\n          continue\n        } else if (i + 1 === length) {\n          // unpaired lead\n          if ((units -= 3) > -1) bytes.push(0xEF, 0xBF, 0xBD)\n          continue\n        }\n\n        // valid lead\n        leadSurrogate = codePoint\n\n        continue\n      }\n\n      // 2 leads in a row\n      if (codePoint < 0xDC00) {\n        if ((units -= 3) > -1) bytes.push(0xEF, 0xBF, 0xBD)\n        leadSurrogate = codePoint\n        continue\n      }\n\n      // valid surrogate pair\n      codePoint = (leadSurrogate - 0xD800 << 10 | codePoint - 0xDC00) + 0x10000\n    } else if (leadSurrogate) {\n      // valid bmp char, but last char was a lead\n      if ((units -= 3) > -1) bytes.push(0xEF, 0xBF, 0xBD)\n    }\n\n    leadSurrogate = null\n\n    // encode utf8\n    if (codePoint < 0x80) {\n      if ((units -= 1) < 0) break\n      bytes.push(codePoint)\n    } else if (codePoint < 0x800) {\n      if ((units -= 2) < 0) break\n      bytes.push(\n        codePoint >> 0x6 | 0xC0,\n        codePoint & 0x3F | 0x80\n      )\n    } else if (codePoint < 0x10000) {\n      if ((units -= 3) < 0) break\n      bytes.push(\n        codePoint >> 0xC | 0xE0,\n        codePoint >> 0x6 & 0x3F | 0x80,\n        codePoint & 0x3F | 0x80\n      )\n    } else if (codePoint < 0x110000) {\n      if ((units -= 4) < 0) break\n      bytes.push(\n        codePoint >> 0x12 | 0xF0,\n        codePoint >> 0xC & 0x3F | 0x80,\n        codePoint >> 0x6 & 0x3F | 0x80,\n        codePoint & 0x3F | 0x80\n      )\n    } else {\n      throw new Error('Invalid code point')\n    }\n  }\n\n  return bytes\n}\n\nfunction asciiToBytes (str) {\n  const byteArray = []\n  for (let i = 0; i < str.length; ++i) {\n    // Node's code seems to be doing this and not & 0x7F..\n    byteArray.push(str.charCodeAt(i) & 0xFF)\n  }\n  return byteArray\n}\n\nfunction utf16leToBytes (str, units) {\n  let c, hi, lo\n  const byteArray = []\n  for (let i = 0; i < str.length; ++i) {\n    if ((units -= 2) < 0) break\n\n    c = str.charCodeAt(i)\n    hi = c >> 8\n    lo = c % 256\n    byteArray.push(lo)\n    byteArray.push(hi)\n  }\n\n  return byteArray\n}\n\nfunction base64ToBytes (str) {\n  return base64.toByteArray(base64clean(str))\n}\n\nfunction blitBuffer (src, dst, offset, length) {\n  let i\n  for (i = 0; i < length; ++i) {\n    if ((i + offset >= dst.length) || (i >= src.length)) break\n    dst[i + offset] = src[i]\n  }\n  return i\n}\n\n// ArrayBuffer or Uint8Array objects from other contexts (i.e. iframes) do not pass\n// the `instanceof` check but they should be treated as of that type.\n// See: https://github.com/feross/buffer/issues/166\nfunction isInstance (obj, type) {\n  return obj instanceof type ||\n    (obj != null && obj.constructor != null && obj.constructor.name != null &&\n      obj.constructor.name === type.name)\n}\nfunction numberIsNaN (obj) {\n  // For IE11 support\n  return obj !== obj // eslint-disable-line no-self-compare\n}\n\n// Create lookup table for `toString('hex')`\n// See: https://github.com/feross/buffer/issues/219\nconst hexSliceLookupTable = (function () {\n  const alphabet = '0123456789abcdef'\n  const table = new Array(256)\n  for (let i = 0; i < 16; ++i) {\n    const i16 = i * 16\n    for (let j = 0; j < 16; ++j) {\n      table[i16 + j] = alphabet[i] + alphabet[j]\n    }\n  }\n  return table\n})()\n\n// Return not function with Error if BigInt not supported\nfunction defineBigIntMethod (fn) {\n  return typeof BigInt === 'undefined' ? BufferBigIntNotDefined : fn\n}\n\nfunction BufferBigIntNotDefined () {\n  throw new Error('BigInt not supported')\n}\n", "export const LIB_VERSION = \"1.4.2\";\n", "import {ChainInfo} from './index'\n// this is generated by the `precompile` npm script\n// using the package.json version itself messes with the generated javascript, so it must be known\n// at compile time\nimport {LIB_VERSION} from './version'\n\nexport function sleep(timeMs: number): Promise<void> {\n    return new Promise(resolve => {\n        if (timeMs <= 0) {\n            resolve()\n        }\n        setTimeout(resolve, timeMs)\n    })\n}\n\nexport function roundAt(time: number, chain: ChainInfo) {\n    if (!Number.isFinite(time)) {\n        throw new Error('Cannot use Infinity or NaN as a beacon time')\n    }\n    if (time < chain.genesis_time * 1000) {\n        throw Error('Cannot request a round before the genesis time')\n    }\n    return Math.floor((time - (chain.genesis_time * 1000)) / (chain.period * 1000)) + 1\n}\n\nexport function roundTime(chain: ChainInfo, round: number) {\n    if (!Number.isFinite(round)) {\n        throw new Error('Cannot use Infinity or NaN as a round number')\n    }\n    round = round < 0 ? 0 : round\n    return (chain.genesis_time + (round - 1) * chain.period) * 1000\n}\n\nexport type HttpOptions = {\n    userAgent?: string\n    headers?: Record<string, string>\n}\n\n// taking a separate `userAgent` param for backwards compatibility\nexport const defaultHttpOptions: HttpOptions = {\n    userAgent: `drand-client-${LIB_VERSION}`,\n}\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport async function jsonOrError(url: string, options: HttpOptions = defaultHttpOptions): Promise<any> {\n    const headers = {...options.headers}\n\n    if (options.userAgent) {\n        headers['User-Agent'] = options.userAgent\n    }\n\n    const response = await fetch(url, {headers})\n    if (!response.ok) {\n        throw Error(`Error response fetching ${url} - got ${response.status}`)\n    }\n\n    return await response.json()\n}\n\nexport async function retryOnError<T>(fn: () => Promise<T>, times: number): Promise<T> {\n    try {\n        return await fn()\n    } catch (err) {\n        if (times === 0) {\n            throw err\n        }\n        return retryOnError(fn, times - 1)\n    }\n}\n", "import {Chain, ChainInfo, ChainOptions, ChainVerificationParams, defaultChainOptions} from './index'\nimport {HttpOptions, jsonOrError} from './util'\n\nclass HttpChain implements Chain {\n    constructor(\n        public baseUrl: string,\n        private options: ChainOptions = defaultChainOptions,\n        private httpOptions: HttpOptions = {}) {\n    }\n\n    async info(): Promise<ChainInfo> {\n        const chainInfo = await jsonOrError(`${this.baseUrl}/info`, this.httpOptions)\n        if (!!this.options.chainVerificationParams && !isValidInfo(chainInfo, this.options.chainVerificationParams)) {\n            throw Error(`The chain info retrieved from ${this.baseUrl} did not match the verification params!`)\n        }\n        return chainInfo\n    }\n}\n\nfunction isValidInfo(chainInfo: ChainInfo, validParams: ChainVerificationParams): boolean {\n    return chainInfo.hash === validParams.chainHash && chainInfo.public_key === validParams.publicKey\n}\n\nclass HttpCachingChain implements Chain {\n    private chain: Chain\n    private cachedInfo?: ChainInfo\n\n    constructor(public baseUrl: string, private options: ChainOptions = defaultChainOptions) {\n        this.chain = new HttpChain(baseUrl, options)\n    }\n\n    async info(): Promise<ChainInfo> {\n        if (!this.cachedInfo) {\n            this.cachedInfo = await this.chain.info()\n        }\n        return this.cachedInfo\n    }\n}\n\nexport {HttpChain}\nexport default HttpCachingChain\n", "import {Chain, ChainClient, ChainOptions, defaultChainOptions, RandomnessBeacon} from './index'\nimport {defaultHttpOptions, HttpOptions, jsonOrError} from './util'\n\nclass HttpChainClient implements ChainClient {\n\n    constructor(\n        private someChain: Chain,\n        public options: ChainOptions = defaultChainOptions,\n        public httpOptions: HttpOptions = defaultHttpOptions) {\n    }\n\n    async get(roundNumber: number): Promise<RandomnessBeacon> {\n        const url = withCachingParams(`${this.someChain.baseUrl}/public/${roundNumber}`, this.options)\n        return await jsonOrError(url, this.httpOptions)\n    }\n\n    async latest(): Promise<RandomnessBeacon> {\n        const url = withCachingParams(`${this.someChain.baseUrl}/public/latest`, this.options)\n        return await jsonOrError(url, this.httpOptions)\n    }\n\n    chain(): Chain {\n        return this.someChain\n    }\n}\n\nfunction withCachingParams(url: string, config: ChainOptions): string {\n    if (config.noCache) {\n        return `${url}?${Date.now()}`\n    }\n    return url\n}\n\nexport default HttpChainClient\n", "export interface SpeedTest {\n    start: () => void\n    stop: () => void\n    average: () => number\n}\n\n// a utility that tracks the last `samples` speed test execution times and returns the mean running time of them.\nexport function createSpeedTest(test: () => Promise<void>, frequencyMs: number, samples = 5): SpeedTest {\n    let queue = new DroppingQueue<number>(samples)\n    let intervalId: ReturnType<typeof setInterval> | null = null\n\n    const executeSpeedTest = async () => {\n        const startTime = Date.now()\n        try {\n            await test()\n            queue.add(Date.now() - startTime)\n        } catch (err) {\n            queue.add(Number.MAX_SAFE_INTEGER)\n        }\n    }\n\n    return {\n        start: () => {\n            if (intervalId != null) {\n                console.warn('Attempted to start a speed test, but it had already been started!')\n                return\n            }\n            intervalId = setInterval(executeSpeedTest, frequencyMs)\n        },\n        stop: () => {\n            if (intervalId !== null) {\n                clearInterval(intervalId)\n                intervalId = null\n                queue = new DroppingQueue<number>(samples)\n            }\n        },\n        average: (): number => {\n            const values = queue.get()\n            if (values.length === 0) {\n                return Number.MAX_SAFE_INTEGER\n            }\n\n            const total = values.reduce((acc, next) => acc + next, 0)\n            return total / values.length\n        }\n    }\n}\n\nclass DroppingQueue<T> {\n    values: Array<T> = []\n\n    constructor(private capacity: number) {\n    }\n\n    add(value: T) {\n        this.values.push(value)\n        if (this.values.length > this.capacity) {\n            this.values.pop()\n        }\n    }\n\n    get(): Array<T> {\n        return this.values\n    }\n}\n", "import {Chain, ChainClient, ChainOptions, defaultChainOptions, RandomnessBeacon} from './index'\nimport HttpCachingChain, {HttpChain} from './http-caching-chain'\nimport {createSpeedTest, SpeedTest} from './speedtest'\nimport HttpChainClient from './http-chain-client'\n\nconst defaultSpeedTestInterval = 1000 * 60 * 5\n\ntype SpeedTestEntry = {\n    test: SpeedTest\n    url: string\n}\n\n// takes an array of drand nodes and periodically speed tests them to work out which is the fastest\n// it then uses the fastest client to make calls using an underlying HTTP client\n// use `.start()` to enable optimisation of the underlying base URLs\n// don't forget to `.stop()` it after you're finished\nclass FastestNodeClient implements ChainClient {\n\n    speedTests: Array<SpeedTestEntry> = []\n    speedTestHttpOptions = { userAgent: 'drand-web-client-speedtest' }\n\n    constructor(\n        public baseUrls: Array<string>,\n        public options: ChainOptions = defaultChainOptions,\n        private speedTestIntervalMs = defaultSpeedTestInterval\n    ) {\n        if (baseUrls.length === 0) {\n            throw Error('Can\\'t optimise an empty `baseUrls` array!')\n        }\n    }\n\n    async latest(): Promise<RandomnessBeacon> {\n        return new HttpChainClient(this.current(), this.options).latest()\n    }\n\n    async get(roundNumber: number): Promise<RandomnessBeacon> {\n        return new HttpChainClient(this.current(), this.options).get(roundNumber)\n    }\n\n    chain(): Chain {\n        return this.current()\n    }\n\n    start() {\n        if (this.baseUrls.length === 1) {\n            console.warn('There was only a single base URL in the `FastestNodeClient` - not running speed testing')\n            return\n        }\n\n        this.speedTests = this.baseUrls.map(url => {\n                const testFn = async () => {\n                    await new HttpChain(url, this.options, this.speedTestHttpOptions).info()\n                    return\n                }\n                const test = createSpeedTest(testFn, this.speedTestIntervalMs)\n                test.start()\n                return {test, url}\n            }\n        )\n    }\n\n    current(): Chain {\n        if (this.speedTests.length === 0) {\n            console.warn('You are not currently running speed tests to choose the fastest client. Run `.start()` to speed test')\n        }\n        const fastestEntry = this.speedTests\n            .slice()\n            .sort((entry1, entry2) => entry1.test.average() - entry2.test.average())\n            .shift()\n\n        if (!fastestEntry) {\n            throw Error('Somehow there were no entries to optimise! This should be impossible by now')\n        }\n\n        return new HttpCachingChain(fastestEntry.url, this.options)\n    }\n\n    stop() {\n        this.speedTests.forEach(entry => entry.test.stop())\n        this.speedTests = []\n    }\n}\n\nexport default FastestNodeClient\n", "import {Chain, ChainOptions, defaultChainOptions, DrandNode, HealthCheckResponse} from './index'\nimport HttpCachingChain from './http-caching-chain'\nimport {jsonOrError} from './util'\n\nclass MultiBeaconNode implements DrandNode {\n    constructor(public baseUrl: string, private options: ChainOptions = defaultChainOptions) {\n    }\n\n    async chains(): Promise<Array<Chain>> {\n        const chains = await jsonOrError(`${this.baseUrl}/chains`)\n        if (!Array.isArray(chains)) {\n            throw Error(`Expected an array from the chains endpoint but got: ${chains}`)\n        }\n        return chains.map((chainHash: string) => new HttpCachingChain(`${this.baseUrl}/${chainHash}`), this.options)\n    }\n\n    async health(): Promise<HealthCheckResponse> {\n        const response = await fetch(`${this.baseUrl}/health`)\n        if (!response.ok) {\n            return {\n                status: response.status,\n                current: -1,\n                expected: -1\n            }\n        }\n\n        const json = await response.json()\n        return {\n            status: response.status,\n            current: json.current ?? -1,\n            expected: json.expected ?? -1,\n        }\n    }\n}\n\nexport default MultiBeaconNode\n", "/**\n * Internal webcrypto alias.\n * We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.\n * See utils.ts for details.\n * @module\n */\ndeclare const globalThis: Record<string, any> | undefined;\nexport const crypto: any =\n  typeof globalThis === 'object' && 'crypto' in globalThis ? globalThis.crypto : undefined;\n", "/**\n * Utilities for hex, bytes, CSPRNG.\n * @module\n */\n/*! noble-hashes - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\n// We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.\n// node.js versions earlier than v19 don't declare it in global scope.\n// For node.js, package.json#exports field mapping rewrites import\n// from `crypto` to `cryptoNode`, which imports native module.\n// Makes the utils un-importable in browsers without a bundler.\n// Once node.js 18 is deprecated (2025-04-30), we can just drop the import.\nimport { crypto } from '@noble/hashes/crypto';\n\n/** Checks if something is Uint8Array. Be careful: nodejs Buffer will return true. */\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\n/** Asserts something is positive integer. */\nexport function anumber(n: number): void {\n  if (!Number.isSafeInteger(n) || n < 0) throw new Error('positive integer expected, got ' + n);\n}\n\n/** Asserts something is Uint8Array. */\nexport function abytes(b: Uint8Array | undefined, ...lengths: number[]): void {\n  if (!isBytes(b)) throw new Error('Uint8Array expected');\n  if (lengths.length > 0 && !lengths.includes(b.length))\n    throw new Error('Uint8Array expected of length ' + lengths + ', got length=' + b.length);\n}\n\n/** Asserts something is hash */\nexport function ahash(h: IHash): void {\n  if (typeof h !== 'function' || typeof h.create !== 'function')\n    throw new Error('Hash should be wrapped by utils.createHasher');\n  anumber(h.outputLen);\n  anumber(h.blockLen);\n}\n\n/** Asserts a hash instance has not been destroyed / finished */\nexport function aexists(instance: any, checkFinished = true): void {\n  if (instance.destroyed) throw new Error('Hash instance has been destroyed');\n  if (checkFinished && instance.finished) throw new Error('Hash#digest() has already been called');\n}\n\n/** Asserts output is properly-sized byte array */\nexport function aoutput(out: any, instance: any): void {\n  abytes(out);\n  const min = instance.outputLen;\n  if (out.length < min) {\n    throw new Error('digestInto() expects output buffer of length at least ' + min);\n  }\n}\n\n/** Generic type encompassing 8/16/32-byte arrays - but not 64-byte. */\n// prettier-ignore\nexport type TypedArray = Int8Array | Uint8ClampedArray | Uint8Array |\n  Uint16Array | Int16Array | Uint32Array | Int32Array;\n\n/** Cast u8 / u16 / u32 to u8. */\nexport function u8(arr: TypedArray): Uint8Array {\n  return new Uint8Array(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** Cast u8 / u16 / u32 to u32. */\nexport function u32(arr: TypedArray): Uint32Array {\n  return new Uint32Array(arr.buffer, arr.byteOffset, Math.floor(arr.byteLength / 4));\n}\n\n/** Zeroize a byte array. Warning: JS provides no guarantees. */\nexport function clean(...arrays: TypedArray[]): void {\n  for (let i = 0; i < arrays.length; i++) {\n    arrays[i].fill(0);\n  }\n}\n\n/** Create DataView of an array for easy byte-level manipulation. */\nexport function createView(arr: TypedArray): DataView {\n  return new DataView(arr.buffer, arr.byteOffset, arr.byteLength);\n}\n\n/** The rotate right (circular right shift) operation for uint32 */\nexport function rotr(word: number, shift: number): number {\n  return (word << (32 - shift)) | (word >>> shift);\n}\n\n/** The rotate left (circular left shift) operation for uint32 */\nexport function rotl(word: number, shift: number): number {\n  return (word << shift) | ((word >>> (32 - shift)) >>> 0);\n}\n\n/** Is current platform little-endian? Most are. Big-Endian platform: IBM */\nexport const isLE: boolean = /* @__PURE__ */ (() =>\n  new Uint8Array(new Uint32Array([0x11223344]).buffer)[0] === 0x44)();\n\n/** The byte swap operation for uint32 */\nexport function byteSwap(word: number): number {\n  return (\n    ((word << 24) & 0xff000000) |\n    ((word << 8) & 0xff0000) |\n    ((word >>> 8) & 0xff00) |\n    ((word >>> 24) & 0xff)\n  );\n}\n/** Conditionally byte swap if on a big-endian platform */\nexport const swap8IfBE: (n: number) => number = isLE\n  ? (n: number) => n\n  : (n: number) => byteSwap(n);\n\n/** @deprecated */\nexport const byteSwapIfBE: typeof swap8IfBE = swap8IfBE;\n/** In place byte swap for Uint32Array */\nexport function byteSwap32(arr: Uint32Array): Uint32Array {\n  for (let i = 0; i < arr.length; i++) {\n    arr[i] = byteSwap(arr[i]);\n  }\n  return arr;\n}\n\nexport const swap32IfBE: (u: Uint32Array) => Uint32Array = isLE\n  ? (u: Uint32Array) => u\n  : byteSwap32;\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean = /* @__PURE__ */ (() =>\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function')();\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\n  // pre-caching improves the speed 6x\n  let hex = '';\n  for (let i = 0; i < bytes.length; i++) {\n    hex += hexes[bytes[i]];\n  }\n  return hex;\n}\n\n// We use optimized technique to convert hex string to byte array\nconst asciis = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('hex string expected, got unpadded hex of length ' + hl);\n  const array = new Uint8Array(al);\n  for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {\n    const n1 = asciiToBase16(hex.charCodeAt(hi));\n    const n2 = asciiToBase16(hex.charCodeAt(hi + 1));\n    if (n1 === undefined || n2 === undefined) {\n      const char = hex[hi] + hex[hi + 1];\n      throw new Error('hex string expected, got non-hex character \"' + char + '\" at index ' + hi);\n    }\n    array[ai] = n1 * 16 + n2; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\n/**\n * There is no setImmediate in browser and setTimeout is slow.\n * Call of async fn will return Promise, which will be fullfiled only on\n * next scheduler queue processing step and this is exactly what we need.\n */\nexport const nextTick = async (): Promise<void> => {};\n\n/** Returns control to thread each 'tick' ms to avoid blocking. */\nexport async function asyncLoop(\n  iters: number,\n  tick: number,\n  cb: (i: number) => void\n): Promise<void> {\n  let ts = Date.now();\n  for (let i = 0; i < iters; i++) {\n    cb(i);\n    // Date.now() is not monotonic, so in case if clock goes backwards we return return control too\n    const diff = Date.now() - ts;\n    if (diff >= 0 && diff < tick) continue;\n    await nextTick();\n    ts += diff;\n  }\n}\n\n// Global symbols, but ts doesn't see them: https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\ndeclare const TextDecoder: any;\n\n/**\n * Converts string to bytes using UTF8 encoding.\n * @example utf8ToBytes('abc') // Uint8Array.from([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n/**\n * Converts bytes to string using UTF8 encoding.\n * @example bytesToUtf8(Uint8Array.from([97, 98, 99])) // 'abc'\n */\nexport function bytesToUtf8(bytes: Uint8Array): string {\n  return new TextDecoder().decode(bytes);\n}\n\n/** Accepted input of hash functions. Strings are converted to byte arrays. */\nexport type Input = string | Uint8Array;\n/**\n * Normalizes (non-hex) string or Uint8Array to Uint8Array.\n * Warning: when Uint8Array is passed, it would NOT get copied.\n * Keep in mind for future mutable operations.\n */\nexport function toBytes(data: Input): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** KDFs can accept string or Uint8Array for user convenience. */\nexport type KDFInput = string | Uint8Array;\n/**\n * Helper for KDFs: consumes uint8array or string.\n * When string is passed, does utf8 decoding, using TextDecoder.\n */\nexport function kdfInputToBytes(data: KDFInput): Uint8Array {\n  if (typeof data === 'string') data = utf8ToBytes(data);\n  abytes(data);\n  return data;\n}\n\n/** Copies several Uint8Arrays into one. */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\ntype EmptyObj = {};\nexport function checkOpts<T1 extends EmptyObj, T2 extends EmptyObj>(\n  defaults: T1,\n  opts?: T2\n): T1 & T2 {\n  if (opts !== undefined && {}.toString.call(opts) !== '[object Object]')\n    throw new Error('options should be object or undefined');\n  const merged = Object.assign(defaults, opts);\n  return merged as T1 & T2;\n}\n\n/** Hash interface. */\nexport type IHash = {\n  (data: Uint8Array): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create: any;\n};\n\n/** For runtime check if class implements interface */\nexport abstract class Hash<T extends Hash<T>> {\n  abstract blockLen: number; // Bytes per block\n  abstract outputLen: number; // Bytes in output\n  abstract update(buf: Input): this;\n  // Writes digest into buf\n  abstract digestInto(buf: Uint8Array): void;\n  abstract digest(): Uint8Array;\n  /**\n   * Resets internal state. Makes Hash instance unusable.\n   * Reset is impossible for keyed hashes if key is consumed into state. If digest is not consumed\n   * by user, they will need to manually call `destroy()` when zeroing is necessary.\n   */\n  abstract destroy(): void;\n  /**\n   * Clones hash instance. Unsafe: doesn't check whether `to` is valid. Can be used as `clone()`\n   * when no options are passed.\n   * Reasons to use `_cloneInto` instead of clone: 1) performance 2) reuse instance => all internal\n   * buffers are overwritten => causes buffer overwrite which is used for digest in some cases.\n   * There are no guarantees for clean-up because it's impossible in JS.\n   */\n  abstract _cloneInto(to?: T): T;\n  // Safe version that clones internal state\n  abstract clone(): T;\n}\n\n/**\n * XOF: streaming API to read digest in chunks.\n * Same as 'squeeze' in keccak/k12 and 'seek' in blake3, but more generic name.\n * When hash used in XOF mode it is up to user to call '.destroy' afterwards, since we cannot\n * destroy state, next call can require more bytes.\n */\nexport type HashXOF<T extends Hash<T>> = Hash<T> & {\n  xof(bytes: number): Uint8Array; // Read 'bytes' bytes from digest stream\n  xofInto(buf: Uint8Array): Uint8Array; // read buf.length bytes from digest stream into buf\n};\n\n/** Hash function */\nexport type CHash = ReturnType<typeof createHasher>;\n/** Hash function with output */\nexport type CHashO = ReturnType<typeof createOptHasher>;\n/** XOF with output */\nexport type CHashXO = ReturnType<typeof createXOFer>;\n\n/** Wraps hash function, creating an interface on top of it */\nexport function createHasher<T extends Hash<T>>(\n  hashCons: () => Hash<T>\n): {\n  (msg: Input): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(): Hash<T>;\n} {\n  const hashC = (msg: Input): Uint8Array => hashCons().update(toBytes(msg)).digest();\n  const tmp = hashCons();\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = () => hashCons();\n  return hashC;\n}\n\nexport function createOptHasher<H extends Hash<H>, T extends Object>(\n  hashCons: (opts?: T) => Hash<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): Hash<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\n\nexport function createXOFer<H extends HashXOF<H>, T extends Object>(\n  hashCons: (opts?: T) => HashXOF<H>\n): {\n  (msg: Input, opts?: T): Uint8Array;\n  outputLen: number;\n  blockLen: number;\n  create(opts?: T): HashXOF<H>;\n} {\n  const hashC = (msg: Input, opts?: T): Uint8Array => hashCons(opts).update(toBytes(msg)).digest();\n  const tmp = hashCons({} as T);\n  hashC.outputLen = tmp.outputLen;\n  hashC.blockLen = tmp.blockLen;\n  hashC.create = (opts?: T) => hashCons(opts);\n  return hashC;\n}\nexport const wrapConstructor: typeof createHasher = createHasher;\nexport const wrapConstructorWithOpts: typeof createOptHasher = createOptHasher;\nexport const wrapXOFConstructorWithOpts: typeof createXOFer = createXOFer;\n\n/** Cryptographically secure PRNG. Uses internal OS-level `crypto.getRandomValues`. */\nexport function randomBytes(bytesLength = 32): Uint8Array {\n  if (crypto && typeof crypto.getRandomValues === 'function') {\n    return crypto.getRandomValues(new Uint8Array(bytesLength));\n  }\n  // Legacy Node.js compatibility\n  if (crypto && typeof crypto.randomBytes === 'function') {\n    return Uint8Array.from(crypto.randomBytes(bytesLength));\n  }\n  throw new Error('crypto.getRandomValues must be defined');\n}\n", "/**\n * Internal Merkle-Damgard hash utils.\n * @module\n */\nimport { type Input, Hash, abytes, aexists, aoutput, clean, createView, toBytes } from './utils.ts';\n\n/** Polyfill for Safari 14. https://caniuse.com/mdn-javascript_builtins_dataview_setbiguint64 */\nexport function setBigUint64(\n  view: DataView,\n  byteOffset: number,\n  value: bigint,\n  isLE: boolean\n): void {\n  if (typeof view.setBigUint64 === 'function') return view.setBigUint64(byteOffset, value, isLE);\n  const _32n = BigInt(32);\n  const _u32_max = BigInt(0xffffffff);\n  const wh = Number((value >> _32n) & _u32_max);\n  const wl = Number(value & _u32_max);\n  const h = isLE ? 4 : 0;\n  const l = isLE ? 0 : 4;\n  view.setUint32(byteOffset + h, wh, isLE);\n  view.setUint32(byteOffset + l, wl, isLE);\n}\n\n/** Choice: a ? b : c */\nexport function Chi(a: number, b: number, c: number): number {\n  return (a & b) ^ (~a & c);\n}\n\n/** Majority function, true if any two inputs is true. */\nexport function Maj(a: number, b: number, c: number): number {\n  return (a & b) ^ (a & c) ^ (b & c);\n}\n\n/**\n * Merkle-Damgard hash construction base class.\n * Could be used to create MD5, RIPEMD, SHA1, SHA2.\n */\nexport abstract class HashMD<T extends HashMD<T>> extends Hash<T> {\n  protected abstract process(buf: DataView, offset: number): void;\n  protected abstract get(): number[];\n  protected abstract set(...args: number[]): void;\n  abstract destroy(): void;\n  protected abstract roundClean(): void;\n\n  readonly blockLen: number;\n  readonly outputLen: number;\n  readonly padOffset: number;\n  readonly isLE: boolean;\n\n  // For partial updates less than block size\n  protected buffer: Uint8Array;\n  protected view: DataView;\n  protected finished = false;\n  protected length = 0;\n  protected pos = 0;\n  protected destroyed = false;\n\n  constructor(blockLen: number, outputLen: number, padOffset: number, isLE: boolean) {\n    super();\n    this.blockLen = blockLen;\n    this.outputLen = outputLen;\n    this.padOffset = padOffset;\n    this.isLE = isLE;\n    this.buffer = new Uint8Array(blockLen);\n    this.view = createView(this.buffer);\n  }\n  update(data: Input): this {\n    aexists(this);\n    data = toBytes(data);\n    abytes(data);\n    const { view, buffer, blockLen } = this;\n    const len = data.length;\n    for (let pos = 0; pos < len; ) {\n      const take = Math.min(blockLen - this.pos, len - pos);\n      // Fast path: we have at least one block in input, cast it to view and process\n      if (take === blockLen) {\n        const dataView = createView(data);\n        for (; blockLen <= len - pos; pos += blockLen) this.process(dataView, pos);\n        continue;\n      }\n      buffer.set(data.subarray(pos, pos + take), this.pos);\n      this.pos += take;\n      pos += take;\n      if (this.pos === blockLen) {\n        this.process(view, 0);\n        this.pos = 0;\n      }\n    }\n    this.length += data.length;\n    this.roundClean();\n    return this;\n  }\n  digestInto(out: Uint8Array): void {\n    aexists(this);\n    aoutput(out, this);\n    this.finished = true;\n    // Padding\n    // We can avoid allocation of buffer for padding completely if it\n    // was previously not allocated here. But it won't change performance.\n    const { buffer, view, blockLen, isLE } = this;\n    let { pos } = this;\n    // append the bit '1' to the message\n    buffer[pos++] = 0b10000000;\n    clean(this.buffer.subarray(pos));\n    // we have less than padOffset left in buffer, so we cannot put length in\n    // current block, need process it and pad again\n    if (this.padOffset > blockLen - pos) {\n      this.process(view, 0);\n      pos = 0;\n    }\n    // Pad until full block byte with zeros\n    for (let i = pos; i < blockLen; i++) buffer[i] = 0;\n    // Note: sha512 requires length to be 128bit integer, but length in JS will overflow before that\n    // You need to write around 2 exabytes (u64_max / 8 / (1024**6)) for this to happen.\n    // So we just write lowest 64 bits of that value.\n    setBigUint64(view, blockLen - 8, BigInt(this.length * 8), isLE);\n    this.process(view, 0);\n    const oview = createView(out);\n    const len = this.outputLen;\n    // NOTE: we do division by 4 later, which should be fused in single op with modulo by JIT\n    if (len % 4) throw new Error('_sha2: outputLen should be aligned to 32bit');\n    const outLen = len / 4;\n    const state = this.get();\n    if (outLen > state.length) throw new Error('_sha2: outputLen bigger than state');\n    for (let i = 0; i < outLen; i++) oview.setUint32(4 * i, state[i], isLE);\n  }\n  digest(): Uint8Array {\n    const { buffer, outputLen } = this;\n    this.digestInto(buffer);\n    const res = buffer.slice(0, outputLen);\n    this.destroy();\n    return res;\n  }\n  _cloneInto(to?: T): T {\n    to ||= new (this.constructor as any)() as T;\n    to.set(...this.get());\n    const { blockLen, buffer, length, finished, destroyed, pos } = this;\n    to.destroyed = destroyed;\n    to.finished = finished;\n    to.length = length;\n    to.pos = pos;\n    if (length % blockLen) to.buffer.set(buffer);\n    return to;\n  }\n  clone(): T {\n    return this._cloneInto();\n  }\n}\n\n/**\n * Initial SHA-2 state: fractional parts of square roots of first 16 primes 2..53.\n * Check out `test/misc/sha2-gen-iv.js` for recomputation guide.\n */\n\n/** Initial SHA256 state. Bits 0..32 of frac part of sqrt of primes 2..19 */\nexport const SHA256_IV: Uint32Array = /* @__PURE__ */ Uint32Array.from([\n  0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19,\n]);\n\n/** Initial SHA224 state. Bits 32..64 of frac part of sqrt of primes 23..53 */\nexport const SHA224_IV: Uint32Array = /* @__PURE__ */ Uint32Array.from([\n  0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939, 0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4,\n]);\n\n/** Initial SHA384 state. Bits 0..64 of frac part of sqrt of primes 23..53 */\nexport const SHA384_IV: Uint32Array = /* @__PURE__ */ Uint32Array.from([\n  0xcbbb9d5d, 0xc1059ed8, 0x629a292a, 0x367cd507, 0x9159015a, 0x3070dd17, 0x152fecd8, 0xf70e5939,\n  0x67332667, 0xffc00b31, 0x8eb44a87, 0x68581511, 0xdb0c2e0d, 0x64f98fa7, 0x47b5481d, 0xbefa4fa4,\n]);\n\n/** Initial SHA512 state. Bits 0..64 of frac part of sqrt of primes 2..19 */\nexport const SHA512_IV: Uint32Array = /* @__PURE__ */ Uint32Array.from([\n  0x6a09e667, 0xf3bcc908, 0xbb67ae85, 0x84caa73b, 0x3c6ef372, 0xfe94f82b, 0xa54ff53a, 0x5f1d36f1,\n  0x510e527f, 0xade682d1, 0x9b05688c, 0x2b3e6c1f, 0x1f83d9ab, 0xfb41bd6b, 0x5be0cd19, 0x137e2179,\n]);\n", "/**\n * Internal helpers for u64. BigUint64Array is too slow as per 2025, so we implement it using Uint32Array.\n * @todo re-check https://issues.chromium.org/issues/42212588\n * @module\n */\nconst U32_MASK64 = /* @__PURE__ */ BigInt(2 ** 32 - 1);\nconst _32n = /* @__PURE__ */ BigInt(32);\n\nfunction fromBig(\n  n: bigint,\n  le = false\n): {\n  h: number;\n  l: number;\n} {\n  if (le) return { h: Number(n & U32_MASK64), l: Number((n >> _32n) & U32_MASK64) };\n  return { h: Number((n >> _32n) & U32_MASK64) | 0, l: Number(n & U32_MASK64) | 0 };\n}\n\nfunction split(lst: bigint[], le = false): Uint32Array[] {\n  const len = lst.length;\n  let Ah = new Uint32Array(len);\n  let Al = new Uint32Array(len);\n  for (let i = 0; i < len; i++) {\n    const { h, l } = fromBig(lst[i], le);\n    [Ah[i], Al[i]] = [h, l];\n  }\n  return [Ah, Al];\n}\n\nconst toBig = (h: number, l: number): bigint => (BigInt(h >>> 0) << _32n) | BigInt(l >>> 0);\n// for Shift in [0, 32)\nconst shrSH = (h: number, _l: number, s: number): number => h >>> s;\nconst shrSL = (h: number, l: number, s: number): number => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in [1, 32)\nconst rotrSH = (h: number, l: number, s: number): number => (h >>> s) | (l << (32 - s));\nconst rotrSL = (h: number, l: number, s: number): number => (h << (32 - s)) | (l >>> s);\n// Right rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotrBH = (h: number, l: number, s: number): number => (h << (64 - s)) | (l >>> (s - 32));\nconst rotrBL = (h: number, l: number, s: number): number => (h >>> (s - 32)) | (l << (64 - s));\n// Right rotate for shift===32 (just swaps l&h)\nconst rotr32H = (_h: number, l: number): number => l;\nconst rotr32L = (h: number, _l: number): number => h;\n// Left rotate for Shift in [1, 32)\nconst rotlSH = (h: number, l: number, s: number): number => (h << s) | (l >>> (32 - s));\nconst rotlSL = (h: number, l: number, s: number): number => (l << s) | (h >>> (32 - s));\n// Left rotate for Shift in (32, 64), NOTE: 32 is special case.\nconst rotlBH = (h: number, l: number, s: number): number => (l << (s - 32)) | (h >>> (64 - s));\nconst rotlBL = (h: number, l: number, s: number): number => (h << (s - 32)) | (l >>> (64 - s));\n\n// JS uses 32-bit signed integers for bitwise operations which means we cannot\n// simple take carry out of low bit sum by shift, we need to use division.\nfunction add(\n  Ah: number,\n  Al: number,\n  Bh: number,\n  Bl: number\n): {\n  h: number;\n  l: number;\n} {\n  const l = (Al >>> 0) + (Bl >>> 0);\n  return { h: (Ah + Bh + ((l / 2 ** 32) | 0)) | 0, l: l | 0 };\n}\n// Addition with more than 2 elements\nconst add3L = (Al: number, Bl: number, Cl: number): number => (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0);\nconst add3H = (low: number, Ah: number, Bh: number, Ch: number): number =>\n  (Ah + Bh + Ch + ((low / 2 ** 32) | 0)) | 0;\nconst add4L = (Al: number, Bl: number, Cl: number, Dl: number): number =>\n  (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0);\nconst add4H = (low: number, Ah: number, Bh: number, Ch: number, Dh: number): number =>\n  (Ah + Bh + Ch + Dh + ((low / 2 ** 32) | 0)) | 0;\nconst add5L = (Al: number, Bl: number, Cl: number, Dl: number, El: number): number =>\n  (Al >>> 0) + (Bl >>> 0) + (Cl >>> 0) + (Dl >>> 0) + (El >>> 0);\nconst add5H = (low: number, Ah: number, Bh: number, Ch: number, Dh: number, Eh: number): number =>\n  (Ah + Bh + Ch + Dh + Eh + ((low / 2 ** 32) | 0)) | 0;\n\n// prettier-ignore\nexport {\n  add, add3H, add3L, add4H, add4L, add5H, add5L, fromBig, rotlBH, rotlBL, rotlSH, rotlSL, rotr32H, rotr32L, rotrBH, rotrBL, rotrSH, rotrSL, shrSH, shrSL, split, toBig\n};\n// prettier-ignore\nconst u64: { fromBig: typeof fromBig; split: typeof split; toBig: (h: number, l: number) => bigint; shrSH: (h: number, _l: number, s: number) => number; shrSL: (h: number, l: number, s: number) => number; rotrSH: (h: number, l: number, s: number) => number; rotrSL: (h: number, l: number, s: number) => number; rotrBH: (h: number, l: number, s: number) => number; rotrBL: (h: number, l: number, s: number) => number; rotr32H: (_h: number, l: number) => number; rotr32L: (h: number, _l: number) => number; rotlSH: (h: number, l: number, s: number) => number; rotlSL: (h: number, l: number, s: number) => number; rotlBH: (h: number, l: number, s: number) => number; rotlBL: (h: number, l: number, s: number) => number; add: typeof add; add3L: (Al: number, Bl: number, Cl: number) => number; add3H: (low: number, Ah: number, Bh: number, Ch: number) => number; add4L: (Al: number, Bl: number, Cl: number, Dl: number) => number; add4H: (low: number, Ah: number, Bh: number, Ch: number, Dh: number) => number; add5H: (low: number, Ah: number, Bh: number, Ch: number, Dh: number, Eh: number) => number; add5L: (Al: number, Bl: number, Cl: number, Dl: number, El: number) => number; } = {\n  fromBig, split, toBig,\n  shrSH, shrSL,\n  rotrSH, rotrSL, rotrBH, rotrBL,\n  rotr32H, rotr32L,\n  rotlSH, rotlSL, rotlBH, rotlBL,\n  add, add3L, add3H, add4L, add4H, add5H, add5L,\n};\nexport default u64;\n", "/**\n * SHA2 hash function. A.k.a. sha256, sha384, sha512, sha512_224, sha512_256.\n * SHA256 is the fastest hash implementable in JS, even faster than Blake3.\n * Check out [RFC 4634](https://datatracker.ietf.org/doc/html/rfc4634) and\n * [FIPS 180-4](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf).\n * @module\n */\nimport { Chi, HashMD, Maj, SHA224_IV, SHA256_IV, SHA384_IV, SHA512_IV } from './_md.ts';\nimport * as u64 from './_u64.ts';\nimport { type CHash, clean, createHasher, rotr } from './utils.ts';\n\n/**\n * Round constants:\n * First 32 bits of fractional parts of the cube roots of the first 64 primes 2..311)\n */\n// prettier-ignore\nconst SHA256_K = /* @__PURE__ */ Uint32Array.from([\n  0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,\n  0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,\n  0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,\n  0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,\n  0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,\n  0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,\n  0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,\n  0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2\n]);\n\n/** Reusable temporary buffer. \"W\" comes straight from spec. */\nconst SHA256_W = /* @__PURE__ */ new Uint32Array(64);\nexport class SHA256 extends HashMD<SHA256> {\n  // We cannot use array here since array allows indexing by variable\n  // which means optimizer/compiler cannot use registers.\n  protected A: number = SHA256_IV[0] | 0;\n  protected B: number = SHA256_IV[1] | 0;\n  protected C: number = SHA256_IV[2] | 0;\n  protected D: number = SHA256_IV[3] | 0;\n  protected E: number = SHA256_IV[4] | 0;\n  protected F: number = SHA256_IV[5] | 0;\n  protected G: number = SHA256_IV[6] | 0;\n  protected H: number = SHA256_IV[7] | 0;\n\n  constructor(outputLen: number = 32) {\n    super(64, outputLen, 8, false);\n  }\n  protected get(): [number, number, number, number, number, number, number, number] {\n    const { A, B, C, D, E, F, G, H } = this;\n    return [A, B, C, D, E, F, G, H];\n  }\n  // prettier-ignore\n  protected set(\n    A: number, B: number, C: number, D: number, E: number, F: number, G: number, H: number\n  ): void {\n    this.A = A | 0;\n    this.B = B | 0;\n    this.C = C | 0;\n    this.D = D | 0;\n    this.E = E | 0;\n    this.F = F | 0;\n    this.G = G | 0;\n    this.H = H | 0;\n  }\n  protected process(view: DataView, offset: number): void {\n    // Extend the first 16 words into the remaining 48 words w[16..63] of the message schedule array\n    for (let i = 0; i < 16; i++, offset += 4) SHA256_W[i] = view.getUint32(offset, false);\n    for (let i = 16; i < 64; i++) {\n      const W15 = SHA256_W[i - 15];\n      const W2 = SHA256_W[i - 2];\n      const s0 = rotr(W15, 7) ^ rotr(W15, 18) ^ (W15 >>> 3);\n      const s1 = rotr(W2, 17) ^ rotr(W2, 19) ^ (W2 >>> 10);\n      SHA256_W[i] = (s1 + SHA256_W[i - 7] + s0 + SHA256_W[i - 16]) | 0;\n    }\n    // Compression function main loop, 64 rounds\n    let { A, B, C, D, E, F, G, H } = this;\n    for (let i = 0; i < 64; i++) {\n      const sigma1 = rotr(E, 6) ^ rotr(E, 11) ^ rotr(E, 25);\n      const T1 = (H + sigma1 + Chi(E, F, G) + SHA256_K[i] + SHA256_W[i]) | 0;\n      const sigma0 = rotr(A, 2) ^ rotr(A, 13) ^ rotr(A, 22);\n      const T2 = (sigma0 + Maj(A, B, C)) | 0;\n      H = G;\n      G = F;\n      F = E;\n      E = (D + T1) | 0;\n      D = C;\n      C = B;\n      B = A;\n      A = (T1 + T2) | 0;\n    }\n    // Add the compressed chunk to the current hash value\n    A = (A + this.A) | 0;\n    B = (B + this.B) | 0;\n    C = (C + this.C) | 0;\n    D = (D + this.D) | 0;\n    E = (E + this.E) | 0;\n    F = (F + this.F) | 0;\n    G = (G + this.G) | 0;\n    H = (H + this.H) | 0;\n    this.set(A, B, C, D, E, F, G, H);\n  }\n  protected roundClean(): void {\n    clean(SHA256_W);\n  }\n  destroy(): void {\n    this.set(0, 0, 0, 0, 0, 0, 0, 0);\n    clean(this.buffer);\n  }\n}\n\nexport class SHA224 extends SHA256 {\n  protected A: number = SHA224_IV[0] | 0;\n  protected B: number = SHA224_IV[1] | 0;\n  protected C: number = SHA224_IV[2] | 0;\n  protected D: number = SHA224_IV[3] | 0;\n  protected E: number = SHA224_IV[4] | 0;\n  protected F: number = SHA224_IV[5] | 0;\n  protected G: number = SHA224_IV[6] | 0;\n  protected H: number = SHA224_IV[7] | 0;\n  constructor() {\n    super(28);\n  }\n}\n\n// SHA2-512 is slower than sha256 in js because u64 operations are slow.\n\n// Round contants\n// First 32 bits of the fractional parts of the cube roots of the first 80 primes 2..409\n// prettier-ignore\nconst K512 = /* @__PURE__ */ (() => u64.split([\n  '0x428a2f98d728ae22', '0x7137449123ef65cd', '0xb5c0fbcfec4d3b2f', '0xe9b5dba58189dbbc',\n  '0x3956c25bf348b538', '0x59f111f1b605d019', '0x923f82a4af194f9b', '0xab1c5ed5da6d8118',\n  '0xd807aa98a3030242', '0x12835b0145706fbe', '0x243185be4ee4b28c', '0x550c7dc3d5ffb4e2',\n  '0x72be5d74f27b896f', '0x80deb1fe3b1696b1', '0x9bdc06a725c71235', '0xc19bf174cf692694',\n  '0xe49b69c19ef14ad2', '0xefbe4786384f25e3', '0x0fc19dc68b8cd5b5', '0x240ca1cc77ac9c65',\n  '0x2de92c6f592b0275', '0x4a7484aa6ea6e483', '0x5cb0a9dcbd41fbd4', '0x76f988da831153b5',\n  '0x983e5152ee66dfab', '0xa831c66d2db43210', '0xb00327c898fb213f', '0xbf597fc7beef0ee4',\n  '0xc6e00bf33da88fc2', '0xd5a79147930aa725', '0x06ca6351e003826f', '0x142929670a0e6e70',\n  '0x27b70a8546d22ffc', '0x2e1b21385c26c926', '0x4d2c6dfc5ac42aed', '0x53380d139d95b3df',\n  '0x650a73548baf63de', '0x766a0abb3c77b2a8', '0x81c2c92e47edaee6', '0x92722c851482353b',\n  '0xa2bfe8a14cf10364', '0xa81a664bbc423001', '0xc24b8b70d0f89791', '0xc76c51a30654be30',\n  '0xd192e819d6ef5218', '0xd69906245565a910', '0xf40e35855771202a', '0x106aa07032bbd1b8',\n  '0x19a4c116b8d2d0c8', '0x1e376c085141ab53', '0x2748774cdf8eeb99', '0x34b0bcb5e19b48a8',\n  '0x391c0cb3c5c95a63', '0x4ed8aa4ae3418acb', '0x5b9cca4f7763e373', '0x682e6ff3d6b2b8a3',\n  '0x748f82ee5defb2fc', '0x78a5636f43172f60', '0x84c87814a1f0ab72', '0x8cc702081a6439ec',\n  '0x90befffa23631e28', '0xa4506cebde82bde9', '0xbef9a3f7b2c67915', '0xc67178f2e372532b',\n  '0xca273eceea26619c', '0xd186b8c721c0c207', '0xeada7dd6cde0eb1e', '0xf57d4f7fee6ed178',\n  '0x06f067aa72176fba', '0x0a637dc5a2c898a6', '0x113f9804bef90dae', '0x1b710b35131c471b',\n  '0x28db77f523047d84', '0x32caab7b40c72493', '0x3c9ebe0a15c9bebc', '0x431d67c49c100d4c',\n  '0x4cc5d4becb3e42b6', '0x597f299cfc657e2a', '0x5fcb6fab3ad6faec', '0x6c44198c4a475817'\n].map(n => BigInt(n))))();\nconst SHA512_Kh = /* @__PURE__ */ (() => K512[0])();\nconst SHA512_Kl = /* @__PURE__ */ (() => K512[1])();\n\n// Reusable temporary buffers\nconst SHA512_W_H = /* @__PURE__ */ new Uint32Array(80);\nconst SHA512_W_L = /* @__PURE__ */ new Uint32Array(80);\n\nexport class SHA512 extends HashMD<SHA512> {\n  // We cannot use array here since array allows indexing by variable\n  // which means optimizer/compiler cannot use registers.\n  // h -- high 32 bits, l -- low 32 bits\n  protected Ah: number = SHA512_IV[0] | 0;\n  protected Al: number = SHA512_IV[1] | 0;\n  protected Bh: number = SHA512_IV[2] | 0;\n  protected Bl: number = SHA512_IV[3] | 0;\n  protected Ch: number = SHA512_IV[4] | 0;\n  protected Cl: number = SHA512_IV[5] | 0;\n  protected Dh: number = SHA512_IV[6] | 0;\n  protected Dl: number = SHA512_IV[7] | 0;\n  protected Eh: number = SHA512_IV[8] | 0;\n  protected El: number = SHA512_IV[9] | 0;\n  protected Fh: number = SHA512_IV[10] | 0;\n  protected Fl: number = SHA512_IV[11] | 0;\n  protected Gh: number = SHA512_IV[12] | 0;\n  protected Gl: number = SHA512_IV[13] | 0;\n  protected Hh: number = SHA512_IV[14] | 0;\n  protected Hl: number = SHA512_IV[15] | 0;\n\n  constructor(outputLen: number = 64) {\n    super(128, outputLen, 16, false);\n  }\n  // prettier-ignore\n  protected get(): [\n    number, number, number, number, number, number, number, number,\n    number, number, number, number, number, number, number, number\n  ] {\n    const { Ah, Al, Bh, Bl, Ch, Cl, Dh, Dl, Eh, El, Fh, Fl, Gh, Gl, Hh, Hl } = this;\n    return [Ah, Al, Bh, Bl, Ch, Cl, Dh, Dl, Eh, El, Fh, Fl, Gh, Gl, Hh, Hl];\n  }\n  // prettier-ignore\n  protected set(\n    Ah: number, Al: number, Bh: number, Bl: number, Ch: number, Cl: number, Dh: number, Dl: number,\n    Eh: number, El: number, Fh: number, Fl: number, Gh: number, Gl: number, Hh: number, Hl: number\n  ): void {\n    this.Ah = Ah | 0;\n    this.Al = Al | 0;\n    this.Bh = Bh | 0;\n    this.Bl = Bl | 0;\n    this.Ch = Ch | 0;\n    this.Cl = Cl | 0;\n    this.Dh = Dh | 0;\n    this.Dl = Dl | 0;\n    this.Eh = Eh | 0;\n    this.El = El | 0;\n    this.Fh = Fh | 0;\n    this.Fl = Fl | 0;\n    this.Gh = Gh | 0;\n    this.Gl = Gl | 0;\n    this.Hh = Hh | 0;\n    this.Hl = Hl | 0;\n  }\n  protected process(view: DataView, offset: number): void {\n    // Extend the first 16 words into the remaining 64 words w[16..79] of the message schedule array\n    for (let i = 0; i < 16; i++, offset += 4) {\n      SHA512_W_H[i] = view.getUint32(offset);\n      SHA512_W_L[i] = view.getUint32((offset += 4));\n    }\n    for (let i = 16; i < 80; i++) {\n      // s0 := (w[i-15] rightrotate 1) xor (w[i-15] rightrotate 8) xor (w[i-15] rightshift 7)\n      const W15h = SHA512_W_H[i - 15] | 0;\n      const W15l = SHA512_W_L[i - 15] | 0;\n      const s0h = u64.rotrSH(W15h, W15l, 1) ^ u64.rotrSH(W15h, W15l, 8) ^ u64.shrSH(W15h, W15l, 7);\n      const s0l = u64.rotrSL(W15h, W15l, 1) ^ u64.rotrSL(W15h, W15l, 8) ^ u64.shrSL(W15h, W15l, 7);\n      // s1 := (w[i-2] rightrotate 19) xor (w[i-2] rightrotate 61) xor (w[i-2] rightshift 6)\n      const W2h = SHA512_W_H[i - 2] | 0;\n      const W2l = SHA512_W_L[i - 2] | 0;\n      const s1h = u64.rotrSH(W2h, W2l, 19) ^ u64.rotrBH(W2h, W2l, 61) ^ u64.shrSH(W2h, W2l, 6);\n      const s1l = u64.rotrSL(W2h, W2l, 19) ^ u64.rotrBL(W2h, W2l, 61) ^ u64.shrSL(W2h, W2l, 6);\n      // SHA256_W[i] = s0 + s1 + SHA256_W[i - 7] + SHA256_W[i - 16];\n      const SUMl = u64.add4L(s0l, s1l, SHA512_W_L[i - 7], SHA512_W_L[i - 16]);\n      const SUMh = u64.add4H(SUMl, s0h, s1h, SHA512_W_H[i - 7], SHA512_W_H[i - 16]);\n      SHA512_W_H[i] = SUMh | 0;\n      SHA512_W_L[i] = SUMl | 0;\n    }\n    let { Ah, Al, Bh, Bl, Ch, Cl, Dh, Dl, Eh, El, Fh, Fl, Gh, Gl, Hh, Hl } = this;\n    // Compression function main loop, 80 rounds\n    for (let i = 0; i < 80; i++) {\n      // S1 := (e rightrotate 14) xor (e rightrotate 18) xor (e rightrotate 41)\n      const sigma1h = u64.rotrSH(Eh, El, 14) ^ u64.rotrSH(Eh, El, 18) ^ u64.rotrBH(Eh, El, 41);\n      const sigma1l = u64.rotrSL(Eh, El, 14) ^ u64.rotrSL(Eh, El, 18) ^ u64.rotrBL(Eh, El, 41);\n      //const T1 = (H + sigma1 + Chi(E, F, G) + SHA256_K[i] + SHA256_W[i]) | 0;\n      const CHIh = (Eh & Fh) ^ (~Eh & Gh);\n      const CHIl = (El & Fl) ^ (~El & Gl);\n      // T1 = H + sigma1 + Chi(E, F, G) + SHA512_K[i] + SHA512_W[i]\n      // prettier-ignore\n      const T1ll = u64.add5L(Hl, sigma1l, CHIl, SHA512_Kl[i], SHA512_W_L[i]);\n      const T1h = u64.add5H(T1ll, Hh, sigma1h, CHIh, SHA512_Kh[i], SHA512_W_H[i]);\n      const T1l = T1ll | 0;\n      // S0 := (a rightrotate 28) xor (a rightrotate 34) xor (a rightrotate 39)\n      const sigma0h = u64.rotrSH(Ah, Al, 28) ^ u64.rotrBH(Ah, Al, 34) ^ u64.rotrBH(Ah, Al, 39);\n      const sigma0l = u64.rotrSL(Ah, Al, 28) ^ u64.rotrBL(Ah, Al, 34) ^ u64.rotrBL(Ah, Al, 39);\n      const MAJh = (Ah & Bh) ^ (Ah & Ch) ^ (Bh & Ch);\n      const MAJl = (Al & Bl) ^ (Al & Cl) ^ (Bl & Cl);\n      Hh = Gh | 0;\n      Hl = Gl | 0;\n      Gh = Fh | 0;\n      Gl = Fl | 0;\n      Fh = Eh | 0;\n      Fl = El | 0;\n      ({ h: Eh, l: El } = u64.add(Dh | 0, Dl | 0, T1h | 0, T1l | 0));\n      Dh = Ch | 0;\n      Dl = Cl | 0;\n      Ch = Bh | 0;\n      Cl = Bl | 0;\n      Bh = Ah | 0;\n      Bl = Al | 0;\n      const All = u64.add3L(T1l, sigma0l, MAJl);\n      Ah = u64.add3H(All, T1h, sigma0h, MAJh);\n      Al = All | 0;\n    }\n    // Add the compressed chunk to the current hash value\n    ({ h: Ah, l: Al } = u64.add(this.Ah | 0, this.Al | 0, Ah | 0, Al | 0));\n    ({ h: Bh, l: Bl } = u64.add(this.Bh | 0, this.Bl | 0, Bh | 0, Bl | 0));\n    ({ h: Ch, l: Cl } = u64.add(this.Ch | 0, this.Cl | 0, Ch | 0, Cl | 0));\n    ({ h: Dh, l: Dl } = u64.add(this.Dh | 0, this.Dl | 0, Dh | 0, Dl | 0));\n    ({ h: Eh, l: El } = u64.add(this.Eh | 0, this.El | 0, Eh | 0, El | 0));\n    ({ h: Fh, l: Fl } = u64.add(this.Fh | 0, this.Fl | 0, Fh | 0, Fl | 0));\n    ({ h: Gh, l: Gl } = u64.add(this.Gh | 0, this.Gl | 0, Gh | 0, Gl | 0));\n    ({ h: Hh, l: Hl } = u64.add(this.Hh | 0, this.Hl | 0, Hh | 0, Hl | 0));\n    this.set(Ah, Al, Bh, Bl, Ch, Cl, Dh, Dl, Eh, El, Fh, Fl, Gh, Gl, Hh, Hl);\n  }\n  protected roundClean(): void {\n    clean(SHA512_W_H, SHA512_W_L);\n  }\n  destroy(): void {\n    clean(this.buffer);\n    this.set(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);\n  }\n}\n\nexport class SHA384 extends SHA512 {\n  protected Ah: number = SHA384_IV[0] | 0;\n  protected Al: number = SHA384_IV[1] | 0;\n  protected Bh: number = SHA384_IV[2] | 0;\n  protected Bl: number = SHA384_IV[3] | 0;\n  protected Ch: number = SHA384_IV[4] | 0;\n  protected Cl: number = SHA384_IV[5] | 0;\n  protected Dh: number = SHA384_IV[6] | 0;\n  protected Dl: number = SHA384_IV[7] | 0;\n  protected Eh: number = SHA384_IV[8] | 0;\n  protected El: number = SHA384_IV[9] | 0;\n  protected Fh: number = SHA384_IV[10] | 0;\n  protected Fl: number = SHA384_IV[11] | 0;\n  protected Gh: number = SHA384_IV[12] | 0;\n  protected Gl: number = SHA384_IV[13] | 0;\n  protected Hh: number = SHA384_IV[14] | 0;\n  protected Hl: number = SHA384_IV[15] | 0;\n\n  constructor() {\n    super(48);\n  }\n}\n\n/**\n * Truncated SHA512/256 and SHA512/224.\n * SHA512_IV is XORed with 0xa5a5a5a5a5a5a5a5, then used as \"intermediary\" IV of SHA512/t.\n * Then t hashes string to produce result IV.\n * See `test/misc/sha2-gen-iv.js`.\n */\n\n/** SHA512/224 IV */\nconst T224_IV = /* @__PURE__ */ Uint32Array.from([\n  0x8c3d37c8, 0x19544da2, 0x73e19966, 0x89dcd4d6, 0x1dfab7ae, 0x32ff9c82, 0x679dd514, 0x582f9fcf,\n  0x0f6d2b69, 0x7bd44da8, 0x77e36f73, 0x04c48942, 0x3f9d85a8, 0x6a1d36c8, 0x1112e6ad, 0x91d692a1,\n]);\n\n/** SHA512/256 IV */\nconst T256_IV = /* @__PURE__ */ Uint32Array.from([\n  0x22312194, 0xfc2bf72c, 0x9f555fa3, 0xc84c64c2, 0x2393b86b, 0x6f53b151, 0x96387719, 0x5940eabd,\n  0x96283ee2, 0xa88effe3, 0xbe5e1e25, 0x53863992, 0x2b0199fc, 0x2c85b8aa, 0x0eb72ddc, 0x81c52ca2,\n]);\n\nexport class SHA512_224 extends SHA512 {\n  protected Ah: number = T224_IV[0] | 0;\n  protected Al: number = T224_IV[1] | 0;\n  protected Bh: number = T224_IV[2] | 0;\n  protected Bl: number = T224_IV[3] | 0;\n  protected Ch: number = T224_IV[4] | 0;\n  protected Cl: number = T224_IV[5] | 0;\n  protected Dh: number = T224_IV[6] | 0;\n  protected Dl: number = T224_IV[7] | 0;\n  protected Eh: number = T224_IV[8] | 0;\n  protected El: number = T224_IV[9] | 0;\n  protected Fh: number = T224_IV[10] | 0;\n  protected Fl: number = T224_IV[11] | 0;\n  protected Gh: number = T224_IV[12] | 0;\n  protected Gl: number = T224_IV[13] | 0;\n  protected Hh: number = T224_IV[14] | 0;\n  protected Hl: number = T224_IV[15] | 0;\n\n  constructor() {\n    super(28);\n  }\n}\n\nexport class SHA512_256 extends SHA512 {\n  protected Ah: number = T256_IV[0] | 0;\n  protected Al: number = T256_IV[1] | 0;\n  protected Bh: number = T256_IV[2] | 0;\n  protected Bl: number = T256_IV[3] | 0;\n  protected Ch: number = T256_IV[4] | 0;\n  protected Cl: number = T256_IV[5] | 0;\n  protected Dh: number = T256_IV[6] | 0;\n  protected Dl: number = T256_IV[7] | 0;\n  protected Eh: number = T256_IV[8] | 0;\n  protected El: number = T256_IV[9] | 0;\n  protected Fh: number = T256_IV[10] | 0;\n  protected Fl: number = T256_IV[11] | 0;\n  protected Gh: number = T256_IV[12] | 0;\n  protected Gl: number = T256_IV[13] | 0;\n  protected Hh: number = T256_IV[14] | 0;\n  protected Hl: number = T256_IV[15] | 0;\n\n  constructor() {\n    super(32);\n  }\n}\n\n/**\n * SHA2-256 hash function from RFC 4634.\n *\n * It is the fastest JS hash, even faster than Blake3.\n * To break sha256 using birthday attack, attackers need to try 2^128 hashes.\n * BTC network is doing 2^70 hashes/sec (2^95 hashes/year) as per 2025.\n */\nexport const sha256: CHash = /* @__PURE__ */ createHasher(() => new SHA256());\n/** SHA2-224 hash function from RFC 4634 */\nexport const sha224: CHash = /* @__PURE__ */ createHasher(() => new SHA224());\n\n/** SHA2-512 hash function from RFC 4634. */\nexport const sha512: CHash = /* @__PURE__ */ createHasher(() => new SHA512());\n/** SHA2-384 hash function from RFC 4634. */\nexport const sha384: CHash = /* @__PURE__ */ createHasher(() => new SHA384());\n\n/**\n * SHA2-512/256 \"truncated\" hash function, with improved resistance to length extension attacks.\n * See the paper on [truncated SHA512](https://eprint.iacr.org/2010/548.pdf).\n */\nexport const sha512_256: CHash = /* @__PURE__ */ createHasher(() => new SHA512_256());\n/**\n * SHA2-512/224 \"truncated\" hash function, with improved resistance to length extension attacks.\n * See the paper on [truncated SHA512](https://eprint.iacr.org/2010/548.pdf).\n */\nexport const sha512_224: CHash = /* @__PURE__ */ createHasher(() => new SHA512_224());\n", "/**\n * Hex, bytes and number utilities.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n\n// 100 lines of code in the file are duplicated from noble-hashes (utils).\n// This is OK: `abstract` directory does not use noble-hashes.\n// User may opt-in into using different hashing library. This way, noble-hashes\n// won't be included into their bundle.\nconst _0n = /* @__PURE__ */ BigInt(0);\nconst _1n = /* @__PURE__ */ BigInt(1);\nexport type Hex = Uint8Array | string; // hex strings are accepted for simplicity\nexport type PrivKey = Hex | bigint; // bigints are accepted to ease learning curve\nexport type CHash = {\n  (message: Uint8Array | string): Uint8Array;\n  blockLen: number;\n  outputLen: number;\n  create(opts?: { dkLen?: number }): any; // For shake\n};\nexport type FHash = (message: Uint8Array | string) => Uint8Array;\n\nexport function isBytes(a: unknown): a is Uint8Array {\n  return a instanceof Uint8Array || (ArrayBuffer.isView(a) && a.constructor.name === 'Uint8Array');\n}\n\nexport function abytes(item: unknown): void {\n  if (!isBytes(item)) throw new Error('Uint8Array expected');\n}\n\nexport function abool(title: string, value: boolean): void {\n  if (typeof value !== 'boolean') throw new Error(title + ' boolean expected, got ' + value);\n}\n\n// Used in weierstrass, der\nexport function numberToHexUnpadded(num: number | bigint): string {\n  const hex = num.toString(16);\n  return hex.length & 1 ? '0' + hex : hex;\n}\n\nexport function hexToNumber(hex: string): bigint {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  return hex === '' ? _0n : BigInt('0x' + hex); // Big Endian\n}\n\n// Built-in hex conversion https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex\nconst hasHexBuiltin: boolean =\n  // @ts-ignore\n  typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function';\n\n// Array where index 0xf0 (240) is mapped to string 'f0'\nconst hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) =>\n  i.toString(16).padStart(2, '0')\n);\n\n/**\n * Convert byte array to hex string. Uses built-in function, when available.\n * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'\n */\nexport function bytesToHex(bytes: Uint8Array): string {\n  abytes(bytes);\n  // @ts-ignore\n  if (hasHexBuiltin) return bytes.toHex();\n  // pre-caching improves the speed 6x\n  let hex = '';\n  for (let i = 0; i < bytes.length; i++) {\n    hex += hexes[bytes[i]];\n  }\n  return hex;\n}\n\n// We use optimized technique to convert hex string to byte array\nconst asciis = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 } as const;\nfunction asciiToBase16(ch: number): number | undefined {\n  if (ch >= asciis._0 && ch <= asciis._9) return ch - asciis._0; // '2' => 50-48\n  if (ch >= asciis.A && ch <= asciis.F) return ch - (asciis.A - 10); // 'B' => 66-(65-10)\n  if (ch >= asciis.a && ch <= asciis.f) return ch - (asciis.a - 10); // 'b' => 98-(97-10)\n  return;\n}\n\n/**\n * Convert hex string to byte array. Uses built-in function, when available.\n * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])\n */\nexport function hexToBytes(hex: string): Uint8Array {\n  if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);\n  // @ts-ignore\n  if (hasHexBuiltin) return Uint8Array.fromHex(hex);\n  const hl = hex.length;\n  const al = hl / 2;\n  if (hl % 2) throw new Error('hex string expected, got unpadded hex of length ' + hl);\n  const array = new Uint8Array(al);\n  for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {\n    const n1 = asciiToBase16(hex.charCodeAt(hi));\n    const n2 = asciiToBase16(hex.charCodeAt(hi + 1));\n    if (n1 === undefined || n2 === undefined) {\n      const char = hex[hi] + hex[hi + 1];\n      throw new Error('hex string expected, got non-hex character \"' + char + '\" at index ' + hi);\n    }\n    array[ai] = n1 * 16 + n2; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163\n  }\n  return array;\n}\n\n// BE: Big Endian, LE: Little Endian\nexport function bytesToNumberBE(bytes: Uint8Array): bigint {\n  return hexToNumber(bytesToHex(bytes));\n}\nexport function bytesToNumberLE(bytes: Uint8Array): bigint {\n  abytes(bytes);\n  return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));\n}\n\nexport function numberToBytesBE(n: number | bigint, len: number): Uint8Array {\n  return hexToBytes(n.toString(16).padStart(len * 2, '0'));\n}\nexport function numberToBytesLE(n: number | bigint, len: number): Uint8Array {\n  return numberToBytesBE(n, len).reverse();\n}\n// Unpadded, rarely used\nexport function numberToVarBytesBE(n: number | bigint): Uint8Array {\n  return hexToBytes(numberToHexUnpadded(n));\n}\n\n/**\n * Takes hex string or Uint8Array, converts to Uint8Array.\n * Validates output length.\n * Will throw error for other types.\n * @param title descriptive title for an error e.g. 'private key'\n * @param hex hex string or Uint8Array\n * @param expectedLength optional, will compare to result array's length\n * @returns\n */\nexport function ensureBytes(title: string, hex: Hex, expectedLength?: number): Uint8Array {\n  let res: Uint8Array;\n  if (typeof hex === 'string') {\n    try {\n      res = hexToBytes(hex);\n    } catch (e) {\n      throw new Error(title + ' must be hex string or Uint8Array, cause: ' + e);\n    }\n  } else if (isBytes(hex)) {\n    // Uint8Array.from() instead of hash.slice() because node.js Buffer\n    // is instance of Uint8Array, and its slice() creates **mutable** copy\n    res = Uint8Array.from(hex);\n  } else {\n    throw new Error(title + ' must be hex string or Uint8Array');\n  }\n  const len = res.length;\n  if (typeof expectedLength === 'number' && len !== expectedLength)\n    throw new Error(title + ' of length ' + expectedLength + ' expected, got ' + len);\n  return res;\n}\n\n/**\n * Copies several Uint8Arrays into one.\n */\nexport function concatBytes(...arrays: Uint8Array[]): Uint8Array {\n  let sum = 0;\n  for (let i = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    abytes(a);\n    sum += a.length;\n  }\n  const res = new Uint8Array(sum);\n  for (let i = 0, pad = 0; i < arrays.length; i++) {\n    const a = arrays[i];\n    res.set(a, pad);\n    pad += a.length;\n  }\n  return res;\n}\n\n// Compares 2 u8a-s in kinda constant time\nexport function equalBytes(a: Uint8Array, b: Uint8Array): boolean {\n  if (a.length !== b.length) return false;\n  let diff = 0;\n  for (let i = 0; i < a.length; i++) diff |= a[i] ^ b[i];\n  return diff === 0;\n}\n\n// Global symbols in both browsers and Node.js since v11\n// See https://github.com/microsoft/TypeScript/issues/31535\ndeclare const TextEncoder: any;\n\n/**\n * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])\n */\nexport function utf8ToBytes(str: string): Uint8Array {\n  if (typeof str !== 'string') throw new Error('string expected');\n  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809\n}\n\n// Is positive bigint\nconst isPosBig = (n: bigint) => typeof n === 'bigint' && _0n <= n;\n\nexport function inRange(n: bigint, min: bigint, max: bigint): boolean {\n  return isPosBig(n) && isPosBig(min) && isPosBig(max) && min <= n && n < max;\n}\n\n/**\n * Asserts min <= n < max. NOTE: It's < max and not <= max.\n * @example\n * aInRange('x', x, 1n, 256n); // would assume x is in (1n..255n)\n */\nexport function aInRange(title: string, n: bigint, min: bigint, max: bigint): void {\n  // Why min <= n < max and not a (min < n < max) OR b (min <= n <= max)?\n  // consider P=256n, min=0n, max=P\n  // - a for min=0 would require -1:          `inRange('x', x, -1n, P)`\n  // - b would commonly require subtraction:  `inRange('x', x, 0n, P - 1n)`\n  // - our way is the cleanest:               `inRange('x', x, 0n, P)\n  if (!inRange(n, min, max))\n    throw new Error('expected valid ' + title + ': ' + min + ' <= n < ' + max + ', got ' + n);\n}\n\n// Bit operations\n\n/**\n * Calculates amount of bits in a bigint.\n * Same as `n.toString(2).length`\n * TODO: merge with nLength in modular\n */\nexport function bitLen(n: bigint): number {\n  let len;\n  for (len = 0; n > _0n; n >>= _1n, len += 1);\n  return len;\n}\n\n/**\n * Gets single bit at position.\n * NOTE: first bit position is 0 (same as arrays)\n * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`\n */\nexport function bitGet(n: bigint, pos: number): bigint {\n  return (n >> BigInt(pos)) & _1n;\n}\n\n/**\n * Sets single bit at position.\n */\nexport function bitSet(n: bigint, pos: number, value: boolean): bigint {\n  return n | ((value ? _1n : _0n) << BigInt(pos));\n}\n\n/**\n * Calculate mask for N bits. Not using ** operator with bigints because of old engines.\n * Same as BigInt(`0b${Array(i).fill('1').join('')}`)\n */\nexport const bitMask = (n: number): bigint => (_1n << BigInt(n)) - _1n;\n\n// DRBG\n\nconst u8n = (len: number) => new Uint8Array(len); // creates Uint8Array\nconst u8fr = (arr: ArrayLike<number>) => Uint8Array.from(arr); // another shortcut\ntype Pred<T> = (v: Uint8Array) => T | undefined;\n/**\n * Minimal HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n * @returns function that will call DRBG until 2nd arg returns something meaningful\n * @example\n *   const drbg = createHmacDRBG<Key>(32, 32, hmac);\n *   drbg(seed, bytesToKey); // bytesToKey must return Key or undefined\n */\nexport function createHmacDrbg<T>(\n  hashLen: number,\n  qByteLen: number,\n  hmacFn: (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array\n): (seed: Uint8Array, predicate: Pred<T>) => T {\n  if (typeof hashLen !== 'number' || hashLen < 2) throw new Error('hashLen must be a number');\n  if (typeof qByteLen !== 'number' || qByteLen < 2) throw new Error('qByteLen must be a number');\n  if (typeof hmacFn !== 'function') throw new Error('hmacFn must be a function');\n  // Step B, Step C: set hashLen to 8*ceil(hlen/8)\n  let v = u8n(hashLen); // Minimal non-full-spec HMAC-DRBG from NIST 800-90 for RFC6979 sigs.\n  let k = u8n(hashLen); // Steps B and C of RFC6979 3.2: set hashLen, in our case always same\n  let i = 0; // Iterations counter, will throw when over 1000\n  const reset = () => {\n    v.fill(1);\n    k.fill(0);\n    i = 0;\n  };\n  const h = (...b: Uint8Array[]) => hmacFn(k, v, ...b); // hmac(k)(v, ...values)\n  const reseed = (seed = u8n(0)) => {\n    // HMAC-DRBG reseed() function. Steps D-G\n    k = h(u8fr([0x00]), seed); // k = hmac(k || v || 0x00 || seed)\n    v = h(); // v = hmac(k || v)\n    if (seed.length === 0) return;\n    k = h(u8fr([0x01]), seed); // k = hmac(k || v || 0x01 || seed)\n    v = h(); // v = hmac(k || v)\n  };\n  const gen = () => {\n    // HMAC-DRBG generate() function\n    if (i++ >= 1000) throw new Error('drbg: tried 1000 values');\n    let len = 0;\n    const out: Uint8Array[] = [];\n    while (len < qByteLen) {\n      v = h();\n      const sl = v.slice();\n      out.push(sl);\n      len += v.length;\n    }\n    return concatBytes(...out);\n  };\n  const genUntil = (seed: Uint8Array, pred: Pred<T>): T => {\n    reset();\n    reseed(seed); // Steps D-G\n    let res: T | undefined = undefined; // Step H: grind until k is in [1..n-1]\n    while (!(res = pred(gen()))) reseed();\n    reset();\n    return res;\n  };\n  return genUntil;\n}\n\n// Validating curves and fields\n\nconst validatorFns = {\n  bigint: (val: any): boolean => typeof val === 'bigint',\n  function: (val: any): boolean => typeof val === 'function',\n  boolean: (val: any): boolean => typeof val === 'boolean',\n  string: (val: any): boolean => typeof val === 'string',\n  stringOrUint8Array: (val: any): boolean => typeof val === 'string' || isBytes(val),\n  isSafeInteger: (val: any): boolean => Number.isSafeInteger(val),\n  array: (val: any): boolean => Array.isArray(val),\n  field: (val: any, object: any): any => (object as any).Fp.isValid(val),\n  hash: (val: any): boolean => typeof val === 'function' && Number.isSafeInteger(val.outputLen),\n} as const;\ntype Validator = keyof typeof validatorFns;\ntype ValMap<T extends Record<string, any>> = { [K in keyof T]?: Validator };\n// type Record<K extends string | number | symbol, T> = { [P in K]: T; }\n\nexport function validateObject<T extends Record<string, any>>(\n  object: T,\n  validators: ValMap<T>,\n  optValidators: ValMap<T> = {}\n): T {\n  const checkField = (fieldName: keyof T, type: Validator, isOptional: boolean) => {\n    const checkVal = validatorFns[type];\n    if (typeof checkVal !== 'function') throw new Error('invalid validator function');\n\n    const val = object[fieldName as keyof typeof object];\n    if (isOptional && val === undefined) return;\n    if (!checkVal(val, object)) {\n      throw new Error(\n        'param ' + String(fieldName) + ' is invalid. Expected ' + type + ', got ' + val\n      );\n    }\n  };\n  for (const [fieldName, type] of Object.entries(validators)) checkField(fieldName, type!, false);\n  for (const [fieldName, type] of Object.entries(optValidators)) checkField(fieldName, type!, true);\n  return object;\n}\n// validate type tests\n// const o: { a: number; b: number; c: number } = { a: 1, b: 5, c: 6 };\n// const z0 = validateObject(o, { a: 'isSafeInteger' }, { c: 'bigint' }); // Ok!\n// // Should fail type-check\n// const z1 = validateObject(o, { a: 'tmp' }, { c: 'zz' });\n// const z2 = validateObject(o, { a: 'isSafeInteger' }, { c: 'zz' });\n// const z3 = validateObject(o, { test: 'boolean', z: 'bug' });\n// const z4 = validateObject(o, { a: 'boolean', z: 'bug' });\n\n/**\n * throws not implemented error\n */\nexport const notImplemented = (): never => {\n  throw new Error('not implemented');\n};\n\n/**\n * Memoizes (caches) computation result.\n * Uses WeakMap: the value is going auto-cleaned by GC after last reference is removed.\n */\nexport function memoized<T extends object, R, O extends any[]>(\n  fn: (arg: T, ...args: O) => R\n): (arg: T, ...args: O) => R {\n  const map = new WeakMap<T, R>();\n  return (arg: T, ...args: O): R => {\n    const val = map.get(arg);\n    if (val !== undefined) return val;\n    const computed = fn(arg, ...args);\n    map.set(arg, computed);\n    return computed;\n  };\n}\n", "/**\n * Utils for modular division and finite fields.\n * A finite field over 11 is integer number operations `mod 11`.\n * There is no division: it is replaced by modular multiplicative inverse.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { anumber } from '@noble/hashes/utils';\nimport {\n  bitMask,\n  bytesToNumberBE,\n  bytesToNumberLE,\n  ensureBytes,\n  numberToBytesBE,\n  numberToBytesLE,\n  validateObject,\n} from './utils.ts';\n\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _3n = /* @__PURE__ */ BigInt(3);\n// prettier-ignore\nconst _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5), _8n = /* @__PURE__ */ BigInt(8);\n// prettier-ignore\nconst _9n =/* @__PURE__ */ BigInt(9), _16n = /* @__PURE__ */ BigInt(16);\n\n// Calculates a modulo b\nexport function mod(a: bigint, b: bigint): bigint {\n  const result = a % b;\n  return result >= _0n ? result : b + result;\n}\n/**\n * Efficiently raise num to power and do modular division.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n * TODO: remove.\n * @example\n * pow(2n, 6n, 11n) // 64n % 11n == 9n\n */\nexport function pow(num: bigint, power: bigint, modulo: bigint): bigint {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (modulo <= _0n) throw new Error('invalid modulus');\n  if (modulo === _1n) return _0n;\n  let res = _1n;\n  while (power > _0n) {\n    if (power & _1n) res = (res * num) % modulo;\n    num = (num * num) % modulo;\n    power >>= _1n;\n  }\n  return res;\n}\n\n/** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */\nexport function pow2(x: bigint, power: bigint, modulo: bigint): bigint {\n  let res = x;\n  while (power-- > _0n) {\n    res *= res;\n    res %= modulo;\n  }\n  return res;\n}\n\n/**\n * Inverses number over modulo.\n * Implemented using [Euclidean GCD](https://brilliant.org/wiki/extended-euclidean-algorithm/).\n */\nexport function invert(number: bigint, modulo: bigint): bigint {\n  if (number === _0n) throw new Error('invert: expected non-zero number');\n  if (modulo <= _0n) throw new Error('invert: expected positive modulus, got ' + modulo);\n  // Fermat's little theorem \"CT-like\" version inv(n) = n^(m-2) mod m is 30x slower.\n  let a = mod(number, modulo);\n  let b = modulo;\n  // prettier-ignore\n  let x = _0n, y = _1n, u = _1n, v = _0n;\n  while (a !== _0n) {\n    // JIT applies optimization if those two lines follow each other\n    const q = b / a;\n    const r = b % a;\n    const m = x - u * q;\n    const n = y - v * q;\n    // prettier-ignore\n    b = a, a = r, x = u, y = v, u = m, v = n;\n  }\n  const gcd = b;\n  if (gcd !== _1n) throw new Error('invert: does not exist');\n  return mod(x, modulo);\n}\n\n/**\n * Tonelli-Shanks square root search algorithm.\n * 1. https://eprint.iacr.org/2012/685.pdf (page 12)\n * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks\n * @param P field order\n * @returns function that takes field Fp (created from P) and number n\n */\nexport function tonelliShanks(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // Do expensive precomputation step\n  // Step 1: By factoring out powers of 2 from p - 1,\n  // find q and s such that p-1 == q*(2^s) with q odd\n  let Q = P - _1n;\n  let S = 0;\n  while (Q % _2n === _0n) {\n    Q /= _2n;\n    S++;\n  }\n\n  // Step 2: Select a non-square z such that (z | p) \u2261 -1 and set c \u2261 zq\n  let Z = _2n;\n  const _Fp = Field(P);\n  while (Z < P && FpIsSquare(_Fp, Z)) {\n    if (Z++ > 1000) throw new Error('Cannot find square root: probably non-prime P');\n  }\n\n  // Fast-path\n  if (S === 1) {\n    const p1div4 = (P + _1n) / _4n;\n    return function tonelliFast<T>(Fp: IField<T>, n: T) {\n      const root = Fp.pow(n, p1div4);\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n  // Slow-path\n  const Q1div2 = (Q + _1n) / _2n;\n  return function tonelliSlow<T>(Fp: IField<T>, n: T): T {\n    // Step 0: Check that n is indeed a square: (n | p) should not be \u2261 -1\n    if (!FpIsSquare(Fp, n)) throw new Error('Cannot find square root');\n    let r = S;\n    // TODO: test on Fp2 and others\n    let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b\n    let x = Fp.pow(n, Q1div2); // first guess at the square root\n    let b = Fp.pow(n, Q); // first guess at the fudge factor\n\n    while (!Fp.eql(b, Fp.ONE)) {\n      // (4. If t = 0, return r = 0)\n      // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm\n      if (Fp.eql(b, Fp.ZERO)) return Fp.ZERO;\n      // Find m such b^(2^m)==1\n      let m = 1;\n      for (let t2 = Fp.sqr(b); m < r; m++) {\n        if (Fp.eql(t2, Fp.ONE)) break;\n        t2 = Fp.sqr(t2); // t2 *= t2\n      }\n      // NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift,\n      // otherwise there will be overflow.\n      const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)\n      g = Fp.sqr(ge); // g = ge * ge\n      x = Fp.mul(x, ge); // x *= ge\n      b = Fp.mul(b, g); // b *= g\n      r = m;\n    }\n    return x;\n  };\n}\n\n/**\n * Square root for a finite field. It will try to check if optimizations are applicable and fall back to 4:\n *\n * 1. P \u2261 3 (mod 4)\n * 2. P \u2261 5 (mod 8)\n * 3. P \u2261 9 (mod 16)\n * 4. Tonelli-Shanks algorithm\n *\n * Different algorithms can give different roots, it is up to user to decide which one they want.\n * For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).\n */\nexport function FpSqrt(P: bigint): <T>(Fp: IField<T>, n: T) => T {\n  // P \u2261 3 (mod 4)\n  // \u221An = n^((P+1)/4)\n  if (P % _4n === _3n) {\n    // Not all roots possible!\n    // const ORDER =\n    //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;\n    // const NUM = 72057594037927816n;\n    return function sqrt3mod4<T>(Fp: IField<T>, n: T) {\n      const p1div4 = (P + _1n) / _4n;\n      const root = Fp.pow(n, p1div4);\n      // Throw if root**2 != n\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // Atkin algorithm for q \u2261 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)\n  if (P % _8n === _5n) {\n    return function sqrt5mod8<T>(Fp: IField<T>, n: T) {\n      const n2 = Fp.mul(n, _2n);\n      const c1 = (P - _5n) / _8n;\n      const v = Fp.pow(n2, c1);\n      const nv = Fp.mul(n, v);\n      const i = Fp.mul(Fp.mul(nv, _2n), v);\n      const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));\n      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n      return root;\n    };\n  }\n\n  // P \u2261 9 (mod 16)\n  if (P % _16n === _9n) {\n    // NOTE: tonelli is too slow for bls-Fp2 calculations even on start\n    // Means we cannot use sqrt for constants at all!\n    //\n    // const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F\n    // const c2 = Fp.sqrt(c1);                //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F\n    // const c3 = Fp.sqrt(Fp.negate(c1));     //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F\n    // const c4 = (P + _7n) / _16n;           //  4. c4 = (q + 7) / 16        # Integer arithmetic\n    // sqrt = (x) => {\n    //   let tv1 = Fp.pow(x, c4);             //  1. tv1 = x^c4\n    //   let tv2 = Fp.mul(c1, tv1);           //  2. tv2 = c1 * tv1\n    //   const tv3 = Fp.mul(c2, tv1);         //  3. tv3 = c2 * tv1\n    //   let tv4 = Fp.mul(c3, tv1);           //  4. tv4 = c3 * tv1\n    //   const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x\n    //   const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x\n    //   tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x\n    //   tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x\n    //   const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x\n    //   return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2\n    // }\n  }\n  // Other cases: Tonelli-Shanks algorithm\n  return tonelliShanks(P);\n}\n\n// Little-endian check for first LE bit (last BE bit);\nexport const isNegativeLE = (num: bigint, modulo: bigint): boolean =>\n  (mod(num, modulo) & _1n) === _1n;\n\n/** Field is not always over prime: for example, Fp2 has ORDER(q)=p^m. */\nexport interface IField<T> {\n  ORDER: bigint;\n  isLE: boolean;\n  BYTES: number;\n  BITS: number;\n  MASK: bigint;\n  ZERO: T;\n  ONE: T;\n  // 1-arg\n  create: (num: T) => T;\n  isValid: (num: T) => boolean;\n  is0: (num: T) => boolean;\n  neg(num: T): T;\n  inv(num: T): T;\n  sqrt(num: T): T;\n  sqr(num: T): T;\n  // 2-args\n  eql(lhs: T, rhs: T): boolean;\n  add(lhs: T, rhs: T): T;\n  sub(lhs: T, rhs: T): T;\n  mul(lhs: T, rhs: T | bigint): T;\n  pow(lhs: T, power: bigint): T;\n  div(lhs: T, rhs: T | bigint): T;\n  // N for NonNormalized (for now)\n  addN(lhs: T, rhs: T): T;\n  subN(lhs: T, rhs: T): T;\n  mulN(lhs: T, rhs: T | bigint): T;\n  sqrN(num: T): T;\n\n  // Optional\n  // Should be same as sgn0 function in\n  // [RFC9380](https://www.rfc-editor.org/rfc/rfc9380#section-4.1).\n  // NOTE: sgn0 is 'negative in LE', which is same as odd. And negative in LE is kinda strange definition anyway.\n  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2\n  // legendre?(num: T): T;\n  pow(lhs: T, power: bigint): T;\n  invertBatch: (lst: T[]) => T[];\n  toBytes(num: T): Uint8Array;\n  fromBytes(bytes: Uint8Array): T;\n  // If c is False, CMOV returns a, otherwise it returns b.\n  cmov(a: T, b: T, c: boolean): T;\n}\n// prettier-ignore\nconst FIELD_FIELDS = [\n  'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',\n  'eql', 'add', 'sub', 'mul', 'pow', 'div',\n  'addN', 'subN', 'mulN', 'sqrN'\n] as const;\nexport function validateField<T>(field: IField<T>): IField<T> {\n  const initial = {\n    ORDER: 'bigint',\n    MASK: 'bigint',\n    BYTES: 'isSafeInteger',\n    BITS: 'isSafeInteger',\n  } as Record<string, string>;\n  const opts = FIELD_FIELDS.reduce((map, val: string) => {\n    map[val] = 'function';\n    return map;\n  }, initial);\n  return validateObject(field, opts);\n}\n\n// Generic field functions\n\n/**\n * Same as `pow` but for Fp: non-constant-time.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n */\nexport function FpPow<T>(Fp: IField<T>, num: T, power: bigint): T {\n  if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n  if (power === _0n) return Fp.ONE;\n  if (power === _1n) return num;\n  // @ts-ignore\n  let p = Fp.ONE;\n  let d = num;\n  while (power > _0n) {\n    if (power & _1n) p = Fp.mul(p, d);\n    d = Fp.sqr(d);\n    power >>= _1n;\n  }\n  return p;\n}\n\n/**\n * Efficiently invert an array of Field elements.\n * Exception-free. Will return `undefined` for 0 elements.\n * @param passZero map 0 to 0 (instead of undefined)\n */\nexport function FpInvertBatch<T>(Fp: IField<T>, nums: T[], passZero = false): T[] {\n  const inverted = new Array(nums.length).fill(passZero ? Fp.ZERO : undefined);\n  // Walk from first to last, multiply them by each other MOD p\n  const multipliedAcc = nums.reduce((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = acc;\n    return Fp.mul(acc, num);\n  }, Fp.ONE);\n  // Invert last element\n  const invertedAcc = Fp.inv(multipliedAcc);\n  // Walk from last to first, multiply them by inverted each other MOD p\n  nums.reduceRight((acc, num, i) => {\n    if (Fp.is0(num)) return acc;\n    inverted[i] = Fp.mul(acc, inverted[i]);\n    return Fp.mul(acc, num);\n  }, invertedAcc);\n  return inverted;\n}\n\n// TODO: remove\nexport function FpDiv<T>(Fp: IField<T>, lhs: T, rhs: T | bigint): T {\n  return Fp.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, Fp.ORDER) : Fp.inv(rhs));\n}\n\n/**\n * Legendre symbol.\n * Legendre constant is used to calculate Legendre symbol (a | p)\n * which denotes the value of a^((p-1)/2) (mod p)..\n *\n * * (a | p) \u2261 1    if a is a square (mod p), quadratic residue\n * * (a | p) \u2261 -1   if a is not a square (mod p), quadratic non residue\n * * (a | p) \u2261 0    if a \u2261 0 (mod p)\n */\nexport function FpLegendre<T>(Fp: IField<T>, n: T): number {\n  const legc = (Fp.ORDER - _1n) / _2n;\n  const powered = Fp.pow(n, legc);\n  const yes = Fp.eql(powered, Fp.ONE);\n  const zero = Fp.eql(powered, Fp.ZERO);\n  const no = Fp.eql(powered, Fp.neg(Fp.ONE));\n  if (!yes && !zero && !no) throw new Error('Cannot find square root: probably non-prime P');\n  return yes ? 1 : zero ? 0 : -1;\n}\n\n// This function returns True whenever the value x is a square in the field F.\nexport function FpIsSquare<T>(Fp: IField<T>, n: T): boolean {\n  const l = FpLegendre(Fp, n);\n  return l === 0 || l === 1;\n}\n\n// CURVE.n lengths\nexport function nLength(\n  n: bigint,\n  nBitLength?: number\n): {\n  nBitLength: number;\n  nByteLength: number;\n} {\n  // Bit size, byte size of CURVE.n\n  if (nBitLength !== undefined) anumber(nBitLength);\n  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;\n  const nByteLength = Math.ceil(_nBitLength / 8);\n  return { nBitLength: _nBitLength, nByteLength };\n}\n\ntype FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;\n/**\n * Initializes a finite field over prime.\n * Major performance optimizations:\n * * a) denormalized operations like mulN instead of mul\n * * b) same object shape: never add or remove keys\n * * c) Object.freeze\n * Fragile: always run a benchmark on a change.\n * Security note: operations don't check 'isValid' for all elements for performance reasons,\n * it is caller responsibility to check this.\n * This is low-level code, please make sure you know what you're doing.\n * @param ORDER prime positive bigint\n * @param bitLen how many bits the field consumes\n * @param isLE (def: false) if encoding / decoding should be in little-endian\n * @param redef optional faster redefinitions of sqrt and other methods\n */\nexport function Field(\n  ORDER: bigint,\n  bitLen?: number,\n  isLE = false,\n  redef: Partial<IField<bigint>> = {}\n): Readonly<FpField> {\n  if (ORDER <= _0n) throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);\n  const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);\n  if (BYTES > 2048) throw new Error('invalid field: expected ORDER of <= 2048 bytes');\n  let sqrtP: ReturnType<typeof FpSqrt>; // cached sqrtP\n  const f: Readonly<FpField> = Object.freeze({\n    ORDER,\n    isLE,\n    BITS,\n    BYTES,\n    MASK: bitMask(BITS),\n    ZERO: _0n,\n    ONE: _1n,\n    create: (num) => mod(num, ORDER),\n    isValid: (num) => {\n      if (typeof num !== 'bigint')\n        throw new Error('invalid field element: expected bigint, got ' + typeof num);\n      return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible\n    },\n    is0: (num) => num === _0n,\n    isOdd: (num) => (num & _1n) === _1n,\n    neg: (num) => mod(-num, ORDER),\n    eql: (lhs, rhs) => lhs === rhs,\n\n    sqr: (num) => mod(num * num, ORDER),\n    add: (lhs, rhs) => mod(lhs + rhs, ORDER),\n    sub: (lhs, rhs) => mod(lhs - rhs, ORDER),\n    mul: (lhs, rhs) => mod(lhs * rhs, ORDER),\n    pow: (num, power) => FpPow(f, num, power),\n    div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),\n\n    // Same as above, but doesn't normalize\n    sqrN: (num) => num * num,\n    addN: (lhs, rhs) => lhs + rhs,\n    subN: (lhs, rhs) => lhs - rhs,\n    mulN: (lhs, rhs) => lhs * rhs,\n\n    inv: (num) => invert(num, ORDER),\n    sqrt:\n      redef.sqrt ||\n      ((n) => {\n        if (!sqrtP) sqrtP = FpSqrt(ORDER);\n        return sqrtP(f, n);\n      }),\n    toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),\n    fromBytes: (bytes) => {\n      if (bytes.length !== BYTES)\n        throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);\n      return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);\n    },\n    // TODO: we don't need it here, move out to separate fn\n    invertBatch: (lst) => FpInvertBatch(f, lst),\n    // We can't move this out because Fp6, Fp12 implement it\n    // and it's unclear what to return in there.\n    cmov: (a, b, c) => (c ? b : a),\n  } as FpField);\n  return Object.freeze(f);\n}\n\nexport function FpSqrtOdd<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n  const root = Fp.sqrt(elm);\n  return Fp.isOdd(root) ? root : Fp.neg(root);\n}\n\nexport function FpSqrtEven<T>(Fp: IField<T>, elm: T): T {\n  if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n  const root = Fp.sqrt(elm);\n  return Fp.isOdd(root) ? Fp.neg(root) : root;\n}\n\n/**\n * \"Constant-time\" private key generation utility.\n * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).\n * Which makes it slightly more biased, less secure.\n * @deprecated use `mapKeyToField` instead\n */\nexport function hashToPrivateScalar(\n  hash: string | Uint8Array,\n  groupOrder: bigint,\n  isLE = false\n): bigint {\n  hash = ensureBytes('privateHash', hash);\n  const hashLen = hash.length;\n  const minLen = nLength(groupOrder).nByteLength + 8;\n  if (minLen < 24 || hashLen < minLen || hashLen > 1024)\n    throw new Error(\n      'hashToPrivateScalar: expected ' + minLen + '-1024 bytes of input, got ' + hashLen\n    );\n  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);\n  return mod(num, groupOrder - _1n) + _1n;\n}\n\n/**\n * Returns total number of bytes consumed by the field element.\n * For example, 32 bytes for usual 256-bit weierstrass curve.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of field\n */\nexport function getFieldBytesLength(fieldOrder: bigint): number {\n  if (typeof fieldOrder !== 'bigint') throw new Error('field order must be bigint');\n  const bitLength = fieldOrder.toString(2).length;\n  return Math.ceil(bitLength / 8);\n}\n\n/**\n * Returns minimal amount of bytes that can be safely reduced\n * by field order.\n * Should be 2^-128 for 128-bit curve such as P256.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of target hash\n */\nexport function getMinHashLength(fieldOrder: bigint): number {\n  const length = getFieldBytesLength(fieldOrder);\n  return length + Math.ceil(length / 2);\n}\n\n/**\n * \"Constant-time\" private key generation utility.\n * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF\n * and convert them into private scalar, with the modulo bias being negligible.\n * Needs at least 48 bytes of input for 32-byte private key.\n * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/\n * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final\n * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5\n * @param hash hash output from SHA3 or a similar function\n * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)\n * @param isLE interpret hash bytes as LE num\n * @returns valid private scalar\n */\nexport function mapHashToField(key: Uint8Array, fieldOrder: bigint, isLE = false): Uint8Array {\n  const len = key.length;\n  const fieldLen = getFieldBytesLength(fieldOrder);\n  const minLen = getMinHashLength(fieldOrder);\n  // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.\n  if (len < 16 || len < minLen || len > 1024)\n    throw new Error('expected ' + minLen + '-1024 bytes of input, got ' + len);\n  const num = isLE ? bytesToNumberLE(key) : bytesToNumberBE(key);\n  // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0\n  const reduced = mod(num, fieldOrder - _1n) + _1n;\n  return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);\n}\n", "/**\n * hash-to-curve from RFC 9380.\n * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.\n * https://www.rfc-editor.org/rfc/rfc9380\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport type { AffinePoint, Group, GroupConstructor } from './curve.ts';\nimport { FpInvertBatch, type IField, mod } from './modular.ts';\nimport type { CHash } from './utils.ts';\nimport { abytes, bytesToNumberBE, concatBytes, utf8ToBytes, validateObject } from './utils.ts';\n\nexport type UnicodeOrBytes = string | Uint8Array;\n\n/**\n * * `DST` is a domain separation tag, defined in section 2.2.5\n * * `p` characteristic of F, where F is a finite field of characteristic p and order q = p^m\n * * `m` is extension degree (1 for prime fields)\n * * `k` is the target security target in bits (e.g. 128), from section 5.1\n * * `expand` is `xmd` (SHA2, SHA3, BLAKE) or `xof` (SHAKE, BLAKE-XOF)\n * * `hash` conforming to `utils.CHash` interface, with `outputLen` / `blockLen` props\n */\nexport type Opts = {\n  DST: UnicodeOrBytes;\n  p: bigint;\n  m: number;\n  k: number;\n  expand: 'xmd' | 'xof';\n  hash: CHash;\n};\n\n// Octet Stream to Integer. \"spec\" implementation of os2ip is 2.5x slower vs bytesToNumberBE.\nconst os2ip = bytesToNumberBE;\n\n// Integer to Octet Stream (numberToBytesBE)\nfunction i2osp(value: number, length: number): Uint8Array {\n  anum(value);\n  anum(length);\n  if (value < 0 || value >= 1 << (8 * length)) throw new Error('invalid I2OSP input: ' + value);\n  const res = Array.from({ length }).fill(0) as number[];\n  for (let i = length - 1; i >= 0; i--) {\n    res[i] = value & 0xff;\n    value >>>= 8;\n  }\n  return new Uint8Array(res);\n}\n\nfunction strxor(a: Uint8Array, b: Uint8Array): Uint8Array {\n  const arr = new Uint8Array(a.length);\n  for (let i = 0; i < a.length; i++) {\n    arr[i] = a[i] ^ b[i];\n  }\n  return arr;\n}\n\nfunction anum(item: unknown): void {\n  if (!Number.isSafeInteger(item)) throw new Error('number expected');\n}\n\n/**\n * Produces a uniformly random byte string using a cryptographic hash function H that outputs b bits.\n * [RFC 9380 5.3.1](https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1).\n */\nexport function expand_message_xmd(\n  msg: Uint8Array,\n  DST: Uint8Array,\n  lenInBytes: number,\n  H: CHash\n): Uint8Array {\n  abytes(msg);\n  abytes(DST);\n  anum(lenInBytes);\n  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n  if (DST.length > 255) DST = H(concatBytes(utf8ToBytes('H2C-OVERSIZE-DST-'), DST));\n  const { outputLen: b_in_bytes, blockLen: r_in_bytes } = H;\n  const ell = Math.ceil(lenInBytes / b_in_bytes);\n  if (lenInBytes > 65535 || ell > 255) throw new Error('expand_message_xmd: invalid lenInBytes');\n  const DST_prime = concatBytes(DST, i2osp(DST.length, 1));\n  const Z_pad = i2osp(0, r_in_bytes);\n  const l_i_b_str = i2osp(lenInBytes, 2); // len_in_bytes_str\n  const b = new Array<Uint8Array>(ell);\n  const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));\n  b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));\n  for (let i = 1; i <= ell; i++) {\n    const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];\n    b[i] = H(concatBytes(...args));\n  }\n  const pseudo_random_bytes = concatBytes(...b);\n  return pseudo_random_bytes.slice(0, lenInBytes);\n}\n\n/**\n * Produces a uniformly random byte string using an extendable-output function (XOF) H.\n * 1. The collision resistance of H MUST be at least k bits.\n * 2. H MUST be an XOF that has been proved indifferentiable from\n *    a random oracle under a reasonable cryptographic assumption.\n * [RFC 9380 5.3.2](https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2).\n */\nexport function expand_message_xof(\n  msg: Uint8Array,\n  DST: Uint8Array,\n  lenInBytes: number,\n  k: number,\n  H: CHash\n): Uint8Array {\n  abytes(msg);\n  abytes(DST);\n  anum(lenInBytes);\n  // https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3\n  // DST = H('H2C-OVERSIZE-DST-' || a_very_long_DST, Math.ceil((lenInBytes * k) / 8));\n  if (DST.length > 255) {\n    const dkLen = Math.ceil((2 * k) / 8);\n    DST = H.create({ dkLen }).update(utf8ToBytes('H2C-OVERSIZE-DST-')).update(DST).digest();\n  }\n  if (lenInBytes > 65535 || DST.length > 255)\n    throw new Error('expand_message_xof: invalid lenInBytes');\n  return (\n    H.create({ dkLen: lenInBytes })\n      .update(msg)\n      .update(i2osp(lenInBytes, 2))\n      // 2. DST_prime = DST || I2OSP(len(DST), 1)\n      .update(DST)\n      .update(i2osp(DST.length, 1))\n      .digest()\n  );\n}\n\n/**\n * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.\n * [RFC 9380 5.2](https://www.rfc-editor.org/rfc/rfc9380#section-5.2).\n * @param msg a byte string containing the message to hash\n * @param count the number of elements of F to output\n * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`, see above\n * @returns [u_0, ..., u_(count - 1)], a list of field elements.\n */\nexport function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][] {\n  validateObject(options, {\n    DST: 'stringOrUint8Array',\n    p: 'bigint',\n    m: 'isSafeInteger',\n    k: 'isSafeInteger',\n    hash: 'hash',\n  });\n  const { p, k, m, hash, expand, DST: _DST } = options;\n  abytes(msg);\n  anum(count);\n  const DST = typeof _DST === 'string' ? utf8ToBytes(_DST) : _DST;\n  const log2p = p.toString(2).length;\n  const L = Math.ceil((log2p + k) / 8); // section 5.1 of ietf draft link above\n  const len_in_bytes = count * m * L;\n  let prb; // pseudo_random_bytes\n  if (expand === 'xmd') {\n    prb = expand_message_xmd(msg, DST, len_in_bytes, hash);\n  } else if (expand === 'xof') {\n    prb = expand_message_xof(msg, DST, len_in_bytes, k, hash);\n  } else if (expand === '_internal_pass') {\n    // for internal tests only\n    prb = msg;\n  } else {\n    throw new Error('expand must be \"xmd\" or \"xof\"');\n  }\n  const u = new Array(count);\n  for (let i = 0; i < count; i++) {\n    const e = new Array(m);\n    for (let j = 0; j < m; j++) {\n      const elm_offset = L * (j + i * m);\n      const tv = prb.subarray(elm_offset, elm_offset + L);\n      e[j] = mod(os2ip(tv), p);\n    }\n    u[i] = e;\n  }\n  return u;\n}\n\nexport type XY<T> = (x: T, y: T) => { x: T; y: T };\nexport type XYRatio<T> = [T[], T[], T[], T[]]; // xn/xd, yn/yd\nexport function isogenyMap<T, F extends IField<T>>(field: F, map: XYRatio<T>): XY<T> {\n  // Make same order as in spec\n  const coeff = map.map((i) => Array.from(i).reverse());\n  return (x: T, y: T) => {\n    const [xn, xd, yn, yd] = coeff.map((val) =>\n      val.reduce((acc, i) => field.add(field.mul(acc, x), i))\n    );\n    // 6.6.3\n    // Exceptional cases of iso_map are inputs that cause the denominator of\n    // either rational function to evaluate to zero; such cases MUST return\n    // the identity point on E.\n    const [xd_inv, yd_inv] = FpInvertBatch(field, [xd, yd], true);\n    x = field.mul(xn, xd_inv); // xNum / xDen\n    y = field.mul(y, field.mul(yn, yd_inv)); // y * (yNum / yDev)\n    return { x, y };\n  };\n}\n\n/** Point interface, which curves must implement to work correctly with the module. */\nexport interface H2CPoint<T> extends Group<H2CPoint<T>> {\n  add(rhs: H2CPoint<T>): H2CPoint<T>;\n  toAffine(iz?: bigint): AffinePoint<T>;\n  clearCofactor(): H2CPoint<T>;\n  assertValidity(): void;\n}\n\nexport interface H2CPointConstructor<T> extends GroupConstructor<H2CPoint<T>> {\n  fromAffine(ap: AffinePoint<T>): H2CPoint<T>;\n}\n\nexport type MapToCurve<T> = (scalar: bigint[]) => AffinePoint<T>;\n\n// Separated from initialization opts, so users won't accidentally change per-curve parameters\n// (changing DST is ok!)\nexport type htfBasicOpts = { DST: UnicodeOrBytes };\nexport type HTFMethod<T> = (msg: Uint8Array, options?: htfBasicOpts) => H2CPoint<T>;\nexport type MapMethod<T> = (scalars: bigint[]) => H2CPoint<T>;\nexport type Hasher<T> = {\n  hashToCurve: HTFMethod<T>;\n  encodeToCurve: HTFMethod<T>;\n  mapToCurve: MapMethod<T>;\n  defaults: Opts & { encodeDST?: UnicodeOrBytes };\n};\n\n/** Creates hash-to-curve methods from EC Point and mapToCurve function. */\nexport function createHasher<T>(\n  Point: H2CPointConstructor<T>,\n  mapToCurve: MapToCurve<T>,\n  defaults: Opts & { encodeDST?: UnicodeOrBytes }\n): Hasher<T> {\n  if (typeof mapToCurve !== 'function') throw new Error('mapToCurve() must be defined');\n  function map(num: bigint[]) {\n    return Point.fromAffine(mapToCurve(num));\n  }\n  function clear(initial: H2CPoint<T>) {\n    const P = initial.clearCofactor();\n    if (P.equals(Point.ZERO)) return Point.ZERO; // zero will throw in assert\n    P.assertValidity();\n    return P;\n  }\n\n  return {\n    defaults,\n\n    // Encodes byte string to elliptic curve.\n    // hash_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n    hashToCurve(msg: Uint8Array, options?: htfBasicOpts): H2CPoint<T> {\n      const u = hash_to_field(msg, 2, { ...defaults, DST: defaults.DST, ...options } as Opts);\n      const u0 = map(u[0]);\n      const u1 = map(u[1]);\n      return clear(u0.add(u1));\n    },\n\n    // Encodes byte string to elliptic curve.\n    // encode_to_curve from https://www.rfc-editor.org/rfc/rfc9380#section-3\n    encodeToCurve(msg: Uint8Array, options?: htfBasicOpts): H2CPoint<T> {\n      const u = hash_to_field(msg, 1, { ...defaults, DST: defaults.encodeDST, ...options } as Opts);\n      return clear(map(u[0]));\n    },\n\n    // Same as encodeToCurve, but without hash\n    mapToCurve(scalars: bigint[]): H2CPoint<T> {\n      if (!Array.isArray(scalars)) throw new Error('expected array of bigints');\n      for (const i of scalars)\n        if (typeof i !== 'bigint') throw new Error('expected array of bigints');\n      return clear(map(scalars));\n    },\n  };\n}\n", "/**\n * Methods for elliptic curve multiplication by scalars.\n * Contains wNAF, pippenger\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { type IField, nLength, validateField } from './modular.ts';\nimport { bitLen, bitMask, validateObject } from './utils.ts';\n\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\n\nexport type AffinePoint<T> = {\n  x: T;\n  y: T;\n} & { z?: never; t?: never };\n\nexport interface Group<T extends Group<T>> {\n  double(): T;\n  negate(): T;\n  add(other: T): T;\n  subtract(other: T): T;\n  equals(other: T): boolean;\n  multiply(scalar: bigint): T;\n}\n\nexport type GroupConstructor<T> = {\n  BASE: T;\n  ZERO: T;\n};\nexport type Mapper<T> = (i: T[]) => T[];\n\nfunction constTimeNegate<T extends Group<T>>(condition: boolean, item: T): T {\n  const neg = item.negate();\n  return condition ? neg : item;\n}\n\nfunction validateW(W: number, bits: number) {\n  if (!Number.isSafeInteger(W) || W <= 0 || W > bits)\n    throw new Error('invalid window size, expected [1..' + bits + '], got W=' + W);\n}\n\n/** Internal wNAF opts for specific W and scalarBits */\nexport type WOpts = {\n  windows: number;\n  windowSize: number;\n  mask: bigint;\n  maxNumber: number;\n  shiftBy: bigint;\n};\n\nfunction calcWOpts(W: number, scalarBits: number): WOpts {\n  validateW(W, scalarBits);\n  const windows = Math.ceil(scalarBits / W) + 1; // W=8 33. Not 32, because we skip zero\n  const windowSize = 2 ** (W - 1); // W=8 128. Not 256, because we skip zero\n  const maxNumber = 2 ** W; // W=8 256\n  const mask = bitMask(W); // W=8 255 == mask 0b11111111\n  const shiftBy = BigInt(W); // W=8 8\n  return { windows, windowSize, mask, maxNumber, shiftBy };\n}\n\nfunction calcOffsets(n: bigint, window: number, wOpts: WOpts) {\n  const { windowSize, mask, maxNumber, shiftBy } = wOpts;\n  let wbits = Number(n & mask); // extract W bits.\n  let nextN = n >> shiftBy; // shift number by W bits.\n\n  // What actually happens here:\n  // const highestBit = Number(mask ^ (mask >> 1n));\n  // let wbits2 = wbits - 1; // skip zero\n  // if (wbits2 & highestBit) { wbits2 ^= Number(mask); // (~);\n\n  // split if bits > max: +224 => 256-32\n  if (wbits > windowSize) {\n    // we skip zero, which means instead of `>= size-1`, we do `> size`\n    wbits -= maxNumber; // -32, can be maxNumber - wbits, but then we need to set isNeg here.\n    nextN += _1n; // +256 (carry)\n  }\n  const offsetStart = window * windowSize;\n  const offset = offsetStart + Math.abs(wbits) - 1; // -1 because we skip zero\n  const isZero = wbits === 0; // is current window slice a 0?\n  const isNeg = wbits < 0; // is current window slice negative?\n  const isNegF = window % 2 !== 0; // fake random statement for noise\n  const offsetF = offsetStart; // fake offset for noise\n  return { nextN, offset, isZero, isNeg, isNegF, offsetF };\n}\n\nfunction validateMSMPoints(points: any[], c: any) {\n  if (!Array.isArray(points)) throw new Error('array expected');\n  points.forEach((p, i) => {\n    if (!(p instanceof c)) throw new Error('invalid point at index ' + i);\n  });\n}\nfunction validateMSMScalars(scalars: any[], field: any) {\n  if (!Array.isArray(scalars)) throw new Error('array of scalars expected');\n  scalars.forEach((s, i) => {\n    if (!field.isValid(s)) throw new Error('invalid scalar at index ' + i);\n  });\n}\n\n// Since points in different groups cannot be equal (different object constructor),\n// we can have single place to store precomputes.\n// Allows to make points frozen / immutable.\nconst pointPrecomputes = new WeakMap<any, any[]>();\nconst pointWindowSizes = new WeakMap<any, number>();\n\nfunction getW(P: any): number {\n  return pointWindowSizes.get(P) || 1;\n}\n\nexport type IWNAF<T extends Group<T>> = {\n  constTimeNegate: <T extends Group<T>>(condition: boolean, item: T) => T;\n  hasPrecomputes(elm: T): boolean;\n  unsafeLadder(elm: T, n: bigint, p?: T): T;\n  precomputeWindow(elm: T, W: number): Group<T>[];\n  getPrecomputes(W: number, P: T, transform: Mapper<T>): T[];\n  wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T };\n  wNAFUnsafe(W: number, precomputes: T[], n: bigint, acc?: T): T;\n  wNAFCached(P: T, n: bigint, transform: Mapper<T>): { p: T; f: T };\n  wNAFCachedUnsafe(P: T, n: bigint, transform: Mapper<T>, prev?: T): T;\n  setWindowSize(P: T, W: number): void;\n};\n\n/**\n * Elliptic curve multiplication of Point by scalar. Fragile.\n * Scalars should always be less than curve order: this should be checked inside of a curve itself.\n * Creates precomputation tables for fast multiplication:\n * - private scalar is split by fixed size windows of W bits\n * - every window point is collected from window's table & added to accumulator\n * - since windows are different, same point inside tables won't be accessed more than once per calc\n * - each multiplication is 'Math.ceil(CURVE_ORDER / \uD835\uDC4A) + 1' point additions (fixed for any scalar)\n * - +1 window is neccessary for wNAF\n * - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication\n *\n * @todo Research returning 2d JS array of windows, instead of a single window.\n * This would allow windows to be in different memory locations\n */\nexport function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number): IWNAF<T> {\n  return {\n    constTimeNegate,\n\n    hasPrecomputes(elm: T) {\n      return getW(elm) !== 1;\n    },\n\n    // non-const time multiplication ladder\n    unsafeLadder(elm: T, n: bigint, p = c.ZERO) {\n      let d: T = elm;\n      while (n > _0n) {\n        if (n & _1n) p = p.add(d);\n        d = d.double();\n        n >>= _1n;\n      }\n      return p;\n    },\n\n    /**\n     * Creates a wNAF precomputation window. Used for caching.\n     * Default window size is set by `utils.precompute()` and is equal to 8.\n     * Number of precomputed points depends on the curve size:\n     * 2^(\uD835\uDC4A\u22121) * (Math.ceil(\uD835\uDC5B / \uD835\uDC4A) + 1), where:\n     * - \uD835\uDC4A is the window size\n     * - \uD835\uDC5B is the bitlength of the curve order.\n     * For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.\n     * @param elm Point instance\n     * @param W window size\n     * @returns precomputed point tables flattened to a single array\n     */\n    precomputeWindow(elm: T, W: number): Group<T>[] {\n      const { windows, windowSize } = calcWOpts(W, bits);\n      const points: T[] = [];\n      let p: T = elm;\n      let base = p;\n      for (let window = 0; window < windows; window++) {\n        base = p;\n        points.push(base);\n        // i=1, bc we skip 0\n        for (let i = 1; i < windowSize; i++) {\n          base = base.add(p);\n          points.push(base);\n        }\n        p = base.double();\n      }\n      return points;\n    },\n\n    /**\n     * Implements ec multiplication using precomputed tables and w-ary non-adjacent form.\n     * @param W window size\n     * @param precomputes precomputed tables\n     * @param n scalar (we don't check here, but should be less than curve order)\n     * @returns real and fake (for const-time) points\n     */\n    wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T } {\n      // Smaller version:\n      // https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541\n      // TODO: check the scalar is less than group order?\n      // wNAF behavior is undefined otherwise. But have to carefully remove\n      // other checks before wNAF. ORDER == bits here.\n      // Accumulators\n      let p = c.ZERO;\n      let f = c.BASE;\n      // This code was first written with assumption that 'f' and 'p' will never be infinity point:\n      // since each addition is multiplied by 2 ** W, it cannot cancel each other. However,\n      // there is negate now: it is possible that negated element from low value\n      // would be the same as high element, which will create carry into next window.\n      // It's not obvious how this can fail, but still worth investigating later.\n      const wo = calcWOpts(W, bits);\n      for (let window = 0; window < wo.windows; window++) {\n        // (n === _0n) is handled and not early-exited. isEven and offsetF are used for noise\n        const { nextN, offset, isZero, isNeg, isNegF, offsetF } = calcOffsets(n, window, wo);\n        n = nextN;\n        if (isZero) {\n          // bits are 0: add garbage to fake point\n          // Important part for const-time getPublicKey: add random \"noise\" point to f.\n          f = f.add(constTimeNegate(isNegF, precomputes[offsetF]));\n        } else {\n          // bits are 1: add to result point\n          p = p.add(constTimeNegate(isNeg, precomputes[offset]));\n        }\n      }\n      // Return both real and fake points: JIT won't eliminate f.\n      // At this point there is a way to F be infinity-point even if p is not,\n      // which makes it less const-time: around 1 bigint multiply.\n      return { p, f };\n    },\n\n    /**\n     * Implements ec unsafe (non const-time) multiplication using precomputed tables and w-ary non-adjacent form.\n     * @param W window size\n     * @param precomputes precomputed tables\n     * @param n scalar (we don't check here, but should be less than curve order)\n     * @param acc accumulator point to add result of multiplication\n     * @returns point\n     */\n    wNAFUnsafe(W: number, precomputes: T[], n: bigint, acc: T = c.ZERO): T {\n      const wo = calcWOpts(W, bits);\n      for (let window = 0; window < wo.windows; window++) {\n        if (n === _0n) break; // Early-exit, skip 0 value\n        const { nextN, offset, isZero, isNeg } = calcOffsets(n, window, wo);\n        n = nextN;\n        if (isZero) {\n          // Window bits are 0: skip processing.\n          // Move to next window.\n          continue;\n        } else {\n          const item = precomputes[offset];\n          acc = acc.add(isNeg ? item.negate() : item); // Re-using acc allows to save adds in MSM\n        }\n      }\n      return acc;\n    },\n\n    getPrecomputes(W: number, P: T, transform: Mapper<T>): T[] {\n      // Calculate precomputes on a first run, reuse them after\n      let comp = pointPrecomputes.get(P);\n      if (!comp) {\n        comp = this.precomputeWindow(P, W) as T[];\n        if (W !== 1) pointPrecomputes.set(P, transform(comp));\n      }\n      return comp;\n    },\n\n    wNAFCached(P: T, n: bigint, transform: Mapper<T>): { p: T; f: T } {\n      const W = getW(P);\n      return this.wNAF(W, this.getPrecomputes(W, P, transform), n);\n    },\n\n    wNAFCachedUnsafe(P: T, n: bigint, transform: Mapper<T>, prev?: T): T {\n      const W = getW(P);\n      if (W === 1) return this.unsafeLadder(P, n, prev); // For W=1 ladder is ~x2 faster\n      return this.wNAFUnsafe(W, this.getPrecomputes(W, P, transform), n, prev);\n    },\n\n    // We calculate precomputes for elliptic curve point multiplication\n    // using windowed method. This specifies window size and\n    // stores precomputed values. Usually only base point would be precomputed.\n\n    setWindowSize(P: T, W: number) {\n      validateW(W, bits);\n      pointWindowSizes.set(P, W);\n      pointPrecomputes.delete(P);\n    },\n  };\n}\n\n/**\n * Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).\n * 30x faster vs naive addition on L=4096, 10x faster than precomputes.\n * For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.\n * Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.\n * @param c Curve Point constructor\n * @param fieldN field over CURVE.N - important that it's not over CURVE.P\n * @param points array of L curve points\n * @param scalars array of L scalars (aka private keys / bigints)\n */\nexport function pippenger<T extends Group<T>>(\n  c: GroupConstructor<T>,\n  fieldN: IField<bigint>,\n  points: T[],\n  scalars: bigint[]\n): T {\n  // If we split scalars by some window (let's say 8 bits), every chunk will only\n  // take 256 buckets even if there are 4096 scalars, also re-uses double.\n  // TODO:\n  // - https://eprint.iacr.org/2024/750.pdf\n  // - https://tches.iacr.org/index.php/TCHES/article/view/10287\n  // 0 is accepted in scalars\n  validateMSMPoints(points, c);\n  validateMSMScalars(scalars, fieldN);\n  if (points.length !== scalars.length)\n    throw new Error('arrays of points and scalars must have equal length');\n  const zero = c.ZERO;\n  const wbits = bitLen(BigInt(points.length));\n  const windowSize = wbits > 12 ? wbits - 3 : wbits > 4 ? wbits - 2 : wbits ? 2 : 1; // in bits\n  const MASK = bitMask(windowSize);\n  const buckets = new Array(Number(MASK) + 1).fill(zero); // +1 for zero array\n  const lastBits = Math.floor((fieldN.BITS - 1) / windowSize) * windowSize;\n  let sum = zero;\n  for (let i = lastBits; i >= 0; i -= windowSize) {\n    buckets.fill(zero);\n    for (let j = 0; j < scalars.length; j++) {\n      const scalar = scalars[j];\n      const wbits = Number((scalar >> BigInt(i)) & MASK);\n      buckets[wbits] = buckets[wbits].add(points[j]);\n    }\n    let resI = zero; // not using this will do small speed-up, but will lose ct\n    // Skip first bucket, because it is zero\n    for (let j = buckets.length - 1, sumI = zero; j > 0; j--) {\n      sumI = sumI.add(buckets[j]);\n      resI = resI.add(sumI);\n    }\n    sum = sum.add(resI);\n    if (i !== 0) for (let j = 0; j < windowSize; j++) sum = sum.double();\n  }\n  return sum as T;\n}\n/**\n * Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).\n * @param c Curve Point constructor\n * @param fieldN field over CURVE.N - important that it's not over CURVE.P\n * @param points array of L curve points\n * @returns function which multiplies points with scaars\n */\nexport function precomputeMSMUnsafe<T extends Group<T>>(\n  c: GroupConstructor<T>,\n  fieldN: IField<bigint>,\n  points: T[],\n  windowSize: number\n): (scalars: bigint[]) => T {\n  /**\n   * Performance Analysis of Window-based Precomputation\n   *\n   * Base Case (256-bit scalar, 8-bit window):\n   * - Standard precomputation requires:\n   *   - 31 additions per scalar \u00D7 256 scalars = 7,936 ops\n   *   - Plus 255 summary additions = 8,191 total ops\n   *   Note: Summary additions can be optimized via accumulator\n   *\n   * Chunked Precomputation Analysis:\n   * - Using 32 chunks requires:\n   *   - 255 additions per chunk\n   *   - 256 doublings\n   *   - Total: (255 \u00D7 32) + 256 = 8,416 ops\n   *\n   * Memory Usage Comparison:\n   * Window Size | Standard Points | Chunked Points\n   * ------------|-----------------|---------------\n   *     4-bit   |     520         |      15\n   *     8-bit   |    4,224        |     255\n   *    10-bit   |   13,824        |   1,023\n   *    16-bit   |  557,056        |  65,535\n   *\n   * Key Advantages:\n   * 1. Enables larger window sizes due to reduced memory overhead\n   * 2. More efficient for smaller scalar counts:\n   *    - 16 chunks: (16 \u00D7 255) + 256 = 4,336 ops\n   *    - ~2x faster than standard 8,191 ops\n   *\n   * Limitations:\n   * - Not suitable for plain precomputes (requires 256 constant doublings)\n   * - Performance degrades with larger scalar counts:\n   *   - Optimal for ~256 scalars\n   *   - Less efficient for 4096+ scalars (Pippenger preferred)\n   */\n  validateW(windowSize, fieldN.BITS);\n  validateMSMPoints(points, c);\n  const zero = c.ZERO;\n  const tableSize = 2 ** windowSize - 1; // table size (without zero)\n  const chunks = Math.ceil(fieldN.BITS / windowSize); // chunks of item\n  const MASK = bitMask(windowSize);\n  const tables = points.map((p: T) => {\n    const res = [];\n    for (let i = 0, acc = p; i < tableSize; i++) {\n      res.push(acc);\n      acc = acc.add(p);\n    }\n    return res;\n  });\n  return (scalars: bigint[]): T => {\n    validateMSMScalars(scalars, fieldN);\n    if (scalars.length > points.length)\n      throw new Error('array of scalars must be smaller than array of points');\n    let res = zero;\n    for (let i = 0; i < chunks; i++) {\n      // No need to double if accumulator is still zero.\n      if (res !== zero) for (let j = 0; j < windowSize; j++) res = res.double();\n      const shiftBy = BigInt(chunks * windowSize - (i + 1) * windowSize);\n      for (let j = 0; j < scalars.length; j++) {\n        const n = scalars[j];\n        const curr = Number((n >> shiftBy) & MASK);\n        if (!curr) continue; // skip zero scalars chunks\n        res = res.add(tables[j][curr - 1]);\n      }\n    }\n    return res;\n  };\n}\n\n/**\n * Generic BasicCurve interface: works even for polynomial fields (BLS): P, n, h would be ok.\n * Though generator can be different (Fp2 / Fp6 for BLS).\n */\nexport type BasicCurve<T> = {\n  Fp: IField<T>; // Field over which we'll do calculations (Fp)\n  n: bigint; // Curve order, total count of valid points in the field\n  nBitLength?: number; // bit length of curve order\n  nByteLength?: number; // byte length of curve order\n  h: bigint; // cofactor. we can assign default=1, but users will just ignore it w/o validation\n  hEff?: bigint; // Number to multiply to clear cofactor\n  Gx: T; // base point X coordinate\n  Gy: T; // base point Y coordinate\n  allowInfinityPoint?: boolean; // bls12-381 requires it. ZERO point is valid, but invalid pubkey\n};\n\nexport function validateBasic<FP, T>(\n  curve: BasicCurve<FP> & T\n): Readonly<\n  {\n    readonly nBitLength: number;\n    readonly nByteLength: number;\n  } & BasicCurve<FP> &\n    T & {\n      p: bigint;\n    }\n> {\n  validateField(curve.Fp);\n  validateObject(\n    curve,\n    {\n      n: 'bigint',\n      h: 'bigint',\n      Gx: 'field',\n      Gy: 'field',\n    },\n    {\n      nBitLength: 'isSafeInteger',\n      nByteLength: 'isSafeInteger',\n    }\n  );\n  // Set defaults\n  return Object.freeze({\n    ...nLength(curve.n, curve.nBitLength),\n    ...curve,\n    ...{ p: curve.Fp.ORDER },\n  } as const);\n}\n", "/**\n * Short Weierstrass curve methods. The formula is: y\u00B2 = x\u00B3 + ax + b.\n *\n * ### Parameters\n *\n * To initialize a weierstrass curve, one needs to pass following params:\n *\n * * a: formula param\n * * b: formula param\n * * Fp: finite Field over which we'll do calculations. Can be complex (Fp2, Fp12)\n * * n: Curve prime subgroup order, total count of valid points in the field\n * * Gx: Base point (x, y) aka generator point x coordinate\n * * Gy: ...y coordinate\n * * h: cofactor, usually 1. h*n = curve group order (n is only subgroup order)\n * * lowS: whether to enable (default) or disable \"low-s\" non-malleable signatures\n *\n * ### Design rationale for types\n *\n * * Interaction between classes from different curves should fail:\n *   `k256.Point.BASE.add(p256.Point.BASE)`\n * * For this purpose we want to use `instanceof` operator, which is fast and works during runtime\n * * Different calls of `curve()` would return different classes -\n *   `curve(params) !== curve(params)`: if somebody decided to monkey-patch their curve,\n *   it won't affect others\n *\n * TypeScript can't infer types for classes created inside a function. Classes is one instance\n * of nominative types in TypeScript and interfaces only check for shape, so it's hard to create\n * unique type for every function call.\n *\n * We can use generic types via some param, like curve opts, but that would:\n *     1. Enable interaction between `curve(params)` and `curve(params)` (curves of same params)\n *     which is hard to debug.\n *     2. Params can be generic and we can't enforce them to be constant value:\n *     if somebody creates curve from non-constant params,\n *     it would be allowed to interact with other curves with non-constant params\n *\n * @todo https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// prettier-ignore\nimport {\n  type AffinePoint, type BasicCurve, type Group, type GroupConstructor,\n  pippenger, validateBasic, wNAF\n} from './curve.ts';\n// prettier-ignore\nimport {\n  Field,\n  FpInvertBatch,\n  type IField, getMinHashLength, invert, mapHashToField, mod, validateField\n} from './modular.ts';\n// prettier-ignore\nimport {\n  type CHash, type Hex, type PrivKey,\n  aInRange, abool,\n  bitMask,\n  bytesToHex, bytesToNumberBE, concatBytes, createHmacDrbg, ensureBytes, hexToBytes,\n  inRange, isBytes, memoized, numberToBytesBE, numberToHexUnpadded, validateObject\n} from './utils.ts';\n\nexport type { AffinePoint };\ntype HmacFnSync = (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array;\ntype EndomorphismOpts = {\n  beta: bigint;\n  splitScalar: (k: bigint) => { k1neg: boolean; k1: bigint; k2neg: boolean; k2: bigint };\n};\nexport type BasicWCurve<T> = BasicCurve<T> & {\n  // Params: a, b\n  a: T;\n  b: T;\n\n  // Optional params\n  allowedPrivateKeyLengths?: readonly number[]; // for P521\n  wrapPrivateKey?: boolean; // bls12-381 requires mod(n) instead of rejecting keys >= n\n  endo?: EndomorphismOpts; // Endomorphism options for Koblitz curves\n  // When a cofactor != 1, there can be an effective methods to:\n  // 1. Determine whether a point is torsion-free\n  isTorsionFree?: (c: ProjConstructor<T>, point: ProjPointType<T>) => boolean;\n  // 2. Clear torsion component\n  clearCofactor?: (c: ProjConstructor<T>, point: ProjPointType<T>) => ProjPointType<T>;\n};\n\nexport type Entropy = Hex | boolean;\nexport type SignOpts = { lowS?: boolean; extraEntropy?: Entropy; prehash?: boolean };\nexport type VerOpts = { lowS?: boolean; prehash?: boolean; format?: 'compact' | 'der' | undefined };\n\nfunction validateSigVerOpts(opts: SignOpts | VerOpts) {\n  if (opts.lowS !== undefined) abool('lowS', opts.lowS);\n  if (opts.prehash !== undefined) abool('prehash', opts.prehash);\n}\n\n// Instance for 3d XYZ points\nexport interface ProjPointType<T> extends Group<ProjPointType<T>> {\n  readonly px: T;\n  readonly py: T;\n  readonly pz: T;\n  get x(): T;\n  get y(): T;\n  toAffine(iz?: T): AffinePoint<T>;\n  toHex(isCompressed?: boolean): string;\n  toRawBytes(isCompressed?: boolean): Uint8Array;\n\n  assertValidity(): void;\n  hasEvenY(): boolean;\n  multiplyUnsafe(scalar: bigint): ProjPointType<T>;\n  multiplyAndAddUnsafe(Q: ProjPointType<T>, a: bigint, b: bigint): ProjPointType<T> | undefined;\n  isTorsionFree(): boolean;\n  clearCofactor(): ProjPointType<T>;\n  _setWindowSize(windowSize: number): void;\n}\n// Static methods for 3d XYZ points\nexport interface ProjConstructor<T> extends GroupConstructor<ProjPointType<T>> {\n  new (x: T, y: T, z: T): ProjPointType<T>;\n  fromAffine(p: AffinePoint<T>): ProjPointType<T>;\n  fromHex(hex: Hex): ProjPointType<T>;\n  fromPrivateKey(privateKey: PrivKey): ProjPointType<T>;\n  normalizeZ(points: ProjPointType<T>[]): ProjPointType<T>[];\n  msm(points: ProjPointType<T>[], scalars: bigint[]): ProjPointType<T>;\n}\n\nexport type CurvePointsType<T> = BasicWCurve<T> & {\n  // Bytes\n  fromBytes?: (bytes: Uint8Array) => AffinePoint<T>;\n  toBytes?: (c: ProjConstructor<T>, point: ProjPointType<T>, isCompressed: boolean) => Uint8Array;\n};\n\nexport type CurvePointsTypeWithLength<T> = Readonly<\n  CurvePointsType<T> & { nByteLength: number; nBitLength: number }\n>;\n\nfunction validatePointOpts<T>(curve: CurvePointsType<T>): CurvePointsTypeWithLength<T> {\n  const opts = validateBasic(curve);\n  validateObject(\n    opts,\n    {\n      a: 'field',\n      b: 'field',\n    },\n    {\n      allowedPrivateKeyLengths: 'array',\n      wrapPrivateKey: 'boolean',\n      isTorsionFree: 'function',\n      clearCofactor: 'function',\n      allowInfinityPoint: 'boolean',\n      fromBytes: 'function',\n      toBytes: 'function',\n    }\n  );\n  const { endo, Fp, a } = opts;\n  if (endo) {\n    if (!Fp.eql(a, Fp.ZERO)) {\n      throw new Error('invalid endomorphism, can only be defined for Koblitz curves that have a=0');\n    }\n    if (\n      typeof endo !== 'object' ||\n      typeof endo.beta !== 'bigint' ||\n      typeof endo.splitScalar !== 'function'\n    ) {\n      throw new Error('invalid endomorphism, expected beta: bigint and splitScalar: function');\n    }\n  }\n  return Object.freeze({ ...opts } as const);\n}\n\nexport type CurvePointsRes<T> = {\n  CURVE: ReturnType<typeof validatePointOpts<T>>;\n  ProjectivePoint: ProjConstructor<T>;\n  normPrivateKeyToScalar: (key: PrivKey) => bigint;\n  weierstrassEquation: (x: T) => T;\n  isWithinCurveOrder: (num: bigint) => boolean;\n};\n\nexport class DERErr extends Error {\n  constructor(m = '') {\n    super(m);\n  }\n}\nexport type IDER = {\n  // asn.1 DER encoding utils\n  Err: typeof DERErr;\n  // Basic building block is TLV (Tag-Length-Value)\n  _tlv: {\n    encode: (tag: number, data: string) => string;\n    // v - value, l - left bytes (unparsed)\n    decode(tag: number, data: Uint8Array): { v: Uint8Array; l: Uint8Array };\n  };\n  // https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,\n  // since we always use positive integers here. It must always be empty:\n  // - add zero byte if exists\n  // - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)\n  _int: {\n    encode(num: bigint): string;\n    decode(data: Uint8Array): bigint;\n  };\n  toSig(hex: string | Uint8Array): { r: bigint; s: bigint };\n  hexFromSig(sig: { r: bigint; s: bigint }): string;\n};\n/**\n * ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:\n *\n *     [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]\n *\n * Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html\n */\nexport const DER: IDER = {\n  // asn.1 DER encoding utils\n  Err: DERErr,\n  // Basic building block is TLV (Tag-Length-Value)\n  _tlv: {\n    encode: (tag: number, data: string): string => {\n      const { Err: E } = DER;\n      if (tag < 0 || tag > 256) throw new E('tlv.encode: wrong tag');\n      if (data.length & 1) throw new E('tlv.encode: unpadded data');\n      const dataLen = data.length / 2;\n      const len = numberToHexUnpadded(dataLen);\n      if ((len.length / 2) & 0b1000_0000) throw new E('tlv.encode: long form length too big');\n      // length of length with long form flag\n      const lenLen = dataLen > 127 ? numberToHexUnpadded((len.length / 2) | 0b1000_0000) : '';\n      const t = numberToHexUnpadded(tag);\n      return t + lenLen + len + data;\n    },\n    // v - value, l - left bytes (unparsed)\n    decode(tag: number, data: Uint8Array): { v: Uint8Array; l: Uint8Array } {\n      const { Err: E } = DER;\n      let pos = 0;\n      if (tag < 0 || tag > 256) throw new E('tlv.encode: wrong tag');\n      if (data.length < 2 || data[pos++] !== tag) throw new E('tlv.decode: wrong tlv');\n      const first = data[pos++];\n      const isLong = !!(first & 0b1000_0000); // First bit of first length byte is flag for short/long form\n      let length = 0;\n      if (!isLong) length = first;\n      else {\n        // Long form: [longFlag(1bit), lengthLength(7bit), length (BE)]\n        const lenLen = first & 0b0111_1111;\n        if (!lenLen) throw new E('tlv.decode(long): indefinite length not supported');\n        if (lenLen > 4) throw new E('tlv.decode(long): byte length is too big'); // this will overflow u32 in js\n        const lengthBytes = data.subarray(pos, pos + lenLen);\n        if (lengthBytes.length !== lenLen) throw new E('tlv.decode: length bytes not complete');\n        if (lengthBytes[0] === 0) throw new E('tlv.decode(long): zero leftmost byte');\n        for (const b of lengthBytes) length = (length << 8) | b;\n        pos += lenLen;\n        if (length < 128) throw new E('tlv.decode(long): not minimal encoding');\n      }\n      const v = data.subarray(pos, pos + length);\n      if (v.length !== length) throw new E('tlv.decode: wrong value length');\n      return { v, l: data.subarray(pos + length) };\n    },\n  },\n  // https://crypto.stackexchange.com/a/57734 Leftmost bit of first byte is 'negative' flag,\n  // since we always use positive integers here. It must always be empty:\n  // - add zero byte if exists\n  // - if next byte doesn't have a flag, leading zero is not allowed (minimal encoding)\n  _int: {\n    encode(num: bigint): string {\n      const { Err: E } = DER;\n      if (num < _0n) throw new E('integer: negative integers are not allowed');\n      let hex = numberToHexUnpadded(num);\n      // Pad with zero byte if negative flag is present\n      if (Number.parseInt(hex[0], 16) & 0b1000) hex = '00' + hex;\n      if (hex.length & 1) throw new E('unexpected DER parsing assertion: unpadded hex');\n      return hex;\n    },\n    decode(data: Uint8Array): bigint {\n      const { Err: E } = DER;\n      if (data[0] & 0b1000_0000) throw new E('invalid signature integer: negative');\n      if (data[0] === 0x00 && !(data[1] & 0b1000_0000))\n        throw new E('invalid signature integer: unnecessary leading zero');\n      return bytesToNumberBE(data);\n    },\n  },\n  toSig(hex: string | Uint8Array): { r: bigint; s: bigint } {\n    // parse DER signature\n    const { Err: E, _int: int, _tlv: tlv } = DER;\n    const data = ensureBytes('signature', hex);\n    const { v: seqBytes, l: seqLeftBytes } = tlv.decode(0x30, data);\n    if (seqLeftBytes.length) throw new E('invalid signature: left bytes after parsing');\n    const { v: rBytes, l: rLeftBytes } = tlv.decode(0x02, seqBytes);\n    const { v: sBytes, l: sLeftBytes } = tlv.decode(0x02, rLeftBytes);\n    if (sLeftBytes.length) throw new E('invalid signature: left bytes after parsing');\n    return { r: int.decode(rBytes), s: int.decode(sBytes) };\n  },\n  hexFromSig(sig: { r: bigint; s: bigint }): string {\n    const { _tlv: tlv, _int: int } = DER;\n    const rs = tlv.encode(0x02, int.encode(sig.r));\n    const ss = tlv.encode(0x02, int.encode(sig.s));\n    const seq = rs + ss;\n    return tlv.encode(0x30, seq);\n  },\n};\n\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);\n\nexport function weierstrassPoints<T>(opts: CurvePointsType<T>): CurvePointsRes<T> {\n  const CURVE = validatePointOpts(opts);\n  const { Fp } = CURVE; // All curves has same field / group length as for now, but they can differ\n  const Fn = Field(CURVE.n, CURVE.nBitLength);\n\n  const toBytes =\n    CURVE.toBytes ||\n    ((_c: ProjConstructor<T>, point: ProjPointType<T>, _isCompressed: boolean) => {\n      const a = point.toAffine();\n      return concatBytes(Uint8Array.from([0x04]), Fp.toBytes(a.x), Fp.toBytes(a.y));\n    });\n  const fromBytes =\n    CURVE.fromBytes ||\n    ((bytes: Uint8Array) => {\n      // const head = bytes[0];\n      const tail = bytes.subarray(1);\n      // if (head !== 0x04) throw new Error('Only non-compressed encoding is supported');\n      const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n      const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n      return { x, y };\n    });\n\n  /**\n   * y\u00B2 = x\u00B3 + ax + b: Short weierstrass curve formula. Takes x, returns y\u00B2.\n   * @returns y\u00B2\n   */\n  function weierstrassEquation(x: T): T {\n    const { a, b } = CURVE;\n    const x2 = Fp.sqr(x); // x * x\n    const x3 = Fp.mul(x2, x); // x2 * x\n    return Fp.add(Fp.add(x3, Fp.mul(x, a)), b); // x3 + a * x + b\n  }\n  // Validate whether the passed curve params are valid.\n  // We check if curve equation works for generator point.\n  // `assertValidity()` won't work: `isTorsionFree()` is not available at this point in bls12-381.\n  // ProjectivePoint class has not been initialized yet.\n  if (!Fp.eql(Fp.sqr(CURVE.Gy), weierstrassEquation(CURVE.Gx)))\n    throw new Error('bad generator point: equation left != right');\n\n  // Valid group elements reside in range 1..n-1\n  function isWithinCurveOrder(num: bigint): boolean {\n    return inRange(num, _1n, CURVE.n);\n  }\n  // Validates if priv key is valid and converts it to bigint.\n  // Supports options allowedPrivateKeyLengths and wrapPrivateKey.\n  function normPrivateKeyToScalar(key: PrivKey): bigint {\n    const { allowedPrivateKeyLengths: lengths, nByteLength, wrapPrivateKey, n: N } = CURVE;\n    if (lengths && typeof key !== 'bigint') {\n      if (isBytes(key)) key = bytesToHex(key);\n      // Normalize to hex string, pad. E.g. P521 would norm 130-132 char hex to 132-char bytes\n      if (typeof key !== 'string' || !lengths.includes(key.length))\n        throw new Error('invalid private key');\n      key = key.padStart(nByteLength * 2, '0');\n    }\n    let num: bigint;\n    try {\n      num =\n        typeof key === 'bigint'\n          ? key\n          : bytesToNumberBE(ensureBytes('private key', key, nByteLength));\n    } catch (error) {\n      throw new Error(\n        'invalid private key, expected hex or ' + nByteLength + ' bytes, got ' + typeof key\n      );\n    }\n    if (wrapPrivateKey) num = mod(num, N); // disabled by default, enabled for BLS\n    aInRange('private key', num, _1n, N); // num in range [1..N-1]\n    return num;\n  }\n\n  function aprjpoint(other: unknown) {\n    if (!(other instanceof Point)) throw new Error('ProjectivePoint expected');\n  }\n\n  // Memoized toAffine / validity check. They are heavy. Points are immutable.\n\n  // Converts Projective point to affine (x, y) coordinates.\n  // Can accept precomputed Z^-1 - for example, from invertBatch.\n  // (x, y, z) \u220B (x=x/z, y=y/z)\n  const toAffineMemo = memoized((p: Point, iz?: T): AffinePoint<T> => {\n    const { px: x, py: y, pz: z } = p;\n    // Fast-path for normalized points\n    if (Fp.eql(z, Fp.ONE)) return { x, y };\n    const is0 = p.is0();\n    // If invZ was 0, we return zero point. However we still want to execute\n    // all operations, so we replace invZ with a random number, 1.\n    if (iz == null) iz = is0 ? Fp.ONE : Fp.inv(z);\n    const ax = Fp.mul(x, iz);\n    const ay = Fp.mul(y, iz);\n    const zz = Fp.mul(z, iz);\n    if (is0) return { x: Fp.ZERO, y: Fp.ZERO };\n    if (!Fp.eql(zz, Fp.ONE)) throw new Error('invZ was invalid');\n    return { x: ax, y: ay };\n  });\n  // NOTE: on exception this will crash 'cached' and no value will be set.\n  // Otherwise true will be return\n  const assertValidMemo = memoized((p: Point) => {\n    if (p.is0()) {\n      // (0, 1, 0) aka ZERO is invalid in most contexts.\n      // In BLS, ZERO can be serialized, so we allow it.\n      // (0, 0, 0) is invalid representation of ZERO.\n      if (CURVE.allowInfinityPoint && !Fp.is0(p.py)) return;\n      throw new Error('bad point: ZERO');\n    }\n    // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`\n    const { x, y } = p.toAffine();\n    // Check if x, y are valid field elements\n    if (!Fp.isValid(x) || !Fp.isValid(y)) throw new Error('bad point: x or y not FE');\n    const left = Fp.sqr(y); // y\u00B2\n    const right = weierstrassEquation(x); // x\u00B3 + ax + b\n    if (!Fp.eql(left, right)) throw new Error('bad point: equation left != right');\n    if (!p.isTorsionFree()) throw new Error('bad point: not in prime-order subgroup');\n    return true;\n  });\n\n  /**\n   * Projective Point works in 3d / projective (homogeneous) coordinates: (x, y, z) \u220B (x=x/z, y=y/z)\n   * Default Point works in 2d / affine coordinates: (x, y)\n   * We're doing calculations in projective, because its operations don't require costly inversion.\n   */\n  class Point implements ProjPointType<T> {\n    static readonly BASE = new Point(CURVE.Gx, CURVE.Gy, Fp.ONE);\n    static readonly ZERO = new Point(Fp.ZERO, Fp.ONE, Fp.ZERO); // 0, 1, 0\n    readonly px: T;\n    readonly py: T;\n    readonly pz: T;\n\n    constructor(px: T, py: T, pz: T) {\n      if (px == null || !Fp.isValid(px)) throw new Error('x required');\n      if (py == null || !Fp.isValid(py) || Fp.is0(py)) throw new Error('y required');\n      if (pz == null || !Fp.isValid(pz)) throw new Error('z required');\n      this.px = px;\n      this.py = py;\n      this.pz = pz;\n      Object.freeze(this);\n    }\n\n    // Does not validate if the point is on-curve.\n    // Use fromHex instead, or call assertValidity() later.\n    static fromAffine(p: AffinePoint<T>): Point {\n      const { x, y } = p || {};\n      if (!p || !Fp.isValid(x) || !Fp.isValid(y)) throw new Error('invalid affine point');\n      if (p instanceof Point) throw new Error('projective point not allowed');\n      const is0 = (i: T) => Fp.eql(i, Fp.ZERO);\n      // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0)\n      if (is0(x) && is0(y)) return Point.ZERO;\n      return new Point(x, y, Fp.ONE);\n    }\n\n    get x(): T {\n      return this.toAffine().x;\n    }\n    get y(): T {\n      return this.toAffine().y;\n    }\n\n    /**\n     * Takes a bunch of Projective Points but executes only one\n     * inversion on all of them. Inversion is very slow operation,\n     * so this improves performance massively.\n     * Optimization: converts a list of projective points to a list of identical points with Z=1.\n     */\n    static normalizeZ(points: Point[]): Point[] {\n      const toInv = FpInvertBatch(\n        Fp,\n        points.map((p) => p.pz)\n      );\n      return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);\n    }\n\n    /**\n     * Converts hash string or Uint8Array to Point.\n     * @param hex short/long ECDSA hex\n     */\n    static fromHex(hex: Hex): Point {\n      const P = Point.fromAffine(fromBytes(ensureBytes('pointHex', hex)));\n      P.assertValidity();\n      return P;\n    }\n\n    // Multiplies generator point by privateKey.\n    static fromPrivateKey(privateKey: PrivKey) {\n      return Point.BASE.multiply(normPrivateKeyToScalar(privateKey));\n    }\n\n    // Multiscalar Multiplication\n    static msm(points: Point[], scalars: bigint[]): Point {\n      return pippenger(Point, Fn, points, scalars);\n    }\n\n    // \"Private method\", don't use it directly\n    _setWindowSize(windowSize: number) {\n      wnaf.setWindowSize(this, windowSize);\n    }\n\n    // A point on curve is valid if it conforms to equation.\n    assertValidity(): void {\n      assertValidMemo(this);\n    }\n\n    hasEvenY(): boolean {\n      const { y } = this.toAffine();\n      if (Fp.isOdd) return !Fp.isOdd(y);\n      throw new Error(\"Field doesn't support isOdd\");\n    }\n\n    /**\n     * Compare one point to another.\n     */\n    equals(other: Point): boolean {\n      aprjpoint(other);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      const { px: X2, py: Y2, pz: Z2 } = other;\n      const U1 = Fp.eql(Fp.mul(X1, Z2), Fp.mul(X2, Z1));\n      const U2 = Fp.eql(Fp.mul(Y1, Z2), Fp.mul(Y2, Z1));\n      return U1 && U2;\n    }\n\n    /**\n     * Flips point to one corresponding to (x, -y) in Affine coordinates.\n     */\n    negate(): Point {\n      return new Point(this.px, Fp.neg(this.py), this.pz);\n    }\n\n    // Renes-Costello-Batina exception-free doubling formula.\n    // There is 30% faster Jacobian formula, but it is not complete.\n    // https://eprint.iacr.org/2015/1060, algorithm 3\n    // Cost: 8M + 3S + 3*a + 2*b3 + 15add.\n    double() {\n      const { a, b } = CURVE;\n      const b3 = Fp.mul(b, _3n);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n      let t0 = Fp.mul(X1, X1); // step 1\n      let t1 = Fp.mul(Y1, Y1);\n      let t2 = Fp.mul(Z1, Z1);\n      let t3 = Fp.mul(X1, Y1);\n      t3 = Fp.add(t3, t3); // step 5\n      Z3 = Fp.mul(X1, Z1);\n      Z3 = Fp.add(Z3, Z3);\n      X3 = Fp.mul(a, Z3);\n      Y3 = Fp.mul(b3, t2);\n      Y3 = Fp.add(X3, Y3); // step 10\n      X3 = Fp.sub(t1, Y3);\n      Y3 = Fp.add(t1, Y3);\n      Y3 = Fp.mul(X3, Y3);\n      X3 = Fp.mul(t3, X3);\n      Z3 = Fp.mul(b3, Z3); // step 15\n      t2 = Fp.mul(a, t2);\n      t3 = Fp.sub(t0, t2);\n      t3 = Fp.mul(a, t3);\n      t3 = Fp.add(t3, Z3);\n      Z3 = Fp.add(t0, t0); // step 20\n      t0 = Fp.add(Z3, t0);\n      t0 = Fp.add(t0, t2);\n      t0 = Fp.mul(t0, t3);\n      Y3 = Fp.add(Y3, t0);\n      t2 = Fp.mul(Y1, Z1); // step 25\n      t2 = Fp.add(t2, t2);\n      t0 = Fp.mul(t2, t3);\n      X3 = Fp.sub(X3, t0);\n      Z3 = Fp.mul(t2, t1);\n      Z3 = Fp.add(Z3, Z3); // step 30\n      Z3 = Fp.add(Z3, Z3);\n      return new Point(X3, Y3, Z3);\n    }\n\n    // Renes-Costello-Batina exception-free addition formula.\n    // There is 30% faster Jacobian formula, but it is not complete.\n    // https://eprint.iacr.org/2015/1060, algorithm 1\n    // Cost: 12M + 0S + 3*a + 3*b3 + 23add.\n    add(other: Point): Point {\n      aprjpoint(other);\n      const { px: X1, py: Y1, pz: Z1 } = this;\n      const { px: X2, py: Y2, pz: Z2 } = other;\n      let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore\n      const a = CURVE.a;\n      const b3 = Fp.mul(CURVE.b, _3n);\n      let t0 = Fp.mul(X1, X2); // step 1\n      let t1 = Fp.mul(Y1, Y2);\n      let t2 = Fp.mul(Z1, Z2);\n      let t3 = Fp.add(X1, Y1);\n      let t4 = Fp.add(X2, Y2); // step 5\n      t3 = Fp.mul(t3, t4);\n      t4 = Fp.add(t0, t1);\n      t3 = Fp.sub(t3, t4);\n      t4 = Fp.add(X1, Z1);\n      let t5 = Fp.add(X2, Z2); // step 10\n      t4 = Fp.mul(t4, t5);\n      t5 = Fp.add(t0, t2);\n      t4 = Fp.sub(t4, t5);\n      t5 = Fp.add(Y1, Z1);\n      X3 = Fp.add(Y2, Z2); // step 15\n      t5 = Fp.mul(t5, X3);\n      X3 = Fp.add(t1, t2);\n      t5 = Fp.sub(t5, X3);\n      Z3 = Fp.mul(a, t4);\n      X3 = Fp.mul(b3, t2); // step 20\n      Z3 = Fp.add(X3, Z3);\n      X3 = Fp.sub(t1, Z3);\n      Z3 = Fp.add(t1, Z3);\n      Y3 = Fp.mul(X3, Z3);\n      t1 = Fp.add(t0, t0); // step 25\n      t1 = Fp.add(t1, t0);\n      t2 = Fp.mul(a, t2);\n      t4 = Fp.mul(b3, t4);\n      t1 = Fp.add(t1, t2);\n      t2 = Fp.sub(t0, t2); // step 30\n      t2 = Fp.mul(a, t2);\n      t4 = Fp.add(t4, t2);\n      t0 = Fp.mul(t1, t4);\n      Y3 = Fp.add(Y3, t0);\n      t0 = Fp.mul(t5, t4); // step 35\n      X3 = Fp.mul(t3, X3);\n      X3 = Fp.sub(X3, t0);\n      t0 = Fp.mul(t3, t1);\n      Z3 = Fp.mul(t5, Z3);\n      Z3 = Fp.add(Z3, t0); // step 40\n      return new Point(X3, Y3, Z3);\n    }\n\n    subtract(other: Point) {\n      return this.add(other.negate());\n    }\n\n    is0() {\n      return this.equals(Point.ZERO);\n    }\n\n    private wNAF(n: bigint): { p: Point; f: Point } {\n      return wnaf.wNAFCached(this, n, Point.normalizeZ);\n    }\n\n    /**\n     * Non-constant-time multiplication. Uses double-and-add algorithm.\n     * It's faster, but should only be used when you don't care about\n     * an exposed private key e.g. sig verification, which works over *public* keys.\n     */\n    multiplyUnsafe(sc: bigint): Point {\n      const { endo, n: N } = CURVE;\n      aInRange('scalar', sc, _0n, N);\n      const I = Point.ZERO;\n      if (sc === _0n) return I;\n      if (this.is0() || sc === _1n) return this;\n\n      // Case a: no endomorphism. Case b: has precomputes.\n      if (!endo || wnaf.hasPrecomputes(this))\n        return wnaf.wNAFCachedUnsafe(this, sc, Point.normalizeZ);\n\n      // Case c: endomorphism\n      let { k1neg, k1, k2neg, k2 } = endo.splitScalar(sc);\n      let k1p = I;\n      let k2p = I;\n      let d: Point = this;\n      while (k1 > _0n || k2 > _0n) {\n        if (k1 & _1n) k1p = k1p.add(d);\n        if (k2 & _1n) k2p = k2p.add(d);\n        d = d.double();\n        k1 >>= _1n;\n        k2 >>= _1n;\n      }\n      if (k1neg) k1p = k1p.negate();\n      if (k2neg) k2p = k2p.negate();\n      k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n      return k1p.add(k2p);\n    }\n\n    /**\n     * Constant time multiplication.\n     * Uses wNAF method. Windowed method may be 10% faster,\n     * but takes 2x longer to generate and consumes 2x memory.\n     * Uses precomputes when available.\n     * Uses endomorphism for Koblitz curves.\n     * @param scalar by which the point would be multiplied\n     * @returns New point\n     */\n    multiply(scalar: bigint): Point {\n      const { endo, n: N } = CURVE;\n      aInRange('scalar', scalar, _1n, N);\n      let point: Point, fake: Point; // Fake point is used to const-time mult\n      if (endo) {\n        const { k1neg, k1, k2neg, k2 } = endo.splitScalar(scalar);\n        let { p: k1p, f: f1p } = this.wNAF(k1);\n        let { p: k2p, f: f2p } = this.wNAF(k2);\n        k1p = wnaf.constTimeNegate(k1neg, k1p);\n        k2p = wnaf.constTimeNegate(k2neg, k2p);\n        k2p = new Point(Fp.mul(k2p.px, endo.beta), k2p.py, k2p.pz);\n        point = k1p.add(k2p);\n        fake = f1p.add(f2p);\n      } else {\n        const { p, f } = this.wNAF(scalar);\n        point = p;\n        fake = f;\n      }\n      // Normalize `z` for both points, but return only real one\n      return Point.normalizeZ([point, fake])[0];\n    }\n\n    /**\n     * Efficiently calculate `aP + bQ`. Unsafe, can expose private key, if used incorrectly.\n     * Not using Strauss-Shamir trick: precomputation tables are faster.\n     * The trick could be useful if both P and Q are not G (not in our case).\n     * @returns non-zero affine point\n     */\n    multiplyAndAddUnsafe(Q: Point, a: bigint, b: bigint): Point | undefined {\n      const G = Point.BASE; // No Strauss-Shamir trick: we have 10% faster G precomputes\n      const mul = (\n        P: Point,\n        a: bigint // Select faster multiply() method\n      ) => (a === _0n || a === _1n || !P.equals(G) ? P.multiplyUnsafe(a) : P.multiply(a));\n      const sum = mul(this, a).add(mul(Q, b));\n      return sum.is0() ? undefined : sum;\n    }\n\n    // Converts Projective point to affine (x, y) coordinates.\n    // Can accept precomputed Z^-1 - for example, from invertBatch.\n    // (x, y, z) \u220B (x=x/z, y=y/z)\n    toAffine(iz?: T): AffinePoint<T> {\n      return toAffineMemo(this, iz);\n    }\n    isTorsionFree(): boolean {\n      const { h: cofactor, isTorsionFree } = CURVE;\n      if (cofactor === _1n) return true; // No subgroups, always torsion-free\n      if (isTorsionFree) return isTorsionFree(Point, this);\n      throw new Error('isTorsionFree() has not been declared for the elliptic curve');\n    }\n    clearCofactor(): Point {\n      const { h: cofactor, clearCofactor } = CURVE;\n      if (cofactor === _1n) return this; // Fast-path\n      if (clearCofactor) return clearCofactor(Point, this) as Point;\n      return this.multiplyUnsafe(CURVE.h);\n    }\n\n    toRawBytes(isCompressed = true): Uint8Array {\n      abool('isCompressed', isCompressed);\n      this.assertValidity();\n      return toBytes(Point, this, isCompressed);\n    }\n\n    toHex(isCompressed = true): string {\n      abool('isCompressed', isCompressed);\n      return bytesToHex(this.toRawBytes(isCompressed));\n    }\n  }\n  const _bits = CURVE.nBitLength;\n  const wnaf = wNAF(Point, CURVE.endo ? Math.ceil(_bits / 2) : _bits);\n  return {\n    CURVE,\n    ProjectivePoint: Point as ProjConstructor<T>,\n    normPrivateKeyToScalar,\n    weierstrassEquation,\n    isWithinCurveOrder,\n  };\n}\n\n// Instance\nexport interface SignatureType {\n  readonly r: bigint;\n  readonly s: bigint;\n  readonly recovery?: number;\n  assertValidity(): void;\n  addRecoveryBit(recovery: number): RecoveredSignatureType;\n  hasHighS(): boolean;\n  normalizeS(): SignatureType;\n  recoverPublicKey(msgHash: Hex): ProjPointType<bigint>;\n  toCompactRawBytes(): Uint8Array;\n  toCompactHex(): string;\n  toDERRawBytes(isCompressed?: boolean): Uint8Array;\n  toDERHex(isCompressed?: boolean): string;\n}\nexport type RecoveredSignatureType = SignatureType & {\n  readonly recovery: number;\n};\n// Static methods\nexport type SignatureConstructor = {\n  new (r: bigint, s: bigint): SignatureType;\n  fromCompact(hex: Hex): SignatureType;\n  fromDER(hex: Hex): SignatureType;\n};\ntype SignatureLike = { r: bigint; s: bigint };\n\nexport type PubKey = Hex | ProjPointType<bigint>;\n\nexport type CurveType = BasicWCurve<bigint> & {\n  hash: CHash; // CHash not FHash because we need outputLen for DRBG\n  hmac: HmacFnSync;\n  randomBytes: (bytesLength?: number) => Uint8Array;\n  lowS?: boolean;\n  bits2int?: (bytes: Uint8Array) => bigint;\n  bits2int_modN?: (bytes: Uint8Array) => bigint;\n};\n\nfunction validateOpts(\n  curve: CurveType\n): Readonly<CurveType & { nByteLength: number; nBitLength: number }> {\n  const opts = validateBasic(curve);\n  validateObject(\n    opts,\n    {\n      hash: 'hash',\n      hmac: 'function',\n      randomBytes: 'function',\n    },\n    {\n      bits2int: 'function',\n      bits2int_modN: 'function',\n      lowS: 'boolean',\n    }\n  );\n  return Object.freeze({ lowS: true, ...opts } as const);\n}\n\nexport type CurveFn = {\n  CURVE: ReturnType<typeof validateOpts>;\n  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;\n  getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;\n  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => RecoveredSignatureType;\n  verify: (signature: Hex | SignatureLike, msgHash: Hex, publicKey: Hex, opts?: VerOpts) => boolean;\n  ProjectivePoint: ProjConstructor<bigint>;\n  Signature: SignatureConstructor;\n  utils: {\n    normPrivateKeyToScalar: (key: PrivKey) => bigint;\n    isValidPrivateKey(privateKey: PrivKey): boolean;\n    randomPrivateKey: () => Uint8Array;\n    precompute: (windowSize?: number, point?: ProjPointType<bigint>) => ProjPointType<bigint>;\n  };\n};\n\n/**\n * Creates short weierstrass curve and ECDSA signature methods for it.\n * @example\n * import { Field } from '@noble/curves/abstract/modular';\n * // Before that, define BigInt-s: a, b, p, n, Gx, Gy\n * const curve = weierstrass({ a, b, Fp: Field(p), n, Gx, Gy, h: 1n })\n */\nexport function weierstrass(curveDef: CurveType): CurveFn {\n  const CURVE = validateOpts(curveDef) as ReturnType<typeof validateOpts>;\n  const { Fp, n: CURVE_ORDER } = CURVE;\n  const compressedLen = Fp.BYTES + 1; // e.g. 33 for 32\n  const uncompressedLen = 2 * Fp.BYTES + 1; // e.g. 65 for 32\n\n  function modN(a: bigint) {\n    return mod(a, CURVE_ORDER);\n  }\n  function invN(a: bigint) {\n    return invert(a, CURVE_ORDER);\n  }\n\n  const {\n    ProjectivePoint: Point,\n    normPrivateKeyToScalar,\n    weierstrassEquation,\n    isWithinCurveOrder,\n  } = weierstrassPoints({\n    ...CURVE,\n    toBytes(_c, point, isCompressed: boolean): Uint8Array {\n      const a = point.toAffine();\n      const x = Fp.toBytes(a.x);\n      const cat = concatBytes;\n      abool('isCompressed', isCompressed);\n      if (isCompressed) {\n        return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);\n      } else {\n        return cat(Uint8Array.from([0x04]), x, Fp.toBytes(a.y));\n      }\n    },\n    fromBytes(bytes: Uint8Array) {\n      const len = bytes.length;\n      const head = bytes[0];\n      const tail = bytes.subarray(1);\n      // this.assertValidity() is done inside of fromHex\n      if (len === compressedLen && (head === 0x02 || head === 0x03)) {\n        const x = bytesToNumberBE(tail);\n        if (!inRange(x, _1n, Fp.ORDER)) throw new Error('Point is not on curve');\n        const y2 = weierstrassEquation(x); // y\u00B2 = x\u00B3 + ax + b\n        let y: bigint;\n        try {\n          y = Fp.sqrt(y2); // y = y\u00B2 ^ (p+1)/4\n        } catch (sqrtError) {\n          const suffix = sqrtError instanceof Error ? ': ' + sqrtError.message : '';\n          throw new Error('Point is not on curve' + suffix);\n        }\n        const isYOdd = (y & _1n) === _1n;\n        // ECDSA\n        const isHeadOdd = (head & 1) === 1;\n        if (isHeadOdd !== isYOdd) y = Fp.neg(y);\n        return { x, y };\n      } else if (len === uncompressedLen && head === 0x04) {\n        const x = Fp.fromBytes(tail.subarray(0, Fp.BYTES));\n        const y = Fp.fromBytes(tail.subarray(Fp.BYTES, 2 * Fp.BYTES));\n        return { x, y };\n      } else {\n        const cl = compressedLen;\n        const ul = uncompressedLen;\n        throw new Error(\n          'invalid Point, expected length of ' + cl + ', or uncompressed ' + ul + ', got ' + len\n        );\n      }\n    },\n  });\n  const numToNByteHex = (num: bigint): string =>\n    bytesToHex(numberToBytesBE(num, CURVE.nByteLength));\n\n  function isBiggerThanHalfOrder(number: bigint) {\n    const HALF = CURVE_ORDER >> _1n;\n    return number > HALF;\n  }\n\n  function normalizeS(s: bigint) {\n    return isBiggerThanHalfOrder(s) ? modN(-s) : s;\n  }\n  // slice bytes num\n  const slcNum = (b: Uint8Array, from: number, to: number) => bytesToNumberBE(b.slice(from, to));\n\n  /**\n   * ECDSA signature with its (r, s) properties. Supports DER & compact representations.\n   */\n  class Signature implements SignatureType {\n    readonly r: bigint;\n    readonly s: bigint;\n    readonly recovery?: number;\n    constructor(r: bigint, s: bigint, recovery?: number) {\n      aInRange('r', r, _1n, CURVE_ORDER); // r in [1..N]\n      aInRange('s', s, _1n, CURVE_ORDER); // s in [1..N]\n      this.r = r;\n      this.s = s;\n      if (recovery != null) this.recovery = recovery;\n      Object.freeze(this);\n    }\n\n    // pair (bytes of r, bytes of s)\n    static fromCompact(hex: Hex) {\n      const l = CURVE.nByteLength;\n      hex = ensureBytes('compactSignature', hex, l * 2);\n      return new Signature(slcNum(hex, 0, l), slcNum(hex, l, 2 * l));\n    }\n\n    // DER encoded ECDSA signature\n    // https://bitcoin.stackexchange.com/questions/57644/what-are-the-parts-of-a-bitcoin-transaction-input-script\n    static fromDER(hex: Hex) {\n      const { r, s } = DER.toSig(ensureBytes('DER', hex));\n      return new Signature(r, s);\n    }\n\n    /**\n     * @todo remove\n     * @deprecated\n     */\n    assertValidity(): void {}\n\n    addRecoveryBit(recovery: number): RecoveredSignature {\n      return new Signature(this.r, this.s, recovery) as RecoveredSignature;\n    }\n\n    recoverPublicKey(msgHash: Hex): typeof Point.BASE {\n      const { r, s, recovery: rec } = this;\n      const h = bits2int_modN(ensureBytes('msgHash', msgHash)); // Truncate hash\n      if (rec == null || ![0, 1, 2, 3].includes(rec)) throw new Error('recovery id invalid');\n      const radj = rec === 2 || rec === 3 ? r + CURVE.n : r;\n      if (radj >= Fp.ORDER) throw new Error('recovery id 2 or 3 invalid');\n      const prefix = (rec & 1) === 0 ? '02' : '03';\n      const R = Point.fromHex(prefix + numToNByteHex(radj));\n      const ir = invN(radj); // r^-1\n      const u1 = modN(-h * ir); // -hr^-1\n      const u2 = modN(s * ir); // sr^-1\n      const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // (sr^-1)R-(hr^-1)G = -(hr^-1)G + (sr^-1)\n      if (!Q) throw new Error('point at infinify'); // unsafe is fine: no priv data leaked\n      Q.assertValidity();\n      return Q;\n    }\n\n    // Signatures should be low-s, to prevent malleability.\n    hasHighS(): boolean {\n      return isBiggerThanHalfOrder(this.s);\n    }\n\n    normalizeS() {\n      return this.hasHighS() ? new Signature(this.r, modN(-this.s), this.recovery) : this;\n    }\n\n    // DER-encoded\n    toDERRawBytes() {\n      return hexToBytes(this.toDERHex());\n    }\n    toDERHex() {\n      return DER.hexFromSig(this);\n    }\n\n    // padded bytes of r, then padded bytes of s\n    toCompactRawBytes() {\n      return hexToBytes(this.toCompactHex());\n    }\n    toCompactHex() {\n      return numToNByteHex(this.r) + numToNByteHex(this.s);\n    }\n  }\n  type RecoveredSignature = Signature & { recovery: number };\n\n  const utils = {\n    isValidPrivateKey(privateKey: PrivKey) {\n      try {\n        normPrivateKeyToScalar(privateKey);\n        return true;\n      } catch (error) {\n        return false;\n      }\n    },\n    normPrivateKeyToScalar: normPrivateKeyToScalar,\n\n    /**\n     * Produces cryptographically secure private key from random of size\n     * (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.\n     */\n    randomPrivateKey: (): Uint8Array => {\n      const length = getMinHashLength(CURVE.n);\n      return mapHashToField(CURVE.randomBytes(length), CURVE.n);\n    },\n\n    /**\n     * Creates precompute table for an arbitrary EC point. Makes point \"cached\".\n     * Allows to massively speed-up `point.multiply(scalar)`.\n     * @returns cached point\n     * @example\n     * const fast = utils.precompute(8, ProjectivePoint.fromHex(someonesPubKey));\n     * fast.multiply(privKey); // much faster ECDH now\n     */\n    precompute(windowSize = 8, point = Point.BASE): typeof Point.BASE {\n      point._setWindowSize(windowSize);\n      point.multiply(BigInt(3)); // 3 is arbitrary, just need any number here\n      return point;\n    },\n  };\n\n  /**\n   * Computes public key for a private key. Checks for validity of the private key.\n   * @param privateKey private key\n   * @param isCompressed whether to return compact (default), or full key\n   * @returns Public key, full when isCompressed=false; short when isCompressed=true\n   */\n  function getPublicKey(privateKey: PrivKey, isCompressed = true): Uint8Array {\n    return Point.fromPrivateKey(privateKey).toRawBytes(isCompressed);\n  }\n\n  /**\n   * Quick and dirty check for item being public key. Does not validate hex, or being on-curve.\n   */\n  function isProbPub(item: PrivKey | PubKey): boolean {\n    const arr = isBytes(item);\n    const str = typeof item === 'string';\n    const len = (arr || str) && (item as Hex).length;\n    if (arr) return len === compressedLen || len === uncompressedLen;\n    if (str) return len === 2 * compressedLen || len === 2 * uncompressedLen;\n    if (item instanceof Point) return true;\n    return false;\n  }\n\n  /**\n   * ECDH (Elliptic Curve Diffie Hellman).\n   * Computes shared public key from private key and public key.\n   * Checks: 1) private key validity 2) shared key is on-curve.\n   * Does NOT hash the result.\n   * @param privateA private key\n   * @param publicB different public key\n   * @param isCompressed whether to return compact (default), or full key\n   * @returns shared public key\n   */\n  function getSharedSecret(privateA: PrivKey, publicB: Hex, isCompressed = true): Uint8Array {\n    if (isProbPub(privateA)) throw new Error('first arg must be private key');\n    if (!isProbPub(publicB)) throw new Error('second arg must be public key');\n    const b = Point.fromHex(publicB); // check for being on-curve\n    return b.multiply(normPrivateKeyToScalar(privateA)).toRawBytes(isCompressed);\n  }\n\n  // RFC6979: ensure ECDSA msg is X bytes and < N. RFC suggests optional truncating via bits2octets.\n  // FIPS 186-4 4.6 suggests the leftmost min(nBitLen, outLen) bits, which matches bits2int.\n  // bits2int can produce res>N, we can do mod(res, N) since the bitLen is the same.\n  // int2octets can't be used; pads small msgs with 0: unacceptatble for trunc as per RFC vectors\n  const bits2int =\n    CURVE.bits2int ||\n    function (bytes: Uint8Array): bigint {\n      // Our custom check \"just in case\"\n      if (bytes.length > 8192) throw new Error('input is too large');\n      // For curves with nBitLength % 8 !== 0: bits2octets(bits2octets(m)) !== bits2octets(m)\n      // for some cases, since bytes.length * 8 is not actual bitLength.\n      const num = bytesToNumberBE(bytes); // check for == u8 done here\n      const delta = bytes.length * 8 - CURVE.nBitLength; // truncate to nBitLength leftmost bits\n      return delta > 0 ? num >> BigInt(delta) : num;\n    };\n  const bits2int_modN =\n    CURVE.bits2int_modN ||\n    function (bytes: Uint8Array): bigint {\n      return modN(bits2int(bytes)); // can't use bytesToNumberBE here\n    };\n  // NOTE: pads output with zero as per spec\n  const ORDER_MASK = bitMask(CURVE.nBitLength);\n  /**\n   * Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.\n   */\n  function int2octets(num: bigint): Uint8Array {\n    aInRange('num < 2^' + CURVE.nBitLength, num, _0n, ORDER_MASK);\n    // works with order, can have different size than numToField!\n    return numberToBytesBE(num, CURVE.nByteLength);\n  }\n\n  // Steps A, D of RFC6979 3.2\n  // Creates RFC6979 seed; converts msg/privKey to numbers.\n  // Used only in sign, not in verify.\n  // NOTE: we cannot assume here that msgHash has same amount of bytes as curve order,\n  // this will be invalid at least for P521. Also it can be bigger for P224 + SHA256\n  function prepSig(msgHash: Hex, privateKey: PrivKey, opts = defaultSigOpts) {\n    if (['recovered', 'canonical'].some((k) => k in opts))\n      throw new Error('sign() legacy options not supported');\n    const { hash, randomBytes } = CURVE;\n    let { lowS, prehash, extraEntropy: ent } = opts; // generates low-s sigs by default\n    if (lowS == null) lowS = true; // RFC6979 3.2: we skip step A, because we already provide hash\n    msgHash = ensureBytes('msgHash', msgHash);\n    validateSigVerOpts(opts);\n    if (prehash) msgHash = ensureBytes('prehashed msgHash', hash(msgHash));\n\n    // We can't later call bits2octets, since nested bits2int is broken for curves\n    // with nBitLength % 8 !== 0. Because of that, we unwrap it here as int2octets call.\n    // const bits2octets = (bits) => int2octets(bits2int_modN(bits))\n    const h1int = bits2int_modN(msgHash);\n    const d = normPrivateKeyToScalar(privateKey); // validate private key, convert to bigint\n    const seedArgs = [int2octets(d), int2octets(h1int)];\n    // extraEntropy. RFC6979 3.6: additional k' (optional).\n    if (ent != null && ent !== false) {\n      // K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')\n      const e = ent === true ? randomBytes(Fp.BYTES) : ent; // generate random bytes OR pass as-is\n      seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes\n    }\n    const seed = concatBytes(...seedArgs); // Step D of RFC6979 3.2\n    const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!\n    // Converts signature params into point w r/s, checks result for validity.\n    function k2sig(kBytes: Uint8Array): RecoveredSignature | undefined {\n      // RFC 6979 Section 3.2, step 3: k = bits2int(T)\n      const k = bits2int(kBytes); // Cannot use fields methods, since it is group element\n      if (!isWithinCurveOrder(k)) return; // Important: all mod() calls here must be done over N\n      const ik = invN(k); // k^-1 mod n\n      const q = Point.BASE.multiply(k).toAffine(); // q = Gk\n      const r = modN(q.x); // r = q.x mod n\n      if (r === _0n) return;\n      // Can use scalar blinding b^-1(bm + bdr) where b \u2208 [1,q\u22121] according to\n      // https://tches.iacr.org/index.php/TCHES/article/view/7337/6509. We've decided against it:\n      // a) dependency on CSPRNG b) 15% slowdown c) doesn't really help since bigints are not CT\n      const s = modN(ik * modN(m + r * d)); // Not using blinding here\n      if (s === _0n) return;\n      let recovery = (q.x === r ? 0 : 2) | Number(q.y & _1n); // recovery bit (2 or 3, when q.x > n)\n      let normS = s;\n      if (lowS && isBiggerThanHalfOrder(s)) {\n        normS = normalizeS(s); // if lowS was passed, ensure s is always\n        recovery ^= 1; // // in the bottom half of N\n      }\n      return new Signature(r, normS, recovery) as RecoveredSignature; // use normS, not s\n    }\n    return { seed, k2sig };\n  }\n  const defaultSigOpts: SignOpts = { lowS: CURVE.lowS, prehash: false };\n  const defaultVerOpts: VerOpts = { lowS: CURVE.lowS, prehash: false };\n\n  /**\n   * Signs message hash with a private key.\n   * ```\n   * sign(m, d, k) where\n   *   (x, y) = G \u00D7 k\n   *   r = x mod n\n   *   s = (m + dr)/k mod n\n   * ```\n   * @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.\n   * @param privKey private key\n   * @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.\n   * @returns signature with recovery param\n   */\n  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): RecoveredSignature {\n    const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.\n    const C = CURVE;\n    const drbg = createHmacDrbg<RecoveredSignature>(C.hash.outputLen, C.nByteLength, C.hmac);\n    return drbg(seed, k2sig); // Steps B, C, D, E, F, G\n  }\n\n  // Enable precomputes. Slows down first publicKey computation by 20ms.\n  Point.BASE._setWindowSize(8);\n  // utils.precompute(8, ProjectivePoint.BASE)\n\n  /**\n   * Verifies a signature against message hash and public key.\n   * Rejects lowS signatures by default: to override,\n   * specify option `{lowS: false}`. Implements section 4.1.4 from https://www.secg.org/sec1-v2.pdf:\n   *\n   * ```\n   * verify(r, s, h, P) where\n   *   U1 = hs^-1 mod n\n   *   U2 = rs^-1 mod n\n   *   R = U1\u22C5G - U2\u22C5P\n   *   mod(R.x, n) == r\n   * ```\n   */\n  function verify(\n    signature: Hex | SignatureLike,\n    msgHash: Hex,\n    publicKey: Hex,\n    opts = defaultVerOpts\n  ): boolean {\n    const sg = signature;\n    msgHash = ensureBytes('msgHash', msgHash);\n    publicKey = ensureBytes('publicKey', publicKey);\n    const { lowS, prehash, format } = opts;\n\n    // Verify opts, deduce signature format\n    validateSigVerOpts(opts);\n    if ('strict' in opts) throw new Error('options.strict was renamed to lowS');\n    if (format !== undefined && format !== 'compact' && format !== 'der')\n      throw new Error('format must be compact or der');\n    const isHex = typeof sg === 'string' || isBytes(sg);\n    const isObj =\n      !isHex &&\n      !format &&\n      typeof sg === 'object' &&\n      sg !== null &&\n      typeof sg.r === 'bigint' &&\n      typeof sg.s === 'bigint';\n    if (!isHex && !isObj)\n      throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');\n\n    let _sig: Signature | undefined = undefined;\n    let P: ProjPointType<bigint>;\n    try {\n      if (isObj) _sig = new Signature(sg.r, sg.s);\n      if (isHex) {\n        // Signature can be represented in 2 ways: compact (2*nByteLength) & DER (variable-length).\n        // Since DER can also be 2*nByteLength bytes, we check for it first.\n        try {\n          if (format !== 'compact') _sig = Signature.fromDER(sg);\n        } catch (derError) {\n          if (!(derError instanceof DER.Err)) throw derError;\n        }\n        if (!_sig && format !== 'der') _sig = Signature.fromCompact(sg);\n      }\n      P = Point.fromHex(publicKey);\n    } catch (error) {\n      return false;\n    }\n    if (!_sig) return false;\n    if (lowS && _sig.hasHighS()) return false;\n    if (prehash) msgHash = CURVE.hash(msgHash);\n    const { r, s } = _sig;\n    const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element\n    const is = invN(s); // s^-1\n    const u1 = modN(h * is); // u1 = hs^-1 mod n\n    const u2 = modN(r * is); // u2 = rs^-1 mod n\n    const R = Point.BASE.multiplyAndAddUnsafe(P, u1, u2)?.toAffine(); // R = u1\u22C5G + u2\u22C5P\n    if (!R) return false;\n    const v = modN(R.x);\n    return v === r;\n  }\n  return {\n    CURVE,\n    getPublicKey,\n    getSharedSecret,\n    sign,\n    verify,\n    ProjectivePoint: Point,\n    Signature,\n    utils,\n  };\n}\n\n/**\n * Implementation of the Shallue and van de Woestijne method for any weierstrass curve.\n * TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.\n * b = True and y = sqrt(u / v) if (u / v) is square in F, and\n * b = False and y = sqrt(Z * (u / v)) otherwise.\n * @param Fp\n * @param Z\n * @returns\n */\nexport function SWUFpSqrtRatio<T>(\n  Fp: IField<T>,\n  Z: T\n): (u: T, v: T) => { isValid: boolean; value: T } {\n  // Generic implementation\n  const q = Fp.ORDER;\n  let l = _0n;\n  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;\n  const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.\n  // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.\n  // 2n ** c1 == 2n << (c1-1)\n  const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);\n  const _2n_pow_c1 = _2n_pow_c1_1 * _2n;\n  const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1)  # Integer arithmetic\n  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic\n  const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic\n  const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1)                  # Integer arithmetic\n  const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2\n  const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)\n  let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {\n    let tv1 = c6; // 1. tv1 = c6\n    let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4\n    let tv3 = Fp.sqr(tv2); // 3. tv3 = tv2^2\n    tv3 = Fp.mul(tv3, v); // 4. tv3 = tv3 * v\n    let tv5 = Fp.mul(u, tv3); // 5. tv5 = u * tv3\n    tv5 = Fp.pow(tv5, c3); // 6. tv5 = tv5^c3\n    tv5 = Fp.mul(tv5, tv2); // 7. tv5 = tv5 * tv2\n    tv2 = Fp.mul(tv5, v); // 8. tv2 = tv5 * v\n    tv3 = Fp.mul(tv5, u); // 9. tv3 = tv5 * u\n    let tv4 = Fp.mul(tv3, tv2); // 10. tv4 = tv3 * tv2\n    tv5 = Fp.pow(tv4, c5); // 11. tv5 = tv4^c5\n    let isQR = Fp.eql(tv5, Fp.ONE); // 12. isQR = tv5 == 1\n    tv2 = Fp.mul(tv3, c7); // 13. tv2 = tv3 * c7\n    tv5 = Fp.mul(tv4, tv1); // 14. tv5 = tv4 * tv1\n    tv3 = Fp.cmov(tv2, tv3, isQR); // 15. tv3 = CMOV(tv2, tv3, isQR)\n    tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)\n    // 17. for i in (c1, c1 - 1, ..., 2):\n    for (let i = c1; i > _1n; i--) {\n      let tv5 = i - _2n; // 18.    tv5 = i - 2\n      tv5 = _2n << (tv5 - _1n); // 19.    tv5 = 2^tv5\n      let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5\n      const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1\n      tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1\n      tv1 = Fp.mul(tv1, tv1); // 23.    tv1 = tv1 * tv1\n      tvv5 = Fp.mul(tv4, tv1); // 24.    tv5 = tv4 * tv1\n      tv3 = Fp.cmov(tv2, tv3, e1); // 25.    tv3 = CMOV(tv2, tv3, e1)\n      tv4 = Fp.cmov(tvv5, tv4, e1); // 26.    tv4 = CMOV(tv5, tv4, e1)\n    }\n    return { isValid: isQR, value: tv3 };\n  };\n  if (Fp.ORDER % _4n === _3n) {\n    // sqrt_ratio_3mod4(u, v)\n    const c1 = (Fp.ORDER - _3n) / _4n; // 1. c1 = (q - 3) / 4     # Integer arithmetic\n    const c2 = Fp.sqrt(Fp.neg(Z)); // 2. c2 = sqrt(-Z)\n    sqrtRatio = (u: T, v: T) => {\n      let tv1 = Fp.sqr(v); // 1. tv1 = v^2\n      const tv2 = Fp.mul(u, v); // 2. tv2 = u * v\n      tv1 = Fp.mul(tv1, tv2); // 3. tv1 = tv1 * tv2\n      let y1 = Fp.pow(tv1, c1); // 4. y1 = tv1^c1\n      y1 = Fp.mul(y1, tv2); // 5. y1 = y1 * tv2\n      const y2 = Fp.mul(y1, c2); // 6. y2 = y1 * c2\n      const tv3 = Fp.mul(Fp.sqr(y1), v); // 7. tv3 = y1^2; 8. tv3 = tv3 * v\n      const isQR = Fp.eql(tv3, u); // 9. isQR = tv3 == u\n      let y = Fp.cmov(y2, y1, isQR); // 10. y = CMOV(y2, y1, isQR)\n      return { isValid: isQR, value: y }; // 11. return (isQR, y) isQR ? y : y*c2\n    };\n  }\n  // No curves uses that\n  // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8\n  return sqrtRatio;\n}\n/**\n * Simplified Shallue-van de Woestijne-Ulas Method\n * https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2\n */\nexport function mapToCurveSimpleSWU<T>(\n  Fp: IField<T>,\n  opts: {\n    A: T;\n    B: T;\n    Z: T;\n  }\n): (u: T) => { x: T; y: T } {\n  validateField(Fp);\n  if (!Fp.isValid(opts.A) || !Fp.isValid(opts.B) || !Fp.isValid(opts.Z))\n    throw new Error('mapToCurveSimpleSWU: invalid opts');\n  const sqrtRatio = SWUFpSqrtRatio(Fp, opts.Z);\n  if (!Fp.isOdd) throw new Error('Fp.isOdd is not implemented!');\n  // Input: u, an element of F.\n  // Output: (x, y), a point on E.\n  return (u: T): { x: T; y: T } => {\n    // prettier-ignore\n    let tv1, tv2, tv3, tv4, tv5, tv6, x, y;\n    tv1 = Fp.sqr(u); // 1.  tv1 = u^2\n    tv1 = Fp.mul(tv1, opts.Z); // 2.  tv1 = Z * tv1\n    tv2 = Fp.sqr(tv1); // 3.  tv2 = tv1^2\n    tv2 = Fp.add(tv2, tv1); // 4.  tv2 = tv2 + tv1\n    tv3 = Fp.add(tv2, Fp.ONE); // 5.  tv3 = tv2 + 1\n    tv3 = Fp.mul(tv3, opts.B); // 6.  tv3 = B * tv3\n    tv4 = Fp.cmov(opts.Z, Fp.neg(tv2), !Fp.eql(tv2, Fp.ZERO)); // 7.  tv4 = CMOV(Z, -tv2, tv2 != 0)\n    tv4 = Fp.mul(tv4, opts.A); // 8.  tv4 = A * tv4\n    tv2 = Fp.sqr(tv3); // 9.  tv2 = tv3^2\n    tv6 = Fp.sqr(tv4); // 10. tv6 = tv4^2\n    tv5 = Fp.mul(tv6, opts.A); // 11. tv5 = A * tv6\n    tv2 = Fp.add(tv2, tv5); // 12. tv2 = tv2 + tv5\n    tv2 = Fp.mul(tv2, tv3); // 13. tv2 = tv2 * tv3\n    tv6 = Fp.mul(tv6, tv4); // 14. tv6 = tv6 * tv4\n    tv5 = Fp.mul(tv6, opts.B); // 15. tv5 = B * tv6\n    tv2 = Fp.add(tv2, tv5); // 16. tv2 = tv2 + tv5\n    x = Fp.mul(tv1, tv3); // 17.   x = tv1 * tv3\n    const { isValid, value } = sqrtRatio(tv2, tv6); // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6)\n    y = Fp.mul(tv1, u); // 19.   y = tv1 * u  -> Z * u^3 * y1\n    y = Fp.mul(y, value); // 20.   y = y * y1\n    x = Fp.cmov(x, tv3, isValid); // 21.   x = CMOV(x, tv3, is_gx1_square)\n    y = Fp.cmov(y, value, isValid); // 22.   y = CMOV(y, y1, is_gx1_square)\n    const e1 = Fp.isOdd!(u) === Fp.isOdd!(y); // 23.  e1 = sgn0(u) == sgn0(y)\n    y = Fp.cmov(Fp.neg(y), y, e1); // 24.   y = CMOV(-y, y, e1)\n    const tv4_inv = FpInvertBatch(Fp, [tv4], true)[0];\n    x = Fp.mul(x, tv4_inv); // 25.   x = x / tv4\n    return { x, y };\n  };\n}\n", "/**\n * BLS (Barreto-Lynn-Scott) family of pairing-friendly curves.\n * BLS != BLS.\n * The file implements BLS (Boneh-Lynn-Shacham) signatures.\n * Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig)\n * families of pairing-friendly curves.\n * Consists of two curves: G1 and G2:\n * - G1 is a subgroup of (x, y) E(Fq) over y\u00B2 = x\u00B3 + 4.\n * - G2 is a subgroup of ((x\u2081, x\u2082+i), (y\u2081, y\u2082+i)) E(Fq\u00B2) over y\u00B2 = x\u00B3 + 4(1 + i) where i is \u221A-1\n * - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in\n *   Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.\n * Pairing is used to aggregate and verify signatures.\n * There are two main ways to use it:\n * 1. Fp for short private keys, Fp\u2082 for signatures\n * 2. Fp for short signatures, Fp\u2082 for private keys\n * @module\n **/\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n// TODO: import { AffinePoint } from './curve.ts';\nimport {\n  type H2CPointConstructor,\n  type htfBasicOpts,\n  type Opts as HTFOpts,\n  type MapToCurve,\n  createHasher,\n} from './hash-to-curve.ts';\nimport { type IField, getMinHashLength, mapHashToField } from './modular.ts';\nimport type { Fp12, Fp12Bls, Fp2, Fp2Bls, Fp6 } from './tower.ts';\nimport { type CHash, type Hex, type PrivKey, ensureBytes, memoized } from './utils.ts';\nimport {\n  type CurvePointsRes,\n  type CurvePointsType,\n  type ProjPointType,\n  weierstrassPoints,\n} from './weierstrass.ts';\n\ntype Fp = bigint; // Can be different field?\n\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n\nexport type TwistType = 'multiplicative' | 'divisive';\n\nexport type ShortSignatureCoder<Fp> = {\n  fromHex(hex: Hex): ProjPointType<Fp>;\n  toRawBytes(point: ProjPointType<Fp>): Uint8Array;\n  toHex(point: ProjPointType<Fp>): string;\n};\n\nexport type SignatureCoder<Fp> = {\n  fromHex(hex: Hex): ProjPointType<Fp>;\n  toRawBytes(point: ProjPointType<Fp>): Uint8Array;\n  toHex(point: ProjPointType<Fp>): string;\n};\n\nexport type PostPrecomputePointAddFn = (\n  Rx: Fp2,\n  Ry: Fp2,\n  Rz: Fp2,\n  Qx: Fp2,\n  Qy: Fp2\n) => { Rx: Fp2; Ry: Fp2; Rz: Fp2 };\nexport type PostPrecomputeFn = (\n  Rx: Fp2,\n  Ry: Fp2,\n  Rz: Fp2,\n  Qx: Fp2,\n  Qy: Fp2,\n  pointAdd: PostPrecomputePointAddFn\n) => void;\nexport type CurveType = {\n  G1: Omit<CurvePointsType<Fp>, 'n'> & {\n    ShortSignature: SignatureCoder<Fp>;\n    mapToCurve: MapToCurve<Fp>;\n    htfDefaults: HTFOpts;\n  };\n  G2: Omit<CurvePointsType<Fp2>, 'n'> & {\n    Signature: SignatureCoder<Fp2>;\n    mapToCurve: MapToCurve<Fp2>;\n    htfDefaults: HTFOpts;\n  };\n  fields: {\n    Fp: IField<Fp>;\n    Fr: IField<bigint>;\n    Fp2: Fp2Bls;\n    Fp6: IField<Fp6>;\n    Fp12: Fp12Bls;\n  };\n  params: {\n    // NOTE: MSB is always ignored and used as marker for length,\n    // otherwise leading zeros will be lost.\n    // Can be different from 'X' (seed) param!\n    ateLoopSize: bigint;\n    xNegative: boolean;\n    r: bigint;\n    twistType: TwistType; // BLS12-381: Multiplicative, BN254: Divisive\n  };\n  htfDefaults: HTFOpts;\n  hash: CHash; // Because we need outputLen for DRBG\n  randomBytes: (bytesLength?: number) => Uint8Array;\n  // This is super ugly hack for untwist point in BN254 after miller loop\n  postPrecompute?: PostPrecomputeFn;\n};\n\ntype PrecomputeSingle = [Fp2, Fp2, Fp2][];\ntype Precompute = PrecomputeSingle[];\n\nexport type CurveFn = {\n  getPublicKey: (privateKey: PrivKey) => Uint8Array;\n  getPublicKeyForShortSignatures: (privateKey: PrivKey) => Uint8Array;\n  sign: {\n    (message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n    (message: ProjPointType<Fp2>, privateKey: PrivKey, htfOpts?: htfBasicOpts): ProjPointType<Fp2>;\n  };\n  signShortSignature: {\n    (message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n    (message: ProjPointType<Fp>, privateKey: PrivKey, htfOpts?: htfBasicOpts): ProjPointType<Fp>;\n  };\n  verify: (\n    signature: Hex | ProjPointType<Fp2>,\n    message: Hex | ProjPointType<Fp2>,\n    publicKey: Hex | ProjPointType<Fp>,\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  verifyShortSignature: (\n    signature: Hex | ProjPointType<Fp>,\n    message: Hex | ProjPointType<Fp>,\n    publicKey: Hex | ProjPointType<Fp2>,\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  verifyBatch: (\n    signature: Hex | ProjPointType<Fp2>,\n    messages: (Hex | ProjPointType<Fp2>)[],\n    publicKeys: (Hex | ProjPointType<Fp>)[],\n    htfOpts?: htfBasicOpts\n  ) => boolean;\n  aggregatePublicKeys: {\n    (publicKeys: Hex[]): Uint8Array;\n    (publicKeys: ProjPointType<Fp>[]): ProjPointType<Fp>;\n  };\n  aggregateSignatures: {\n    (signatures: Hex[]): Uint8Array;\n    (signatures: ProjPointType<Fp2>[]): ProjPointType<Fp2>;\n  };\n  aggregateShortSignatures: {\n    (signatures: Hex[]): Uint8Array;\n    (signatures: ProjPointType<Fp>[]): ProjPointType<Fp>;\n  };\n  millerLoopBatch: (pairs: [Precompute, Fp, Fp][]) => Fp12;\n  pairing: (P: ProjPointType<Fp>, Q: ProjPointType<Fp2>, withFinalExponent?: boolean) => Fp12;\n  pairingBatch: (\n    pairs: { g1: ProjPointType<Fp>; g2: ProjPointType<Fp2> }[],\n    withFinalExponent?: boolean\n  ) => Fp12;\n  G1: CurvePointsRes<Fp> & ReturnType<typeof createHasher<Fp>>;\n  G2: CurvePointsRes<Fp2> & ReturnType<typeof createHasher<Fp2>>;\n  Signature: SignatureCoder<Fp2>;\n  ShortSignature: ShortSignatureCoder<Fp>;\n  params: {\n    ateLoopSize: bigint;\n    r: bigint;\n    G1b: bigint;\n    G2b: Fp2;\n  };\n  fields: {\n    Fp: IField<Fp>;\n    Fp2: Fp2Bls;\n    Fp6: IField<Fp6>;\n    Fp12: Fp12Bls;\n    Fr: IField<bigint>;\n  };\n  utils: {\n    randomPrivateKey: () => Uint8Array;\n    calcPairingPrecomputes: (p: ProjPointType<Fp2>) => Precompute;\n  };\n};\n\n// Not used with BLS12-381 (no sequential `11` in X). Useful for other curves.\nfunction NAfDecomposition(a: bigint) {\n  const res = [];\n  // a>1 because of marker bit\n  for (; a > _1n; a >>= _1n) {\n    if ((a & _1n) === _0n) res.unshift(0);\n    else if ((a & _3n) === _3n) {\n      res.unshift(-1);\n      a += _1n;\n    } else res.unshift(1);\n  }\n  return res;\n}\n\nexport function bls(CURVE: CurveType): CurveFn {\n  // Fields are specific for curve, so for now we'll need to pass them with opts\n  const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields;\n  const BLS_X_IS_NEGATIVE = CURVE.params.xNegative;\n  const TWIST: TwistType = CURVE.params.twistType;\n  // Point on G1 curve: (x, y)\n  const G1_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G1 });\n  const G1 = Object.assign(\n    G1_,\n    createHasher(G1_.ProjectivePoint, CURVE.G1.mapToCurve, {\n      ...CURVE.htfDefaults,\n      ...CURVE.G1.htfDefaults,\n    })\n  );\n  // Point on G2 curve (complex numbers): (x\u2081, x\u2082+i), (y\u2081, y\u2082+i)\n  const G2_ = weierstrassPoints({ n: Fr.ORDER, ...CURVE.G2 });\n  const G2 = Object.assign(\n    G2_,\n    createHasher(G2_.ProjectivePoint as H2CPointConstructor<Fp2>, CURVE.G2.mapToCurve, {\n      ...CURVE.htfDefaults,\n      ...CURVE.G2.htfDefaults,\n    })\n  );\n  type G1 = typeof G1.ProjectivePoint.BASE;\n  type G2 = typeof G2.ProjectivePoint.BASE;\n\n  // Applies sparse multiplication as line function\n  let lineFunction: (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) => Fp12;\n  if (TWIST === 'multiplicative') {\n    lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>\n      Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py));\n  } else if (TWIST === 'divisive') {\n    // NOTE: it should be [c0, c1, c2], but we use different order here to reduce complexity of\n    // precompute calculations.\n    lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>\n      Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0);\n  } else throw new Error('bls: unknown twist type');\n\n  const Fp2div2 = Fp2.div(Fp2.ONE, Fp2.mul(Fp2.ONE, _2n));\n  function pointDouble(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2) {\n    const t0 = Fp2.sqr(Ry); // Ry\u00B2\n    const t1 = Fp2.sqr(Rz); // Rz\u00B2\n    const t2 = Fp2.mulByB(Fp2.mul(t1, _3n)); // 3 * T1 * B\n    const t3 = Fp2.mul(t2, _3n); // 3 * T2\n    const t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)\u00B2 - T1 - T0\n    const c0 = Fp2.sub(t2, t0); // T2 - T0 (i)\n    const c1 = Fp2.mul(Fp2.sqr(Rx), _3n); // 3 * Rx\u00B2\n    const c2 = Fp2.neg(t4); // -T4 (-h)\n\n    ell.push([c0, c1, c2]);\n\n    Rx = Fp2.mul(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), Fp2div2); // ((T0 - T3) * Rx * Ry) / 2\n    Ry = Fp2.sub(Fp2.sqr(Fp2.mul(Fp2.add(t0, t3), Fp2div2)), Fp2.mul(Fp2.sqr(t2), _3n)); // ((T0 + T3) / 2)\u00B2 - 3 * T2\u00B2\n    Rz = Fp2.mul(t0, t4); // T0 * T4\n    return { Rx, Ry, Rz };\n  }\n  function pointAdd(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2, Qx: Fp2, Qy: Fp2) {\n    // Addition\n    const t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz\n    const t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz\n    const c0 = Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)); // T0 * Qx - T1 * Qy == Ry * Qx  - Rx * Qy\n    const c1 = Fp2.neg(t0); // -T0 == Qy * Rz - Ry\n    const c2 = t1; // == Rx - Qx * Rz\n\n    ell.push([c0, c1, c2]);\n\n    const t2 = Fp2.sqr(t1); // T1\u00B2\n    const t3 = Fp2.mul(t2, t1); // T2 * T1\n    const t4 = Fp2.mul(t2, Rx); // T2 * Rx\n    const t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0\u00B2 * Rz\n    Rx = Fp2.mul(t1, t5); // T1 * T5\n    Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry\n    Rz = Fp2.mul(Rz, t3); // Rz * T3\n    return { Rx, Ry, Rz };\n  }\n\n  // Pre-compute coefficients for sparse multiplication\n  // Point addition and point double calculations is reused for coefficients\n  // pointAdd happens only if bit set, so wNAF is reasonable. Unfortunately we cannot combine\n  // add + double in windowed precomputes here, otherwise it would be single op (since X is static)\n  const ATE_NAF = NAfDecomposition(CURVE.params.ateLoopSize);\n\n  const calcPairingPrecomputes = memoized((point: G2) => {\n    const p = point;\n    const { x, y } = p.toAffine();\n    // prettier-ignore\n    const Qx = x, Qy = y, negQy = Fp2.neg(y);\n    // prettier-ignore\n    let Rx = Qx, Ry = Qy, Rz = Fp2.ONE;\n    const ell: Precompute = [];\n    for (const bit of ATE_NAF) {\n      const cur: PrecomputeSingle = [];\n      ({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz));\n      if (bit) ({ Rx, Ry, Rz } = pointAdd(cur, Rx, Ry, Rz, Qx, bit === -1 ? negQy : Qy));\n      ell.push(cur);\n    }\n    if (CURVE.postPrecompute) {\n      const last = ell[ell.length - 1];\n      CURVE.postPrecompute(Rx, Ry, Rz, Qx, Qy, pointAdd.bind(null, last));\n    }\n    return ell;\n  });\n\n  // Main pairing logic is here. Computes product of miller loops + final exponentiate\n  // Applies calculated precomputes\n  type MillerInput = [Precompute, Fp, Fp][];\n  function millerLoopBatch(pairs: MillerInput, withFinalExponent: boolean = false) {\n    let f12 = Fp12.ONE;\n    if (pairs.length) {\n      const ellLen = pairs[0][0].length;\n      for (let i = 0; i < ellLen; i++) {\n        f12 = Fp12.sqr(f12); // This allows us to do sqr only one time for all pairings\n        // NOTE: we apply multiple pairings in parallel here\n        for (const [ell, Px, Py] of pairs) {\n          for (const [c0, c1, c2] of ell[i]) f12 = lineFunction(c0, c1, c2, f12, Px, Py);\n        }\n      }\n    }\n    if (BLS_X_IS_NEGATIVE) f12 = Fp12.conjugate(f12);\n    return withFinalExponent ? Fp12.finalExponentiate(f12) : f12;\n  }\n  type PairingInput = { g1: G1; g2: G2 };\n  // Calculates product of multiple pairings\n  // This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))`\n  function pairingBatch(pairs: PairingInput[], withFinalExponent: boolean = true) {\n    const res: MillerInput = [];\n    // Cache precomputed toAffine for all points\n    G1.ProjectivePoint.normalizeZ(pairs.map(({ g1 }) => g1));\n    G2.ProjectivePoint.normalizeZ(pairs.map(({ g2 }) => g2));\n    for (const { g1, g2 } of pairs) {\n      if (g1.equals(G1.ProjectivePoint.ZERO) || g2.equals(G2.ProjectivePoint.ZERO))\n        throw new Error('pairing is not available for ZERO point');\n      // This uses toAffine inside\n      g1.assertValidity();\n      g2.assertValidity();\n      const Qa = g1.toAffine();\n      res.push([calcPairingPrecomputes(g2), Qa.x, Qa.y]);\n    }\n    return millerLoopBatch(res, withFinalExponent);\n  }\n  // Calculates bilinear pairing\n  function pairing(Q: G1, P: G2, withFinalExponent: boolean = true): Fp12 {\n    return pairingBatch([{ g1: Q, g2: P }], withFinalExponent);\n  }\n\n  const utils = {\n    randomPrivateKey: (): Uint8Array => {\n      const length = getMinHashLength(Fr.ORDER);\n      return mapHashToField(CURVE.randomBytes(length), Fr.ORDER);\n    },\n    calcPairingPrecomputes,\n  };\n\n  const { ShortSignature } = CURVE.G1;\n  const { Signature } = CURVE.G2;\n\n  type G1Hex = Hex | G1;\n  type G2Hex = Hex | G2;\n  function normP1(point: G1Hex): G1 {\n    return point instanceof G1.ProjectivePoint ? (point as G1) : G1.ProjectivePoint.fromHex(point);\n  }\n  function normP1Hash(point: G1Hex, htfOpts?: htfBasicOpts): G1 {\n    return point instanceof G1.ProjectivePoint\n      ? point\n      : (G1.hashToCurve(ensureBytes('point', point), htfOpts) as G1);\n  }\n  function normP2(point: G2Hex): G2 {\n    return point instanceof G2.ProjectivePoint ? point : Signature.fromHex(point);\n  }\n  function normP2Hash(point: G2Hex, htfOpts?: htfBasicOpts): G2 {\n    return point instanceof G2.ProjectivePoint\n      ? point\n      : (G2.hashToCurve(ensureBytes('point', point), htfOpts) as G2);\n  }\n\n  // Multiplies generator (G1) by private key.\n  // P = pk x G\n  function getPublicKey(privateKey: PrivKey): Uint8Array {\n    return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n  }\n\n  // Multiplies generator (G2) by private key.\n  // P = pk x G\n  function getPublicKeyForShortSignatures(privateKey: PrivKey): Uint8Array {\n    return G2.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);\n  }\n\n  // Executes `hashToCurve` on the message and then multiplies the result by private key.\n  // S = pk x H(m)\n  function sign(message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;\n  function sign(message: G2, privateKey: PrivKey, htfOpts?: htfBasicOpts): G2;\n  function sign(message: G2Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array | G2 {\n    const msgPoint = normP2Hash(message, htfOpts);\n    msgPoint.assertValidity();\n    const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n    if (message instanceof G2.ProjectivePoint) return sigPoint;\n    return Signature.toRawBytes(sigPoint);\n  }\n\n  function signShortSignature(\n    message: Hex,\n    privateKey: PrivKey,\n    htfOpts?: htfBasicOpts\n  ): Uint8Array;\n  function signShortSignature(message: G1, privateKey: PrivKey, htfOpts?: htfBasicOpts): G1;\n  function signShortSignature(\n    message: G1Hex,\n    privateKey: PrivKey,\n    htfOpts?: htfBasicOpts\n  ): Uint8Array | G1 {\n    const msgPoint = normP1Hash(message, htfOpts);\n    msgPoint.assertValidity();\n    const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey));\n    if (message instanceof G1.ProjectivePoint) return sigPoint;\n    return ShortSignature.toRawBytes(sigPoint);\n  }\n\n  // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n  // e(P, H(m)) == e(G, S)\n  function verify(\n    signature: G2Hex,\n    message: G2Hex,\n    publicKey: G1Hex,\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    const P = normP1(publicKey);\n    const Hm = normP2Hash(message, htfOpts);\n    const G = G1.ProjectivePoint.BASE;\n    const S = normP2(signature);\n    const exp = pairingBatch([\n      { g1: P.negate(), g2: Hm }, // ePHM = pairing(P.negate(), Hm, false);\n      { g1: G, g2: S }, // eGS = pairing(G, S, false);\n    ]);\n    return Fp12.eql(exp, Fp12.ONE);\n  }\n\n  // Checks if pairing of public key & hash is equal to pairing of generator & signature.\n  // e(S, G) == e(H(m), P)\n  function verifyShortSignature(\n    signature: G1Hex,\n    message: G1Hex,\n    publicKey: G2Hex,\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    const P = normP2(publicKey);\n    const Hm = normP1Hash(message, htfOpts);\n    const G = G2.ProjectivePoint.BASE;\n    const S = normP1(signature);\n    const exp = pairingBatch([\n      { g1: Hm, g2: P }, // eHmP = pairing(Hm, P, false);\n      { g1: S, g2: G.negate() }, // eSG = pairing(S, G.negate(), false);\n    ]);\n    return Fp12.eql(exp, Fp12.ONE);\n  }\n\n  function aNonEmpty(arr: any[]) {\n    if (!Array.isArray(arr) || arr.length === 0) throw new Error('expected non-empty array');\n  }\n\n  // Adds a bunch of public key points together.\n  // pk1 + pk2 + pk3 = pkA\n  function aggregatePublicKeys(publicKeys: Hex[]): Uint8Array;\n  function aggregatePublicKeys(publicKeys: G1[]): G1;\n  function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {\n    aNonEmpty(publicKeys);\n    const agg = publicKeys.map(normP1).reduce((sum, p) => sum.add(p), G1.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (publicKeys[0] instanceof G1.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    // toRawBytes ensures point validity\n    return aggAffine.toRawBytes(true);\n  }\n\n  // Adds a bunch of signature points together.\n  function aggregateSignatures(signatures: Hex[]): Uint8Array;\n  function aggregateSignatures(signatures: G2[]): G2;\n  function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {\n    aNonEmpty(signatures);\n    const agg = signatures.map(normP2).reduce((sum, s) => sum.add(s), G2.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (signatures[0] instanceof G2.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    return Signature.toRawBytes(aggAffine);\n  }\n\n  // Adds a bunch of signature points together.\n  function aggregateShortSignatures(signatures: Hex[]): Uint8Array;\n  function aggregateShortSignatures(signatures: G1[]): G1;\n  function aggregateShortSignatures(signatures: G1Hex[]): Uint8Array | G1 {\n    aNonEmpty(signatures);\n    const agg = signatures.map(normP1).reduce((sum, s) => sum.add(s), G1.ProjectivePoint.ZERO);\n    const aggAffine = agg; //.toAffine();\n    if (signatures[0] instanceof G1.ProjectivePoint) {\n      aggAffine.assertValidity();\n      return aggAffine;\n    }\n    return ShortSignature.toRawBytes(aggAffine);\n  }\n\n  // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407\n  // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))\n  function verifyBatch(\n    signature: G2Hex,\n    // TODO: maybe `{message: G2Hex, publicKey: G1Hex}[]` instead?\n    messages: G2Hex[],\n    publicKeys: G1Hex[],\n    htfOpts?: htfBasicOpts\n  ): boolean {\n    aNonEmpty(messages);\n    if (publicKeys.length !== messages.length)\n      throw new Error('amount of public keys and messages should be equal');\n    const sig = normP2(signature);\n    const nMessages = messages.map((i) => normP2Hash(i, htfOpts));\n    const nPublicKeys = publicKeys.map(normP1);\n    // NOTE: this works only for exact same object\n    const messagePubKeyMap = new Map<G2, G1[]>();\n    for (let i = 0; i < nPublicKeys.length; i++) {\n      const pub = nPublicKeys[i];\n      const msg = nMessages[i];\n      let keys = messagePubKeyMap.get(msg);\n      if (keys === undefined) {\n        keys = [];\n        messagePubKeyMap.set(msg, keys);\n      }\n      keys.push(pub);\n    }\n    const paired = [];\n    try {\n      for (const [msg, keys] of messagePubKeyMap) {\n        const groupPublicKey = keys.reduce((acc, msg) => acc.add(msg));\n        paired.push({ g1: groupPublicKey, g2: msg });\n      }\n      paired.push({ g1: G1.ProjectivePoint.BASE.negate(), g2: sig });\n      return Fp12.eql(pairingBatch(paired), Fp12.ONE);\n    } catch {\n      return false;\n    }\n  }\n\n  G1.ProjectivePoint.BASE._setWindowSize(4);\n\n  return {\n    getPublicKey,\n    getPublicKeyForShortSignatures,\n    sign,\n    signShortSignature,\n    verify,\n    verifyBatch,\n    verifyShortSignature,\n    aggregatePublicKeys,\n    aggregateSignatures,\n    aggregateShortSignatures,\n    millerLoopBatch,\n    pairing,\n    pairingBatch,\n    G1,\n    G2,\n    Signature,\n    ShortSignature,\n    fields: {\n      Fr,\n      Fp,\n      Fp2,\n      Fp6,\n      Fp12,\n    },\n    params: {\n      ateLoopSize: CURVE.params.ateLoopSize,\n      r: CURVE.params.r,\n      G1b: CURVE.G1.b,\n      G2b: CURVE.G2.b,\n    },\n    utils,\n  };\n}\n", "/**\n * Towered extension fields.\n * Rather than implementing a massive 12th-degree extension directly, it is more efficient\n * to build it up from smaller extensions: a tower of extensions.\n *\n * For BLS12-381, the Fp12 field is implemented as a quadratic (degree two) extension,\n * on top of a cubic (degree three) extension, on top of a quadratic extension of Fp.\n *\n * For more info: \"Pairings for beginners\" by Costello, section 7.3.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport * as mod from './modular.ts';\nimport { bitLen, bitMask, concatBytes, notImplemented } from './utils.ts';\nimport type { ProjConstructor, ProjPointType } from './weierstrass.ts';\n\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);\n\n// Fp\u2082 over complex plane\nexport type BigintTuple = [bigint, bigint];\nexport type Fp = bigint;\n// Finite extension field over irreducible polynominal.\n// Fp(u) / (u\u00B2 - \u03B2) where \u03B2 = -1\nexport type Fp2 = { c0: bigint; c1: bigint };\nexport type BigintSix = [bigint, bigint, bigint, bigint, bigint, bigint];\nexport type Fp6 = { c0: Fp2; c1: Fp2; c2: Fp2 };\nexport type Fp12 = { c0: Fp6; c1: Fp6 }; // Fp\u2081\u2082 = Fp\u2086\u00B2 => Fp\u2082\u00B3, Fp\u2086(w) / (w\u00B2 - \u03B3) where \u03B3 = v\n// prettier-ignore\nexport type BigintTwelve = [\n  bigint, bigint, bigint, bigint, bigint, bigint,\n  bigint, bigint, bigint, bigint, bigint, bigint\n];\n\nexport type Fp2Bls = mod.IField<Fp2> & {\n  reim: (num: Fp2) => { re: Fp; im: Fp };\n  mulByB: (num: Fp2) => Fp2;\n  frobeniusMap(num: Fp2, power: number): Fp2;\n  fromBigTuple(num: [bigint, bigint]): Fp2;\n};\n\nexport type Fp12Bls = mod.IField<Fp12> & {\n  frobeniusMap(num: Fp12, power: number): Fp12;\n  mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n  mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n  conjugate(num: Fp12): Fp12;\n  finalExponentiate(num: Fp12): Fp12;\n  fromBigTwelve(num: BigintTwelve): Fp12;\n};\n\nfunction calcFrobeniusCoefficients<T>(\n  Fp: mod.IField<T>,\n  nonResidue: T,\n  modulus: bigint,\n  degree: number,\n  num: number = 1,\n  divisor?: number\n) {\n  const _divisor = BigInt(divisor === undefined ? degree : divisor);\n  const towerModulus: any = modulus ** BigInt(degree);\n  const res: T[][] = [];\n  for (let i = 0; i < num; i++) {\n    const a = BigInt(i + 1);\n    const powers: T[] = [];\n    for (let j = 0, qPower = _1n; j < degree; j++) {\n      const power = ((a * qPower - a) / _divisor) % towerModulus;\n      powers.push(Fp.pow(nonResidue, power));\n      qPower *= modulus;\n    }\n    res.push(powers);\n  }\n  return res;\n}\n\n// This works same at least for bls12-381, bn254 and bls12-377\nexport function psiFrobenius(\n  Fp: mod.IField<Fp>,\n  Fp2: Fp2Bls,\n  base: Fp2\n): {\n  psi: (x: Fp2, y: Fp2) => [Fp2, Fp2];\n  psi2: (x: Fp2, y: Fp2) => [Fp2, Fp2];\n  G2psi: (c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) => ProjPointType<Fp2>;\n  G2psi2: (c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) => ProjPointType<Fp2>;\n  PSI_X: Fp2;\n  PSI_Y: Fp2;\n  PSI2_X: Fp2;\n  PSI2_Y: Fp2;\n} {\n  // \u03A8 endomorphism\n  const PSI_X = Fp2.pow(base, (Fp.ORDER - _1n) / _3n); // u^((p-1)/3)\n  const PSI_Y = Fp2.pow(base, (Fp.ORDER - _1n) / _2n); // u^((p-1)/2)\n  function psi(x: Fp2, y: Fp2): [Fp2, Fp2] {\n    // This x10 faster than previous version in bls12-381\n    const x2 = Fp2.mul(Fp2.frobeniusMap(x, 1), PSI_X);\n    const y2 = Fp2.mul(Fp2.frobeniusMap(y, 1), PSI_Y);\n    return [x2, y2];\n  }\n  // \u03A8\u00B2(P) endomorphism (psi2(x) = psi(psi(x)))\n  const PSI2_X = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _3n); // u^((p^2 - 1)/3)\n  // This equals -1, which causes y to be Fp2.neg(y).\n  // But not sure if there are case when this is not true?\n  const PSI2_Y = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _2n); // u^((p^2 - 1)/3)\n  if (!Fp2.eql(PSI2_Y, Fp2.neg(Fp2.ONE))) throw new Error('psiFrobenius: PSI2_Y!==-1');\n  function psi2(x: Fp2, y: Fp2): [Fp2, Fp2] {\n    return [Fp2.mul(x, PSI2_X), Fp2.neg(y)];\n  }\n  // Map points\n  const mapAffine =\n    <T>(fn: (x: T, y: T) => [T, T]) =>\n    (c: ProjConstructor<T>, P: ProjPointType<T>) => {\n      const affine = P.toAffine();\n      const p = fn(affine.x, affine.y);\n      return c.fromAffine({ x: p[0], y: p[1] });\n    };\n  const G2psi = mapAffine(psi);\n  const G2psi2 = mapAffine(psi2);\n  return { psi, psi2, G2psi, G2psi2, PSI_X, PSI_Y, PSI2_X, PSI2_Y };\n}\n\nexport type Tower12Opts = {\n  ORDER: bigint;\n  NONRESIDUE?: Fp;\n  // Fp2\n  FP2_NONRESIDUE: BigintTuple;\n  Fp2sqrt?: (num: Fp2) => Fp2;\n  Fp2mulByB: (num: Fp2) => Fp2;\n  // Fp12\n  Fp12cyclotomicSquare: (num: Fp12) => Fp12;\n  Fp12cyclotomicExp: (num: Fp12, n: bigint) => Fp12;\n  Fp12finalExponentiate: (num: Fp12) => Fp12;\n};\n\nexport function tower12(opts: Tower12Opts): {\n  Fp: Readonly<mod.IField<bigint> & Required<Pick<mod.IField<bigint>, 'isOdd'>>>;\n  Fp2: mod.IField<Fp2> & {\n    NONRESIDUE: Fp2;\n    fromBigTuple: (tuple: BigintTuple | bigint[]) => Fp2;\n    reim: (num: Fp2) => { re: bigint; im: bigint };\n    mulByNonresidue: (num: Fp2) => Fp2;\n    mulByB: (num: Fp2) => Fp2;\n    frobeniusMap(num: Fp2, power: number): Fp2;\n  };\n  Fp6: mod.IField<Fp6> & {\n    fromBigSix: (tuple: BigintSix) => Fp6;\n    mulByNonresidue: (num: Fp6) => Fp6;\n    frobeniusMap(num: Fp6, power: number): Fp6;\n    mul1(num: Fp6, b1: Fp2): Fp6;\n    mul01(num: Fp6, b0: Fp2, b1: Fp2): Fp6;\n    mulByFp2(lhs: Fp6, rhs: Fp2): Fp6;\n  };\n  Fp4Square: (a: Fp2, b: Fp2) => { first: Fp2; second: Fp2 };\n  Fp12: mod.IField<Fp12> & {\n    fromBigTwelve: (t: BigintTwelve) => Fp12;\n    frobeniusMap(num: Fp12, power: number): Fp12;\n    mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n    mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n    mulByFp2(lhs: Fp12, rhs: Fp2): Fp12;\n    conjugate(num: Fp12): Fp12;\n    finalExponentiate(num: Fp12): Fp12;\n    _cyclotomicSquare(num: Fp12): Fp12;\n    _cyclotomicExp(num: Fp12, n: bigint): Fp12;\n  };\n} {\n  const { ORDER } = opts;\n  // Fp\n  const Fp = mod.Field(ORDER);\n  const FpNONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));\n  const Fpdiv2 = Fp.div(Fp.ONE, _2n); // 1/2\n\n  // Fp2\n  const FP2_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, FpNONRESIDUE, Fp.ORDER, 2)[0];\n  const Fp2Add = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({\n    c0: Fp.add(c0, r0),\n    c1: Fp.add(c1, r1),\n  });\n  const Fp2Subtract = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({\n    c0: Fp.sub(c0, r0),\n    c1: Fp.sub(c1, r1),\n  });\n  const Fp2Multiply = ({ c0, c1 }: Fp2, rhs: Fp2) => {\n    if (typeof rhs === 'bigint') return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };\n    // (a+bi)(c+di) = (ac\u2212bd) + (ad+bc)i\n    const { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp.mul(c0, r0); // c0 * o0\n    let t2 = Fp.mul(c1, r1); // c1 * o1\n    // (T1 - T2) + ((c0 + c1) * (r0 + r1) - (T1 + T2))*i\n    const o0 = Fp.sub(t1, t2);\n    const o1 = Fp.sub(Fp.mul(Fp.add(c0, c1), Fp.add(r0, r1)), Fp.add(t1, t2));\n    return { c0: o0, c1: o1 };\n  };\n  const Fp2Square = ({ c0, c1 }: Fp2) => {\n    const a = Fp.add(c0, c1);\n    const b = Fp.sub(c0, c1);\n    const c = Fp.add(c0, c0);\n    return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };\n  };\n  type Fp2Utils = {\n    NONRESIDUE: Fp2;\n    fromBigTuple: (tuple: BigintTuple | bigint[]) => Fp2;\n    reim: (num: Fp2) => { re: bigint; im: bigint };\n    mulByNonresidue: (num: Fp2) => Fp2;\n    mulByB: (num: Fp2) => Fp2;\n    frobeniusMap(num: Fp2, power: number): Fp2;\n  };\n  const Fp2fromBigTuple = (tuple: BigintTuple | bigint[]) => {\n    if (tuple.length !== 2) throw new Error('invalid tuple');\n    const fps = tuple.map((n) => Fp.create(n)) as [Fp, Fp];\n    return { c0: fps[0], c1: fps[1] };\n  };\n\n  const FP2_ORDER = ORDER * ORDER;\n  const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);\n  const Fp2: mod.IField<Fp2> & Fp2Utils = {\n    ORDER: FP2_ORDER,\n    isLE: Fp.isLE,\n    NONRESIDUE: Fp2Nonresidue,\n    BITS: bitLen(FP2_ORDER),\n    BYTES: Math.ceil(bitLen(FP2_ORDER) / 8),\n    MASK: bitMask(bitLen(FP2_ORDER)),\n    ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },\n    ONE: { c0: Fp.ONE, c1: Fp.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => typeof c0 === 'bigint' && typeof c1 === 'bigint',\n    is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),\n    eql: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.eql(c0, r0) && Fp.eql(c1, r1),\n    neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),\n    pow: (num, power) => mod.FpPow(Fp2, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),\n    // Normalized\n    add: Fp2Add,\n    sub: Fp2Subtract,\n    mul: Fp2Multiply,\n    sqr: Fp2Square,\n    // NonNormalized stuff\n    addN: Fp2Add,\n    subN: Fp2Subtract,\n    mulN: Fp2Multiply,\n    sqrN: Fp2Square,\n    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?\n    div: (lhs, rhs) =>\n      Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),\n    inv: ({ c0: a, c1: b }) => {\n      // We wish to find the multiplicative inverse of a nonzero\n      // element a + bu in Fp2. We leverage an identity\n      //\n      // (a + bu)(a - bu) = a\u00B2 + b\u00B2\n      //\n      // which holds because u\u00B2 = -1. This can be rewritten as\n      //\n      // (a + bu)(a - bu)/(a\u00B2 + b\u00B2) = 1\n      //\n      // because a\u00B2 + b\u00B2 = 0 has no nonzero solutions for (a, b).\n      // This gives that (a - bu)/(a\u00B2 + b\u00B2) is the inverse\n      // of (a + bu). Importantly, this can be computing using\n      // only a single inversion in Fp.\n      const factor = Fp.inv(Fp.create(a * a + b * b));\n      return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };\n    },\n    sqrt: (num) => {\n      if (opts.Fp2sqrt) return opts.Fp2sqrt(num);\n      // This is generic for all quadratic extensions (Fp2)\n      const { c0, c1 } = num;\n      if (Fp.is0(c1)) {\n        // if c0 is quadratic residue\n        if (mod.FpLegendre(Fp, c0) === 1) return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });\n        else return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, FpNONRESIDUE)) });\n      }\n      const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), FpNONRESIDUE)));\n      let d = Fp.mul(Fp.add(a, c0), Fpdiv2);\n      const legendre = mod.FpLegendre(Fp, d);\n      // -1, Quadratic non residue\n      if (legendre === -1) d = Fp.sub(d, a);\n      const a0 = Fp.sqrt(d);\n      const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, Fpdiv2), a0) });\n      if (!Fp2.eql(Fp2.sqr(candidateSqrt), num)) throw new Error('Cannot find square root');\n      // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num\n      const x1 = candidateSqrt;\n      const x2 = Fp2.neg(x1);\n      const { re: re1, im: im1 } = Fp2.reim(x1);\n      const { re: re2, im: im2 } = Fp2.reim(x2);\n      if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;\n      return x2;\n    },\n    // Same as sgn0_m_eq_2 in RFC 9380\n    isOdd: (x: Fp2) => {\n      const { re: x0, im: x1 } = Fp2.reim(x);\n      const sign_0 = x0 % _2n;\n      const zero_0 = x0 === _0n;\n      const sign_1 = x1 % _2n;\n      return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;\n    },\n    // Bytes util\n    fromBytes(b: Uint8Array): Fp2 {\n      if (b.length !== Fp2.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };\n    },\n    toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n      c0: Fp.cmov(c0, r0, c),\n      c1: Fp.cmov(c1, r1, c),\n    }),\n    reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),\n    // multiply by u + 1\n    mulByNonresidue: ({ c0, c1 }) => Fp2.mul({ c0, c1 }, Fp2Nonresidue),\n    mulByB: opts.Fp2mulByB,\n    fromBigTuple: Fp2fromBigTuple,\n    frobeniusMap: ({ c0, c1 }, power: number): Fp2 => ({\n      c0,\n      c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),\n    }),\n  };\n  // Fp6\n  const Fp6Add = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({\n    c0: Fp2.add(c0, r0),\n    c1: Fp2.add(c1, r1),\n    c2: Fp2.add(c2, r2),\n  });\n  const Fp6Subtract = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({\n    c0: Fp2.sub(c0, r0),\n    c1: Fp2.sub(c1, r1),\n    c2: Fp2.sub(c2, r2),\n  });\n  const Fp6Multiply = ({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) => {\n    if (typeof rhs === 'bigint') {\n      return {\n        c0: Fp2.mul(c0, rhs),\n        c1: Fp2.mul(c1, rhs),\n        c2: Fp2.mul(c2, rhs),\n      };\n    }\n    const { c0: r0, c1: r1, c2: r2 } = rhs;\n    const t0 = Fp2.mul(c0, r0); // c0 * o0\n    const t1 = Fp2.mul(c1, r1); // c1 * o1\n    const t2 = Fp2.mul(c2, r2); // c2 * o2\n    return {\n      // t0 + (c1 + c2) * (r1 * r2) - (T1 + T2) * (u + 1)\n      c0: Fp2.add(\n        t0,\n        Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), Fp2.add(r1, r2)), Fp2.add(t1, t2)))\n      ),\n      // (c0 + c1) * (r0 + r1) - (T0 + T1) + T2 * (u + 1)\n      c1: Fp2.add(\n        Fp2.sub(Fp2.mul(Fp2.add(c0, c1), Fp2.add(r0, r1)), Fp2.add(t0, t1)),\n        Fp2.mulByNonresidue(t2)\n      ),\n      // T1 + (c0 + c2) * (r0 + r2) - T0 + T2\n      c2: Fp2.sub(Fp2.add(t1, Fp2.mul(Fp2.add(c0, c2), Fp2.add(r0, r2))), Fp2.add(t0, t2)),\n    };\n  };\n  const Fp6Square = ({ c0, c1, c2 }: Fp6) => {\n    let t0 = Fp2.sqr(c0); // c0\u00B2\n    let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1\n    let t3 = Fp2.mul(Fp2.mul(c1, c2), _2n); // 2 * c1 * c2\n    let t4 = Fp2.sqr(c2); // c2\u00B2\n    return {\n      c0: Fp2.add(Fp2.mulByNonresidue(t3), t0), // T3 * (u + 1) + T0\n      c1: Fp2.add(Fp2.mulByNonresidue(t4), t1), // T4 * (u + 1) + T1\n      // T1 + (c0 - c1 + c2)\u00B2 + T3 - T0 - T4\n      c2: Fp2.sub(Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.sqr(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0), t4),\n    };\n  };\n  type Fp6Utils = {\n    fromBigSix: (tuple: BigintSix) => Fp6;\n    mulByNonresidue: (num: Fp6) => Fp6;\n    frobeniusMap(num: Fp6, power: number): Fp6;\n    mul1(num: Fp6, b1: Fp2): Fp6;\n    mul01(num: Fp6, b0: Fp2, b1: Fp2): Fp6;\n    mulByFp2(lhs: Fp6, rhs: Fp2): Fp6;\n  };\n\n  const [FP6_FROBENIUS_COEFFICIENTS_1, FP6_FROBENIUS_COEFFICIENTS_2] = calcFrobeniusCoefficients(\n    Fp2,\n    Fp2Nonresidue,\n    Fp.ORDER,\n    6,\n    2,\n    3\n  );\n\n  const Fp6: mod.IField<Fp6> & Fp6Utils = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    isLE: Fp2.isLE,\n    BITS: 3 * Fp2.BITS,\n    BYTES: 3 * Fp2.BYTES,\n    MASK: bitMask(3 * Fp2.BITS),\n    ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),\n    is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),\n    neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),\n    eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) =>\n      Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),\n    sqrt: notImplemented,\n    // Do we need division by bigint at all? Should be done via order:\n    div: (lhs, rhs) =>\n      Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp6, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),\n    // Normalized\n    add: Fp6Add,\n    sub: Fp6Subtract,\n    mul: Fp6Multiply,\n    sqr: Fp6Square,\n    // NonNormalized stuff\n    addN: Fp6Add,\n    subN: Fp6Subtract,\n    mulN: Fp6Multiply,\n    sqrN: Fp6Square,\n\n    inv: ({ c0, c1, c2 }) => {\n      let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0\u00B2 - c2 * c1 * (u + 1)\n      let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2\u00B2 * (u + 1) - c0 * c1\n      let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1\u00B2 - c0 * c2\n      // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)\n      let t4 = Fp2.inv(\n        Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0))\n      );\n      return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };\n    },\n    // Bytes utils\n    fromBytes: (b: Uint8Array): Fp6 => {\n      if (b.length !== Fp6.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return {\n        c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),\n        c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),\n        c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),\n      };\n    },\n    toBytes: ({ c0, c1, c2 }): Uint8Array =>\n      concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),\n    cmov: ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c) => ({\n      c0: Fp2.cmov(c0, r0, c),\n      c1: Fp2.cmov(c1, r1, c),\n      c2: Fp2.cmov(c2, r2, c),\n    }),\n    fromBigSix: (t: BigintSix): Fp6 => {\n      if (!Array.isArray(t) || t.length !== 6) throw new Error('invalid Fp6 usage');\n      return {\n        c0: Fp2.fromBigTuple(t.slice(0, 2)),\n        c1: Fp2.fromBigTuple(t.slice(2, 4)),\n        c2: Fp2.fromBigTuple(t.slice(4, 6)),\n      };\n    },\n    frobeniusMap: ({ c0, c1, c2 }, power: number) => ({\n      c0: Fp2.frobeniusMap(c0, power),\n      c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),\n      c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),\n    }),\n    mulByFp2: ({ c0, c1, c2 }, rhs: Fp2): Fp6 => ({\n      c0: Fp2.mul(c0, rhs),\n      c1: Fp2.mul(c1, rhs),\n      c2: Fp2.mul(c2, rhs),\n    }),\n    mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),\n    // Sparse multiplication\n    mul1: ({ c0, c1, c2 }, b1: Fp2): Fp6 => ({\n      c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),\n      c1: Fp2.mul(c0, b1),\n      c2: Fp2.mul(c1, b1),\n    }),\n    // Sparse multiplication\n    mul01({ c0, c1, c2 }, b0: Fp2, b1: Fp2): Fp6 {\n      let t0 = Fp2.mul(c0, b0); // c0 * b0\n      let t1 = Fp2.mul(c1, b1); // c1 * b1\n      return {\n        // ((c1 + c2) * b1 - T1) * (u + 1) + T0\n        c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),\n        // (b0 + b1) * (c0 + c1) - T0 - T1\n        c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),\n        // (c0 + c2) * b0 - T0 + T1\n        c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),\n      };\n    },\n  };\n\n  // Fp12\n  const FP12_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(\n    Fp2,\n    Fp2Nonresidue,\n    Fp.ORDER,\n    12,\n    1,\n    6\n  )[0];\n\n  const Fp12Add = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({\n    c0: Fp6.add(c0, r0),\n    c1: Fp6.add(c1, r1),\n  });\n  const Fp12Subtract = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({\n    c0: Fp6.sub(c0, r0),\n    c1: Fp6.sub(c1, r1),\n  });\n  const Fp12Multiply = ({ c0, c1 }: Fp12, rhs: Fp12 | bigint) => {\n    if (typeof rhs === 'bigint') return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };\n    let { c0: r0, c1: r1 } = rhs;\n    let t1 = Fp6.mul(c0, r0); // c0 * r0\n    let t2 = Fp6.mul(c1, r1); // c1 * r1\n    return {\n      c0: Fp6.add(t1, Fp6.mulByNonresidue(t2)), // T1 + T2 * v\n      // (c0 + c1) * (r0 + r1) - (T1 + T2)\n      c1: Fp6.sub(Fp6.mul(Fp6.add(c0, c1), Fp6.add(r0, r1)), Fp6.add(t1, t2)),\n    };\n  };\n  const Fp12Square = ({ c0, c1 }: Fp12) => {\n    let ab = Fp6.mul(c0, c1); // c0 * c1\n    return {\n      // (c1 * v + c0) * (c0 + c1) - AB - AB * v\n      c0: Fp6.sub(\n        Fp6.sub(Fp6.mul(Fp6.add(Fp6.mulByNonresidue(c1), c0), Fp6.add(c0, c1)), ab),\n        Fp6.mulByNonresidue(ab)\n      ),\n      c1: Fp6.add(ab, ab),\n    }; // AB + AB\n  };\n  function Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } {\n    const a2 = Fp2.sqr(a);\n    const b2 = Fp2.sqr(b);\n    return {\n      first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b\u00B2 * Nonresidue + a\u00B2\n      second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)\u00B2 - a\u00B2 - b\u00B2\n    };\n  }\n  type Fp12Utils = {\n    fromBigTwelve: (t: BigintTwelve) => Fp12;\n    frobeniusMap(num: Fp12, power: number): Fp12;\n    mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;\n    mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;\n    mulByFp2(lhs: Fp12, rhs: Fp2): Fp12;\n    conjugate(num: Fp12): Fp12;\n    finalExponentiate(num: Fp12): Fp12;\n    _cyclotomicSquare(num: Fp12): Fp12;\n    _cyclotomicExp(num: Fp12, n: bigint): Fp12;\n  };\n\n  const Fp12: mod.IField<Fp12> & Fp12Utils = {\n    ORDER: Fp2.ORDER, // TODO: unused, but need to verify\n    isLE: Fp6.isLE,\n    BITS: 2 * Fp6.BITS,\n    BYTES: 2 * Fp6.BYTES,\n    MASK: bitMask(2 * Fp6.BITS),\n    ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },\n    ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },\n    create: (num) => num,\n    isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),\n    is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),\n    neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),\n    eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),\n    sqrt: notImplemented,\n    inv: ({ c0, c1 }) => {\n      let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0\u00B2 - c1\u00B2 * v)\n      return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w\n    },\n    div: (lhs, rhs) =>\n      Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),\n    pow: (num, power) => mod.FpPow(Fp12, num, power),\n    invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),\n    // Normalized\n    add: Fp12Add,\n    sub: Fp12Subtract,\n    mul: Fp12Multiply,\n    sqr: Fp12Square,\n    // NonNormalized stuff\n    addN: Fp12Add,\n    subN: Fp12Subtract,\n    mulN: Fp12Multiply,\n    sqrN: Fp12Square,\n\n    // Bytes utils\n    fromBytes: (b: Uint8Array): Fp12 => {\n      if (b.length !== Fp12.BYTES) throw new Error('fromBytes invalid length=' + b.length);\n      return {\n        c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),\n        c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),\n      };\n    },\n    toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),\n    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({\n      c0: Fp6.cmov(c0, r0, c),\n      c1: Fp6.cmov(c1, r1, c),\n    }),\n    // Utils\n    // toString() {\n    //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');\n    // },\n    // fromTuple(c: [Fp6, Fp6]) {\n    //   return new Fp12(...c);\n    // }\n    fromBigTwelve: (t: BigintTwelve): Fp12 => ({\n      c0: Fp6.fromBigSix(t.slice(0, 6) as BigintSix),\n      c1: Fp6.fromBigSix(t.slice(6, 12) as BigintSix),\n    }),\n    // Raises to q**i -th power\n    frobeniusMap(lhs, power: number) {\n      const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);\n      const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];\n      return {\n        c0: Fp6.frobeniusMap(lhs.c0, power),\n        c1: Fp6.create({\n          c0: Fp2.mul(c0, coeff),\n          c1: Fp2.mul(c1, coeff),\n          c2: Fp2.mul(c2, coeff),\n        }),\n      };\n    },\n    mulByFp2: ({ c0, c1 }, rhs: Fp2): Fp12 => ({\n      c0: Fp6.mulByFp2(c0, rhs),\n      c1: Fp6.mulByFp2(c1, rhs),\n    }),\n    conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.neg(c1) }),\n    // Sparse multiplication\n    mul014: ({ c0, c1 }, o0: Fp2, o1: Fp2, o4: Fp2) => {\n      let t0 = Fp6.mul01(c0, o0, o1);\n      let t1 = Fp6.mul1(c1, o4);\n      return {\n        c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0\n        // (c1 + c0) * [o0, o1+o4] - T0 - T1\n        c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),\n      };\n    },\n    mul034: ({ c0, c1 }, o0: Fp2, o3: Fp2, o4: Fp2) => {\n      const a = Fp6.create({\n        c0: Fp2.mul(c0.c0, o0),\n        c1: Fp2.mul(c0.c1, o0),\n        c2: Fp2.mul(c0.c2, o0),\n      });\n      const b = Fp6.mul01(c1, o3, o4);\n      const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);\n      return {\n        c0: Fp6.add(Fp6.mulByNonresidue(b), a),\n        c1: Fp6.sub(e, Fp6.add(a, b)),\n      };\n    },\n\n    // A cyclotomic group is a subgroup of Fp^n defined by\n    //   G\u03A6\u2099(p) = {\u03B1 \u2208 Fp\u207F : \u03B1^\u03A6\u2099(p) = 1}\n    // The result of any pairing is in a cyclotomic subgroup\n    // https://eprint.iacr.org/2009/565.pdf\n    _cyclotomicSquare: opts.Fp12cyclotomicSquare,\n    _cyclotomicExp: opts.Fp12cyclotomicExp,\n    // https://eprint.iacr.org/2010/354.pdf\n    // https://eprint.iacr.org/2009/565.pdf\n    finalExponentiate: opts.Fp12finalExponentiate,\n  };\n\n  return { Fp, Fp2, Fp6, Fp4Square, Fp12 };\n}\n", "/**\n * bls12-381 is pairing-friendly Barreto-Lynn-Scott elliptic curve construction allowing to:\n * * Construct zk-SNARKs at the ~120-bit security\n * * Efficiently verify N aggregate signatures with 1 pairing and N ec additions:\n *   the Boneh-Lynn-Shacham signature scheme is orders of magnitude more efficient than Schnorr\n *\n * ### Summary\n * 1. BLS Relies on Bilinear Pairing (expensive)\n * 2. Private Keys: 32 bytes\n * 3. Public Keys: 48 bytes: 381 bit affine x coordinate, encoded into 48 big-endian bytes.\n * 4. Signatures: 96 bytes: two 381 bit integers (affine x coordinate), encoded into two 48 big-endian byte arrays.\n *     - The signature is a point on the G2 subgroup, which is defined over a finite field\n *       with elements twice as big as the G1 curve (G2 is over Fp2 rather than Fp. Fp2 is analogous to the\n *       complex numbers).\n *     - We also support reversed 96-byte pubkeys & 48-byte short signatures.\n * 5. The 12 stands for the Embedding degree.\n *\n * ### Formulas\n * - `P = pk x G` - public keys\n * - `S = pk x H(m)` - signing\n * - `e(P, H(m)) == e(G, S)` - verification using pairings\n * - `e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))` - signature aggregation\n *\n * ### Compatibility and notes\n * 1. It is compatible with Algorand, Chia, Dfinity, Ethereum, Filecoin, ZEC.\n * Filecoin uses little endian byte arrays for private keys - make sure to reverse byte order.\n * 2. Some projects use G2 for public keys and G1 for signatures. It's called \"short signature\".\n * 3. Curve security level is about 120 bits as per [Barbulescu-Duquesne 2017](https://hal.science/hal-01534101/file/main.pdf)\n * 4. Compatible with specs:\n *    [cfrg-pairing-friendly-curves-11](https://tools.ietf.org/html/draft-irtf-cfrg-pairing-friendly-curves-11),\n *    [cfrg-bls-signature-05](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-bls-signature-05),\n *    RFC 9380.\n *\n * ### Params\n * To verify curve parameters, see\n * [pairing-friendly-curves spec](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-pairing-friendly-curves-11).\n * Basic math is done over finite fields over p.\n * More complicated math is done over polynominal extension fields.\n * To simplify calculations in Fp12, we construct extension tower:\n *\n * Embedding degree (k): 12\n * Seed (X): -15132376222941642752\n * Fr:  (x\u2074-x\u00B2+1)\n * Fp: ((x-1)\u00B2 \u22C5 r(x)/3+x)\n * (E/Fp): Y\u00B2=X\u00B3+4\n * (E\u209C/Fp\u00B2): Y\u00B2 = X\u00B3+4(u+1) (M-type twist)\n * Ate loop size: X\n *\n * ### Towers\n * - Fp\u2081\u2082 = Fp\u2086\u00B2 => Fp\u2082\u00B3\n * - Fp(u) / (u\u00B2 - \u03B2) where \u03B2 = -1\n * - Fp\u2082(v) / (v\u00B3 - \u03BE) where \u03BE = u + 1\n * - Fp\u2086(w) / (w\u00B2 - \u03B3) where \u03B3 = v\n * - Fp\u00B2[u] = Fp/u\u00B2+1\n * - Fp\u2076[v] = Fp\u00B2/v\u00B3-1-u\n * - Fp\u00B9\u00B2[w] = Fp\u2076/w\u00B2-v\n *\n * @todo construct bls & bn fp/fr from seed.\n * @module\n */\n/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\nimport { sha256 } from '@noble/hashes/sha2';\nimport { randomBytes } from '@noble/hashes/utils';\nimport { bls, type CurveFn } from './abstract/bls.ts';\nimport { Field } from './abstract/modular.ts';\nimport {\n  bitGet,\n  bitLen,\n  bytesToHex,\n  bytesToNumberBE,\n  concatBytes as concatB,\n  ensureBytes,\n  type Hex,\n  numberToBytesBE,\n} from './abstract/utils.ts';\n// Types\nimport { isogenyMap } from './abstract/hash-to-curve.ts';\nimport type { Fp, Fp12, Fp2, Fp6 } from './abstract/tower.ts';\nimport { psiFrobenius, tower12 } from './abstract/tower.ts';\nimport {\n  type AffinePoint,\n  mapToCurveSimpleSWU,\n  type ProjPointType,\n} from './abstract/weierstrass.ts';\n\n// Be friendly to bad ECMAScript parsers by not using bigint literals\n// prettier-ignore\nconst _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);\n\n// The BLS parameter x (seed) for BLS12-381. NOTE: it is negative!\nconst BLS_X = BigInt('0xd201000000010000');\nconst BLS_X_LEN = bitLen(BLS_X);\n\n// CURVE FIELDS\nconst { Fp, Fp2, Fp6, Fp4Square, Fp12 } = tower12({\n  // Order of Fp\n  ORDER: BigInt(\n    '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'\n  ),\n  // Finite extension field over irreducible polynominal.\n  // Fp(u) / (u\u00B2 - \u03B2) where \u03B2 = -1\n  FP2_NONRESIDUE: [_1n, _1n],\n  Fp2mulByB: ({ c0, c1 }) => {\n    const t0 = Fp.mul(c0, _4n); // 4 * c0\n    const t1 = Fp.mul(c1, _4n); // 4 * c1\n    // (T0-T1) + (T0+T1)*i\n    return { c0: Fp.sub(t0, t1), c1: Fp.add(t0, t1) };\n  },\n  // Fp12\n  // A cyclotomic group is a subgroup of Fp^n defined by\n  //   G\u03A6\u2099(p) = {\u03B1 \u2208 Fp\u207F : \u03B1^\u03A6\u2099(p) = 1}\n  // The result of any pairing is in a cyclotomic subgroup\n  // https://eprint.iacr.org/2009/565.pdf\n  Fp12cyclotomicSquare: ({ c0, c1 }): Fp12 => {\n    const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;\n    const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;\n    const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);\n    const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);\n    const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);\n    const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)\n    return {\n      c0: Fp6.create({\n        c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3\n        c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5\n        c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),\n      }), // 2 * (T7 - c0c2)  + T7\n      c1: Fp6.create({\n        c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9\n        c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4\n        c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),\n      }),\n    }; // 2 * (T6 + c1c2) + T6\n  },\n  Fp12cyclotomicExp(num, n) {\n    let z = Fp12.ONE;\n    for (let i = BLS_X_LEN - 1; i >= 0; i--) {\n      z = Fp12._cyclotomicSquare(z);\n      if (bitGet(n, i)) z = Fp12.mul(z, num);\n    }\n    return z;\n  },\n  // https://eprint.iacr.org/2010/354.pdf\n  // https://eprint.iacr.org/2009/565.pdf\n  Fp12finalExponentiate: (num) => {\n    const x = BLS_X;\n    // this^(q\u2076) / this\n    const t0 = Fp12.div(Fp12.frobeniusMap(num, 6), num);\n    // t0^(q\u00B2) * t0\n    const t1 = Fp12.mul(Fp12.frobeniusMap(t0, 2), t0);\n    const t2 = Fp12.conjugate(Fp12._cyclotomicExp(t1, x));\n    const t3 = Fp12.mul(Fp12.conjugate(Fp12._cyclotomicSquare(t1)), t2);\n    const t4 = Fp12.conjugate(Fp12._cyclotomicExp(t3, x));\n    const t5 = Fp12.conjugate(Fp12._cyclotomicExp(t4, x));\n    const t6 = Fp12.mul(Fp12.conjugate(Fp12._cyclotomicExp(t5, x)), Fp12._cyclotomicSquare(t2));\n    const t7 = Fp12.conjugate(Fp12._cyclotomicExp(t6, x));\n    const t2_t5_pow_q2 = Fp12.frobeniusMap(Fp12.mul(t2, t5), 2);\n    const t4_t1_pow_q3 = Fp12.frobeniusMap(Fp12.mul(t4, t1), 3);\n    const t6_t1c_pow_q1 = Fp12.frobeniusMap(Fp12.mul(t6, Fp12.conjugate(t1)), 1);\n    const t7_t3c_t1 = Fp12.mul(Fp12.mul(t7, Fp12.conjugate(t3)), t1);\n    // (t2 * t5)^(q\u00B2) * (t4 * t1)^(q\u00B3) * (t6 * t1.conj)^(q^1) * t7 * t3.conj * t1\n    return Fp12.mul(Fp12.mul(Fp12.mul(t2_t5_pow_q2, t4_t1_pow_q3), t6_t1c_pow_q1), t7_t3c_t1);\n  },\n});\n\n// Finite field over r.\n// This particular field is not used anywhere in bls12-381, but it is still useful.\nconst Fr = Field(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001'));\n\n// END OF CURVE FIELDS\n\n// HashToCurve\n\n// 3-isogeny map from E' to E https://www.rfc-editor.org/rfc/rfc9380#appendix-E.3\nconst isogenyMapG2 = isogenyMap(\n  Fp2,\n  [\n    // xNum\n    [\n      [\n        '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',\n        '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6',\n      ],\n      [\n        '0x0',\n        '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71a',\n      ],\n      [\n        '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71e',\n        '0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38d',\n      ],\n      [\n        '0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1',\n        '0x0',\n      ],\n    ],\n    // xDen\n    [\n      [\n        '0x0',\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63',\n      ],\n      [\n        '0xc',\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9f',\n      ],\n      ['0x1', '0x0'], // LAST 1\n    ],\n    // yNum\n    [\n      [\n        '0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',\n        '0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706',\n      ],\n      [\n        '0x0',\n        '0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97be',\n      ],\n      [\n        '0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71c',\n        '0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38f',\n      ],\n      [\n        '0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10',\n        '0x0',\n      ],\n    ],\n    // yDen\n    [\n      [\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb',\n      ],\n      [\n        '0x0',\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3',\n      ],\n      [\n        '0x12',\n        '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99',\n      ],\n      ['0x1', '0x0'], // LAST 1\n    ],\n  ].map((i) => i.map((pair) => Fp2.fromBigTuple(pair.map(BigInt)))) as [Fp2[], Fp2[], Fp2[], Fp2[]]\n);\n// 11-isogeny map from E' to E\nconst isogenyMapG1 = isogenyMap(\n  Fp,\n  [\n    // xNum\n    [\n      '0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7',\n      '0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb',\n      '0xd54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0',\n      '0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861',\n      '0xe99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9',\n      '0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983',\n      '0xd6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84',\n      '0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e',\n      '0x80d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317',\n      '0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e',\n      '0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b',\n      '0x6e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229',\n    ],\n    // xDen\n    [\n      '0x8ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c',\n      '0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff',\n      '0xb2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19',\n      '0x3425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8',\n      '0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e',\n      '0xe7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5',\n      '0x772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a',\n      '0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e',\n      '0xa10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641',\n      '0x95fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a',\n      '0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n    // yNum\n    [\n      '0x90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33',\n      '0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696',\n      '0xcc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6',\n      '0x1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb',\n      '0x8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb',\n      '0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0',\n      '0x4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2',\n      '0x987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29',\n      '0x9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587',\n      '0xe1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30',\n      '0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132',\n      '0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e',\n      '0xb182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8',\n      '0x245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133',\n      '0x5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b',\n      '0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604',\n    ],\n    // yDen\n    [\n      '0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1',\n      '0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d',\n      '0x58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2',\n      '0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416',\n      '0xbe0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d',\n      '0x8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac',\n      '0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c',\n      '0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9',\n      '0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a',\n      '0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55',\n      '0x4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8',\n      '0xaccbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092',\n      '0xad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc',\n      '0x2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7',\n      '0xe0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f',\n      '0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001', // LAST 1\n    ],\n  ].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]\n);\n\n// SWU Map - Fp2 to G2': y\u00B2 = x\u00B3 + 240i * x + 1012 + 1012i\nconst G2_SWU = mapToCurveSimpleSWU(Fp2, {\n  A: Fp2.create({ c0: Fp.create(_0n), c1: Fp.create(BigInt(240)) }), // A' = 240 * I\n  B: Fp2.create({ c0: Fp.create(BigInt(1012)), c1: Fp.create(BigInt(1012)) }), // B' = 1012 * (1 + I)\n  Z: Fp2.create({ c0: Fp.create(BigInt(-2)), c1: Fp.create(BigInt(-1)) }), // Z: -(2 + I)\n});\n// Optimized SWU Map - Fp to G1\nconst G1_SWU = mapToCurveSimpleSWU(Fp, {\n  A: Fp.create(\n    BigInt(\n      '0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d'\n    )\n  ),\n  B: Fp.create(\n    BigInt(\n      '0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0'\n    )\n  ),\n  Z: Fp.create(BigInt(11)),\n});\n\n// Endomorphisms (for fast cofactor clearing)\n// \u03A8(P) endomorphism\nconst { G2psi, G2psi2 } = psiFrobenius(Fp, Fp2, Fp2.div(Fp2.ONE, Fp2.NONRESIDUE)); // 1/(u+1)\n\n// Default hash_to_field options are for hash to G2.\n//\n// Parameter definitions are in section 5.3 of the spec unless otherwise noted.\n// Parameter values come from section 8.8.2 of the spec.\n// https://www.rfc-editor.org/rfc/rfc9380#section-8.8.2\n//\n// Base field F is GF(p^m)\n// p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab\n// m = 2 (or 1 for G1 see section 8.8.1)\n// k = 128\nconst htfDefaults = Object.freeze({\n  // DST: a domain separation tag\n  // defined in section 2.2.5\n  // Use utils.getDSTLabel(), utils.setDSTLabel(value)\n  DST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',\n  encodeDST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',\n  // p: the characteristic of F\n  //    where F is a finite field of characteristic p and order q = p^m\n  p: Fp.ORDER,\n  // m: the extension degree of F, m >= 1\n  //     where F is a finite field of characteristic p and order q = p^m\n  m: 2,\n  // k: the target security level for the suite in bits\n  // defined in section 5.1\n  k: 128,\n  // option to use a message that has already been processed by\n  // expand_message_xmd\n  expand: 'xmd',\n  // Hash functions for: expand_message_xmd is appropriate for use with a\n  // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.\n  // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247\n  hash: sha256,\n} as const);\n\n// Encoding utils\n// Point on G1 curve: (x, y)\n\n// Compressed point of infinity\nconst COMPRESSED_ZERO = setMask(Fp.toBytes(_0n), { infinity: true, compressed: true }); // set compressed & point-at-infinity bits\n\nfunction parseMask(bytes: Uint8Array) {\n  // Copy, so we can remove mask data. It will be removed also later, when Fp.create will call modulo.\n  bytes = bytes.slice();\n  const mask = bytes[0] & 0b1110_0000;\n  const compressed = !!((mask >> 7) & 1); // compression bit (0b1000_0000)\n  const infinity = !!((mask >> 6) & 1); // point at infinity bit (0b0100_0000)\n  const sort = !!((mask >> 5) & 1); // sort bit (0b0010_0000)\n  bytes[0] &= 0b0001_1111; // clear mask (zero first 3 bits)\n  return { compressed, infinity, sort, value: bytes };\n}\n\nfunction setMask(\n  bytes: Uint8Array,\n  mask: { compressed?: boolean; infinity?: boolean; sort?: boolean }\n) {\n  if (bytes[0] & 0b1110_0000) throw new Error('setMask: non-empty mask');\n  if (mask.compressed) bytes[0] |= 0b1000_0000;\n  if (mask.infinity) bytes[0] |= 0b0100_0000;\n  if (mask.sort) bytes[0] |= 0b0010_0000;\n  return bytes;\n}\n\nfunction signatureG1ToRawBytes(point: ProjPointType<Fp>) {\n  point.assertValidity();\n  const isZero = point.equals(bls12_381.G1.ProjectivePoint.ZERO);\n  const { x, y } = point.toAffine();\n  if (isZero) return COMPRESSED_ZERO.slice();\n  const P = Fp.ORDER;\n  const sort = Boolean((y * _2n) / P);\n  return setMask(numberToBytesBE(x, Fp.BYTES), { compressed: true, sort });\n}\n\nfunction signatureG2ToRawBytes(point: ProjPointType<Fp2>) {\n  // NOTE: by some reasons it was missed in bls12-381, looks like bug\n  point.assertValidity();\n  const len = Fp.BYTES;\n  if (point.equals(bls12_381.G2.ProjectivePoint.ZERO))\n    return concatB(COMPRESSED_ZERO, numberToBytesBE(_0n, len));\n  const { x, y } = point.toAffine();\n  const { re: x0, im: x1 } = Fp2.reim(x);\n  const { re: y0, im: y1 } = Fp2.reim(y);\n  const tmp = y1 > _0n ? y1 * _2n : y0 * _2n;\n  const sort = Boolean((tmp / Fp.ORDER) & _1n);\n  const z2 = x0;\n  return concatB(\n    setMask(numberToBytesBE(x1, len), { sort, compressed: true }),\n    numberToBytesBE(z2, len)\n  );\n}\n\n/**\n * bls12-381 pairing-friendly curve.\n * @example\n * import { bls12_381 as bls } from '@noble/curves/bls12-381';\n * // G1 keys, G2 signatures\n * const privateKey = '67d53f170b908cabb9eb326c3c337762d59289a8fec79f7bc9254b584b73265c';\n * const message = '64726e3da8';\n * const publicKey = bls.getPublicKey(privateKey);\n * const signature = bls.sign(message, privateKey);\n * const isValid = bls.verify(signature, message, publicKey);\n */\nexport const bls12_381: CurveFn = bls({\n  // Fields\n  fields: {\n    Fp,\n    Fp2,\n    Fp6,\n    Fp12,\n    Fr,\n  },\n  // G1 is the order-q subgroup of E1(Fp) : y\u00B2 = x\u00B3 + 4, #E1(Fp) = h1q, where\n  // characteristic; z + (z\u2074 - z\u00B2 + 1)(z - 1)\u00B2/3\n  G1: {\n    Fp,\n    // cofactor; (z - 1)\u00B2/3\n    h: BigInt('0x396c8c005555e1568c00aaab0000aaab'),\n    // generator's coordinates\n    // x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507\n    // y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569\n    Gx: BigInt(\n      '0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb'\n    ),\n    Gy: BigInt(\n      '0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1'\n    ),\n    a: Fp.ZERO,\n    b: _4n,\n    htfDefaults: { ...htfDefaults, m: 1, DST: 'BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_' },\n    wrapPrivateKey: true,\n    allowInfinityPoint: true,\n    // Checks is the point resides in prime-order subgroup.\n    // point.isTorsionFree() should return true for valid points\n    // It returns false for shitty points.\n    // https://eprint.iacr.org/2021/1130.pdf\n    isTorsionFree: (c, point): boolean => {\n      // \u03C6 endomorphism\n      const cubicRootOfUnityModP = BigInt(\n        '0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe'\n      );\n      const phi = new c(Fp.mul(point.px, cubicRootOfUnityModP), point.py, point.pz);\n\n      // todo: unroll\n      const xP = point.multiplyUnsafe(BLS_X).negate(); // [x]P\n      const u2P = xP.multiplyUnsafe(BLS_X); // [u2]P\n      return u2P.equals(phi);\n\n      // https://eprint.iacr.org/2019/814.pdf\n      // (z\u00B2 \u2212 1)/3\n      // const c1 = BigInt('0x396c8c005555e1560000000055555555');\n      // const P = this;\n      // const S = P.sigma();\n      // const Q = S.double();\n      // const S2 = S.sigma();\n      // // [(z\u00B2 \u2212 1)/3](2\u03C3(P) \u2212 P \u2212 \u03C3\u00B2(P)) \u2212 \u03C3\u00B2(P) = O\n      // const left = Q.subtract(P).subtract(S2).multiplyUnsafe(c1);\n      // const C = left.subtract(S2);\n      // return C.isZero();\n    },\n    // Clear cofactor of G1\n    // https://eprint.iacr.org/2019/403\n    clearCofactor: (_c, point) => {\n      // return this.multiplyUnsafe(CURVE.h);\n      return point.multiplyUnsafe(BLS_X).add(point); // x*P + P\n    },\n    mapToCurve: (scalars: bigint[]) => {\n      const { x, y } = G1_SWU(Fp.create(scalars[0]));\n      return isogenyMapG1(x, y);\n    },\n    fromBytes: (bytes: Uint8Array): AffinePoint<Fp> => {\n      const { compressed, infinity, sort, value } = parseMask(bytes);\n      if (value.length === 48 && compressed) {\n        // TODO: Fp.bytes\n        const P = Fp.ORDER;\n        const compressedValue = bytesToNumberBE(value);\n        // Zero\n        const x = Fp.create(compressedValue & Fp.MASK);\n        if (infinity) {\n          if (x !== _0n) throw new Error('G1: non-empty compressed point at infinity');\n          return { x: _0n, y: _0n };\n        }\n        const right = Fp.add(Fp.pow(x, _3n), Fp.create(bls12_381.params.G1b)); // y\u00B2 = x\u00B3 + b\n        let y = Fp.sqrt(right);\n        if (!y) throw new Error('invalid compressed G1 point');\n        if ((y * _2n) / P !== BigInt(sort)) y = Fp.neg(y);\n        return { x: Fp.create(x), y: Fp.create(y) };\n      } else if (value.length === 96 && !compressed) {\n        // Check if the infinity flag is set\n        const x = bytesToNumberBE(value.subarray(0, Fp.BYTES));\n        const y = bytesToNumberBE(value.subarray(Fp.BYTES));\n        if (infinity) {\n          if (x !== _0n || y !== _0n) throw new Error('G1: non-empty point at infinity');\n          return bls12_381.G1.ProjectivePoint.ZERO.toAffine();\n        }\n        return { x: Fp.create(x), y: Fp.create(y) };\n      } else {\n        throw new Error('invalid point G1, expected 48/96 bytes');\n      }\n    },\n    toBytes: (c, point, isCompressed) => {\n      const isZero = point.equals(c.ZERO);\n      const { x, y } = point.toAffine();\n      if (isCompressed) {\n        if (isZero) return COMPRESSED_ZERO.slice();\n        const P = Fp.ORDER;\n        const sort = Boolean((y * _2n) / P);\n        return setMask(numberToBytesBE(x, Fp.BYTES), { compressed: true, sort });\n      } else {\n        if (isZero) {\n          // 2x PUBLIC_KEY_LENGTH\n          const x = concatB(new Uint8Array([0x40]), new Uint8Array(2 * Fp.BYTES - 1));\n          return x;\n        } else {\n          return concatB(numberToBytesBE(x, Fp.BYTES), numberToBytesBE(y, Fp.BYTES));\n        }\n      }\n    },\n    ShortSignature: {\n      fromHex(hex: Hex): ProjPointType<Fp> {\n        const { infinity, sort, value } = parseMask(ensureBytes('signatureHex', hex, 48));\n        const P = Fp.ORDER;\n        const compressedValue = bytesToNumberBE(value);\n        // Zero\n        if (infinity) return bls12_381.G1.ProjectivePoint.ZERO;\n        const x = Fp.create(compressedValue & Fp.MASK);\n        const right = Fp.add(Fp.pow(x, _3n), Fp.create(bls12_381.params.G1b)); // y\u00B2 = x\u00B3 + b\n        let y = Fp.sqrt(right);\n        if (!y) throw new Error('invalid compressed G1 point');\n        const aflag = BigInt(sort);\n        if ((y * _2n) / P !== aflag) y = Fp.neg(y);\n        const point = bls12_381.G1.ProjectivePoint.fromAffine({ x, y });\n        point.assertValidity();\n        return point;\n      },\n      toRawBytes(point: ProjPointType<Fp>) {\n        return signatureG1ToRawBytes(point);\n      },\n      toHex(point: ProjPointType<Fp>) {\n        return bytesToHex(signatureG1ToRawBytes(point));\n      },\n    },\n  },\n  // G2 is the order-q subgroup of E2(Fp\u00B2) : y\u00B2 = x\u00B3+4(1+\u221A\u22121),\n  // where Fp2 is Fp[\u221A\u22121]/(x2+1). #E2(Fp2 ) = h2q, where\n  // G\u00B2 - 1\n  // h2q\n  G2: {\n    Fp: Fp2,\n    // cofactor\n    h: BigInt(\n      '0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5'\n    ),\n    Gx: Fp2.fromBigTuple([\n      BigInt(\n        '0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8'\n      ),\n      BigInt(\n        '0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e'\n      ),\n    ]),\n    // y =\n    // 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582,\n    // 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905\n    Gy: Fp2.fromBigTuple([\n      BigInt(\n        '0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801'\n      ),\n      BigInt(\n        '0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be'\n      ),\n    ]),\n    a: Fp2.ZERO,\n    b: Fp2.fromBigTuple([_4n, _4n]),\n    hEff: BigInt(\n      '0xbc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551'\n    ),\n    htfDefaults: { ...htfDefaults },\n    wrapPrivateKey: true,\n    allowInfinityPoint: true,\n    mapToCurve: (scalars: bigint[]) => {\n      const { x, y } = G2_SWU(Fp2.fromBigTuple(scalars));\n      return isogenyMapG2(x, y);\n    },\n    // Checks is the point resides in prime-order subgroup.\n    // point.isTorsionFree() should return true for valid points\n    // It returns false for shitty points.\n    // https://eprint.iacr.org/2021/1130.pdf\n    isTorsionFree: (c, P): boolean => {\n      return P.multiplyUnsafe(BLS_X).negate().equals(G2psi(c, P)); // \u03C8(P) == [u](P)\n      // Older version: https://eprint.iacr.org/2019/814.pdf\n      // \u03A8\u00B2(P) => \u03A8\u00B3(P) => [z]\u03A8\u00B3(P) where z = -x => [z]\u03A8\u00B3(P) - \u03A8\u00B2(P) + P == O\n      // return P.psi2().psi().mulNegX().subtract(psi2).add(P).isZero();\n    },\n    // Maps the point into the prime-order subgroup G2.\n    // clear_cofactor_bls12381_g2 from cfrg-hash-to-curve-11\n    // https://eprint.iacr.org/2017/419.pdf\n    // prettier-ignore\n    clearCofactor: (c, P) => {\n      const x = BLS_X;\n      let t1 = P.multiplyUnsafe(x).negate();  // [-x]P\n      let t2 = G2psi(c, P);                   // \u03A8(P)\n      let t3 = P.double();                    // 2P\n      t3 = G2psi2(c, t3);                     // \u03A8\u00B2(2P)\n      t3 = t3.subtract(t2);                   // \u03A8\u00B2(2P) - \u03A8(P)\n      t2 = t1.add(t2);                        // [-x]P + \u03A8(P)\n      t2 = t2.multiplyUnsafe(x).negate();     // [x\u00B2]P - [x]\u03A8(P)\n      t3 = t3.add(t2);                        // \u03A8\u00B2(2P) - \u03A8(P) + [x\u00B2]P - [x]\u03A8(P)\n      t3 = t3.subtract(t1);                   // \u03A8\u00B2(2P) - \u03A8(P) + [x\u00B2]P - [x]\u03A8(P) + [x]P\n      const Q = t3.subtract(P);               // \u03A8\u00B2(2P) - \u03A8(P) + [x\u00B2]P - [x]\u03A8(P) + [x]P - 1P\n      return Q;                               // [x\u00B2-x-1]P + [x-1]\u03A8(P) + \u03A8\u00B2(2P)\n    },\n    fromBytes: (bytes: Uint8Array): AffinePoint<Fp2> => {\n      const { compressed, infinity, sort, value } = parseMask(bytes);\n      if (\n        (!compressed && !infinity && sort) || // 00100000\n        (!compressed && infinity && sort) || // 01100000\n        (sort && infinity && compressed) // 11100000\n      ) {\n        throw new Error('invalid encoding flag: ' + (bytes[0] & 0b1110_0000));\n      }\n      const L = Fp.BYTES;\n      const slc = (b: Uint8Array, from: number, to?: number) => bytesToNumberBE(b.slice(from, to));\n      if (value.length === 96 && compressed) {\n        const b = bls12_381.params.G2b;\n        const P = Fp.ORDER;\n        if (infinity) {\n          // check that all bytes are 0\n          if (value.reduce((p, c) => (p !== 0 ? c + 1 : c), 0) > 0) {\n            throw new Error('invalid compressed G2 point');\n          }\n          return { x: Fp2.ZERO, y: Fp2.ZERO };\n        }\n        const x_1 = slc(value, 0, L);\n        const x_0 = slc(value, L, 2 * L);\n        const x = Fp2.create({ c0: Fp.create(x_0), c1: Fp.create(x_1) });\n        const right = Fp2.add(Fp2.pow(x, _3n), b); // y\u00B2 = x\u00B3 + 4 * (u+1) = x\u00B3 + b\n        let y = Fp2.sqrt(right);\n        const Y_bit = y.c1 === _0n ? (y.c0 * _2n) / P : (y.c1 * _2n) / P ? _1n : _0n;\n        y = sort && Y_bit > 0 ? y : Fp2.neg(y);\n        return { x, y };\n      } else if (value.length === 192 && !compressed) {\n        if (infinity) {\n          if (value.reduce((p, c) => (p !== 0 ? c + 1 : c), 0) > 0) {\n            throw new Error('invalid uncompressed G2 point');\n          }\n          return { x: Fp2.ZERO, y: Fp2.ZERO };\n        }\n        const x1 = slc(value, 0, L);\n        const x0 = slc(value, L, 2 * L);\n        const y1 = slc(value, 2 * L, 3 * L);\n        const y0 = slc(value, 3 * L, 4 * L);\n        return { x: Fp2.fromBigTuple([x0, x1]), y: Fp2.fromBigTuple([y0, y1]) };\n      } else {\n        throw new Error('invalid point G2, expected 96/192 bytes');\n      }\n    },\n    toBytes: (c, point, isCompressed) => {\n      const { BYTES: len, ORDER: P } = Fp;\n      const isZero = point.equals(c.ZERO);\n      const { x, y } = point.toAffine();\n      if (isCompressed) {\n        if (isZero) return concatB(COMPRESSED_ZERO, numberToBytesBE(_0n, len));\n        const flag = Boolean(y.c1 === _0n ? (y.c0 * _2n) / P : (y.c1 * _2n) / P);\n        return concatB(\n          setMask(numberToBytesBE(x.c1, len), { compressed: true, sort: flag }),\n          numberToBytesBE(x.c0, len)\n        );\n      } else {\n        if (isZero) return concatB(new Uint8Array([0x40]), new Uint8Array(4 * len - 1)); // bytes[0] |= 1 << 6;\n        const { re: x0, im: x1 } = Fp2.reim(x);\n        const { re: y0, im: y1 } = Fp2.reim(y);\n        return concatB(\n          numberToBytesBE(x1, len),\n          numberToBytesBE(x0, len),\n          numberToBytesBE(y1, len),\n          numberToBytesBE(y0, len)\n        );\n      }\n    },\n    Signature: {\n      // TODO: Optimize, it's very slow because of sqrt.\n      fromHex(hex: Hex): ProjPointType<Fp2> {\n        const { infinity, sort, value } = parseMask(ensureBytes('signatureHex', hex));\n        const P = Fp.ORDER;\n        const half = value.length / 2;\n        if (half !== 48 && half !== 96)\n          throw new Error('invalid compressed signature length, must be 96 or 192');\n        const z1 = bytesToNumberBE(value.slice(0, half));\n        const z2 = bytesToNumberBE(value.slice(half));\n        // Indicates the infinity point\n        if (infinity) return bls12_381.G2.ProjectivePoint.ZERO;\n        const x1 = Fp.create(z1 & Fp.MASK);\n        const x2 = Fp.create(z2);\n        const x = Fp2.create({ c0: x2, c1: x1 });\n        const y2 = Fp2.add(Fp2.pow(x, _3n), bls12_381.params.G2b); // y\u00B2 = x\u00B3 + 4\n        // The slow part\n        let y = Fp2.sqrt(y2);\n        if (!y) throw new Error('Failed to find a square root');\n\n        // Choose the y whose leftmost bit of the imaginary part is equal to the a_flag1\n        // If y1 happens to be zero, then use the bit of y0\n        const { re: y0, im: y1 } = Fp2.reim(y);\n        const aflag1 = BigInt(sort);\n        const isGreater = y1 > _0n && (y1 * _2n) / P !== aflag1;\n        const isZero = y1 === _0n && (y0 * _2n) / P !== aflag1;\n        if (isGreater || isZero) y = Fp2.neg(y);\n        const point = bls12_381.G2.ProjectivePoint.fromAffine({ x, y });\n        point.assertValidity();\n        return point;\n      },\n      toRawBytes(point: ProjPointType<Fp2>) {\n        return signatureG2ToRawBytes(point);\n      },\n      toHex(point: ProjPointType<Fp2>) {\n        return bytesToHex(signatureG2ToRawBytes(point));\n      },\n    },\n  },\n  params: {\n    ateLoopSize: BLS_X, // The BLS parameter x for BLS12-381\n    r: Fr.ORDER, // order; z\u2074 \u2212 z\u00B2 + 1; CURVE.n from other curves\n    xNegative: true,\n    twistType: 'multiplicative',\n  },\n  htfDefaults,\n  hash: sha256,\n  randomBytes,\n});\n", "import {bls12_381 as bls} from '@noble/curves/bls12-381'\nimport {bn254} from '@kevincharm/noble-bn254-drand'\nimport {sha256} from '@noble/hashes/sha2'\nimport {keccak_256} from '@noble/hashes/sha3'\nimport {CHash, ensureBytes} from '@noble/curves/abstract/utils'\nimport {Buffer} from 'buffer'\nimport {\n    G2ChainedBeacon,\n    ChainInfo,\n    isChainedBeacon,\n    isUnchainedBeacon,\n    RandomnessBeacon,\n    G2UnchainedBeacon,\n    isG1G2SwappedBeacon,\n    G1UnchainedBeacon,\n    isG1Rfc9380, isBn254OnG1\n} from './index'\n\ntype PointG1 = typeof bls.G1.ProjectivePoint.ZERO\ntype PointG2 = typeof bls.G2.ProjectivePoint.ZERO\n\nasync function verifyBeacon(chainInfo: ChainInfo, beacon: RandomnessBeacon, expectedRound: number): Promise<boolean> {\n    const publicKey = chainInfo.public_key\n\n    if (beacon.round !== expectedRound) {\n        console.error('round was not the expected round')\n        return false\n    }\n\n    if (!await randomnessIsValid(beacon)) {\n        console.error('randomness did not match the signature')\n        return false\n    }\n\n    if (isChainedBeacon(beacon, chainInfo)) {\n        return bls.verify(beacon.signature, await chainedBeaconMessage(beacon), publicKey)\n    }\n\n    if (isUnchainedBeacon(beacon, chainInfo)) {\n        return bls.verify(beacon.signature, await unchainedBeaconMessage(beacon), publicKey)\n    }\n\n    if (isG1G2SwappedBeacon(beacon, chainInfo)) {\n        return verifySigOnG1(beacon.signature, await unchainedBeaconMessage(beacon), publicKey)\n    }\n\n    if (isG1Rfc9380(beacon, chainInfo)) {\n        return verifySigOnG1(beacon.signature, await unchainedBeaconMessage(beacon), publicKey, 'BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_')\n    }\n\n    if (isBn254OnG1(beacon, chainInfo)) {\n        return bn254.verifyShortSignature(beacon.signature, await unchainedBeaconMessage(beacon, keccak_256), publicKey, {\n            DST: 'BLS_SIG_BN254G1_XMD:KECCAK-256_SVDW_RO_NUL_'\n        })\n    }\n\n    console.error(`Beacon type ${chainInfo.schemeID} was not supported or the beacon was not of the purported type`)\n    return false\n\n}\n\n// @noble/curves/bls12-381 has not yet implemented public keys on G2, so we've implemented a manual verification for beacons on G1\ntype G1Hex = Uint8Array | string | PointG1;\ntype G2Hex = Uint8Array | string | PointG2;\n\nfunction normP1(point: G1Hex): PointG1 {\n    return point instanceof bls.G1.ProjectivePoint ? point : bls.G1.ProjectivePoint.fromHex(point);\n}\n\nfunction normP2(point: G2Hex): PointG2 {\n    return point instanceof bls.G2.ProjectivePoint ? point : bls.G2.ProjectivePoint.fromHex(point);\n}\n\nfunction normP1Hash(point: G1Hex, domainSeparationTag: string): PointG1 {\n    return point instanceof bls.G1.ProjectivePoint ? point : (bls.G1.hashToCurve(ensureBytes('point', point), {DST: domainSeparationTag}) as PointG1);\n}\n\nexport async function verifySigOnG1(\n    signature: G1Hex,\n    message: G1Hex,\n    publicKey: G2Hex,\n    // default DST is the invalid one used for 'bls-unchained-on-g1' for backwards compat\n    domainSeparationTag = 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_'\n): Promise<boolean> {\n    const P = normP2(publicKey);\n    const Hm = normP1Hash(message, domainSeparationTag);\n    const G = bls.G2.ProjectivePoint.BASE;\n    const S = normP1(signature);\n    const ePHm = bls.pairing(Hm, P.negate(), true);\n    const eGS = bls.pairing(S, G, true);\n    const exp = bls.fields.Fp12.mul(eGS, ePHm);\n    return bls.fields.Fp12.eql(exp, bls.fields.Fp12.ONE);\n}\n\nasync function chainedBeaconMessage(beacon: G2ChainedBeacon): Promise<Uint8Array> {\n    const message = Buffer.concat([\n        signatureBuffer(beacon.previous_signature),\n        roundBuffer(beacon.round)\n    ])\n\n    return sha256(message)\n}\n\nasync function unchainedBeaconMessage(beacon: G2UnchainedBeacon | G1UnchainedBeacon, hashFn: CHash = sha256): Promise<Uint8Array> {\n    return hashFn(roundBuffer(beacon.round))\n}\n\nfunction signatureBuffer(sig: string) {\n    return Buffer.from(sig, 'hex')\n}\n\nfunction roundBuffer(round: number) {\n    const buffer = Buffer.alloc(8)\n    buffer.writeBigUInt64BE(BigInt(round))\n    return buffer\n}\n\nasync function randomnessIsValid(beacon: RandomnessBeacon): Promise<boolean> {\n    const expectedRandomness = sha256(Buffer.from(beacon.signature, 'hex'))\n    return Buffer.from(beacon.randomness, 'hex').compare(expectedRandomness) == 0\n}\n\nexport {verifyBeacon, roundBuffer}\n", "/**\n * SHA3 (keccak) hash function, based on a new \"Sponge function\" design.\n * Different from older hashes, the internal state is bigger than output size.\n *\n * Check out [FIPS-202](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.202.pdf),\n * [Website](https://keccak.team/keccak.html),\n * [the differences between SHA-3 and Keccak](https://crypto.stackexchange.com/questions/15727/what-are-the-key-differences-between-the-draft-sha-3-standard-and-the-keccak-sub).\n *\n * Check out `sha3-addons` module for cSHAKE, k12, and others.\n * @module\n */\nimport { rotlBH, rotlBL, rotlSH, rotlSL, split } from './_u64.ts';\n// prettier-ignore\nimport {\n  abytes, aexists, anumber, aoutput,\n  clean, createHasher, createXOFer, Hash,\n  swap32IfBE,\n  toBytes, u32,\n  type CHash, type CHashXO, type HashXOF, type Input\n} from './utils.ts';\n\n// No __PURE__ annotations in sha3 header:\n// EVERYTHING is in fact used on every export.\n// Various per round constants calculations\nconst _0n = BigInt(0);\nconst _1n = BigInt(1);\nconst _2n = BigInt(2);\nconst _7n = BigInt(7);\nconst _256n = BigInt(256);\nconst _0x71n = BigInt(0x71);\nconst SHA3_PI: number[] = [];\nconst SHA3_ROTL: number[] = [];\nconst _SHA3_IOTA: bigint[] = [];\nfor (let round = 0, R = _1n, x = 1, y = 0; round < 24; round++) {\n  // Pi\n  [x, y] = [y, (2 * x + 3 * y) % 5];\n  SHA3_PI.push(2 * (5 * y + x));\n  // Rotational\n  SHA3_ROTL.push((((round + 1) * (round + 2)) / 2) % 64);\n  // Iota\n  let t = _0n;\n  for (let j = 0; j < 7; j++) {\n    R = ((R << _1n) ^ ((R >> _7n) * _0x71n)) % _256n;\n    if (R & _2n) t ^= _1n << ((_1n << /* @__PURE__ */ BigInt(j)) - _1n);\n  }\n  _SHA3_IOTA.push(t);\n}\nconst IOTAS = split(_SHA3_IOTA, true);\nconst SHA3_IOTA_H = IOTAS[0];\nconst SHA3_IOTA_L = IOTAS[1];\n\n// Left rotation (without 0, 32, 64)\nconst rotlH = (h: number, l: number, s: number) => (s > 32 ? rotlBH(h, l, s) : rotlSH(h, l, s));\nconst rotlL = (h: number, l: number, s: number) => (s > 32 ? rotlBL(h, l, s) : rotlSL(h, l, s));\n\n/** `keccakf1600` internal function, additionally allows to adjust round count. */\nexport function keccakP(s: Uint32Array, rounds: number = 24): void {\n  const B = new Uint32Array(5 * 2);\n  // NOTE: all indices are x2 since we store state as u32 instead of u64 (bigints to slow in js)\n  for (let round = 24 - rounds; round < 24; round++) {\n    // Theta \u03B8\n    for (let x = 0; x < 10; x++) B[x] = s[x] ^ s[x + 10] ^ s[x + 20] ^ s[x + 30] ^ s[x + 40];\n    for (let x = 0; x < 10; x += 2) {\n      const idx1 = (x + 8) % 10;\n      const idx0 = (x + 2) % 10;\n      const B0 = B[idx0];\n      const B1 = B[idx0 + 1];\n      const Th = rotlH(B0, B1, 1) ^ B[idx1];\n      const Tl = rotlL(B0, B1, 1) ^ B[idx1 + 1];\n      for (let y = 0; y < 50; y += 10) {\n        s[x + y] ^= Th;\n        s[x + y + 1] ^= Tl;\n      }\n    }\n    // Rho (\u03C1) and Pi (\u03C0)\n    let curH = s[2];\n    let curL = s[3];\n    for (let t = 0; t < 24; t++) {\n      const shift = SHA3_ROTL[t];\n      const Th = rotlH(curH, curL, shift);\n      const Tl = rotlL(curH, curL, shift);\n      const PI = SHA3_PI[t];\n      curH = s[PI];\n      curL = s[PI + 1];\n      s[PI] = Th;\n      s[PI + 1] = Tl;\n    }\n    // Chi (\u03C7)\n    for (let y = 0; y < 50; y += 10) {\n      for (let x = 0; x < 10; x++) B[x] = s[y + x];\n      for (let x = 0; x < 10; x++) s[y + x] ^= ~B[(x + 2) % 10] & B[(x + 4) % 10];\n    }\n    // Iota (\u03B9)\n    s[0] ^= SHA3_IOTA_H[round];\n    s[1] ^= SHA3_IOTA_L[round];\n  }\n  clean(B);\n}\n\n/** Keccak sponge function. */\nexport class Keccak extends Hash<Keccak> implements HashXOF<Keccak> {\n  protected state: Uint8Array;\n  protected pos = 0;\n  protected posOut = 0;\n  protected finished = false;\n  protected state32: Uint32Array;\n  protected destroyed = false;\n\n  public blockLen: number;\n  public suffix: number;\n  public outputLen: number;\n  protected enableXOF = false;\n  protected rounds: number;\n\n  // NOTE: we accept arguments in bytes instead of bits here.\n  constructor(\n    blockLen: number,\n    suffix: number,\n    outputLen: number,\n    enableXOF = false,\n    rounds: number = 24\n  ) {\n    super();\n    this.blockLen = blockLen;\n    this.suffix = suffix;\n    this.outputLen = outputLen;\n    this.enableXOF = enableXOF;\n    this.rounds = rounds;\n    // Can be passed from user as dkLen\n    anumber(outputLen);\n    // 1600 = 5x5 matrix of 64bit.  1600 bits === 200 bytes\n    // 0 < blockLen < 200\n    if (!(0 < blockLen && blockLen < 200))\n      throw new Error('only keccak-f1600 function is supported');\n    this.state = new Uint8Array(200);\n    this.state32 = u32(this.state);\n  }\n  clone(): Keccak {\n    return this._cloneInto();\n  }\n  protected keccak(): void {\n    swap32IfBE(this.state32);\n    keccakP(this.state32, this.rounds);\n    swap32IfBE(this.state32);\n    this.posOut = 0;\n    this.pos = 0;\n  }\n  update(data: Input): this {\n    aexists(this);\n    data = toBytes(data);\n    abytes(data);\n    const { blockLen, state } = this;\n    const len = data.length;\n    for (let pos = 0; pos < len; ) {\n      const take = Math.min(blockLen - this.pos, len - pos);\n      for (let i = 0; i < take; i++) state[this.pos++] ^= data[pos++];\n      if (this.pos === blockLen) this.keccak();\n    }\n    return this;\n  }\n  protected finish(): void {\n    if (this.finished) return;\n    this.finished = true;\n    const { state, suffix, pos, blockLen } = this;\n    // Do the padding\n    state[pos] ^= suffix;\n    if ((suffix & 0x80) !== 0 && pos === blockLen - 1) this.keccak();\n    state[blockLen - 1] ^= 0x80;\n    this.keccak();\n  }\n  protected writeInto(out: Uint8Array): Uint8Array {\n    aexists(this, false);\n    abytes(out);\n    this.finish();\n    const bufferOut = this.state;\n    const { blockLen } = this;\n    for (let pos = 0, len = out.length; pos < len; ) {\n      if (this.posOut >= blockLen) this.keccak();\n      const take = Math.min(blockLen - this.posOut, len - pos);\n      out.set(bufferOut.subarray(this.posOut, this.posOut + take), pos);\n      this.posOut += take;\n      pos += take;\n    }\n    return out;\n  }\n  xofInto(out: Uint8Array): Uint8Array {\n    // Sha3/Keccak usage with XOF is probably mistake, only SHAKE instances can do XOF\n    if (!this.enableXOF) throw new Error('XOF is not possible for this instance');\n    return this.writeInto(out);\n  }\n  xof(bytes: number): Uint8Array {\n    anumber(bytes);\n    return this.xofInto(new Uint8Array(bytes));\n  }\n  digestInto(out: Uint8Array): Uint8Array {\n    aoutput(out, this);\n    if (this.finished) throw new Error('digest() was already called');\n    this.writeInto(out);\n    this.destroy();\n    return out;\n  }\n  digest(): Uint8Array {\n    return this.digestInto(new Uint8Array(this.outputLen));\n  }\n  destroy(): void {\n    this.destroyed = true;\n    clean(this.state);\n  }\n  _cloneInto(to?: Keccak): Keccak {\n    const { blockLen, suffix, outputLen, rounds, enableXOF } = this;\n    to ||= new Keccak(blockLen, suffix, outputLen, enableXOF, rounds);\n    to.state32.set(this.state32);\n    to.pos = this.pos;\n    to.posOut = this.posOut;\n    to.finished = this.finished;\n    to.rounds = rounds;\n    // Suffix can change in cSHAKE\n    to.suffix = suffix;\n    to.outputLen = outputLen;\n    to.enableXOF = enableXOF;\n    to.destroyed = this.destroyed;\n    return to;\n  }\n}\n\nconst gen = (suffix: number, blockLen: number, outputLen: number) =>\n  createHasher(() => new Keccak(blockLen, suffix, outputLen));\n\n/** SHA3-224 hash function. */\nexport const sha3_224: CHash = /* @__PURE__ */ (() => gen(0x06, 144, 224 / 8))();\n/** SHA3-256 hash function. Different from keccak-256. */\nexport const sha3_256: CHash = /* @__PURE__ */ (() => gen(0x06, 136, 256 / 8))();\n/** SHA3-384 hash function. */\nexport const sha3_384: CHash = /* @__PURE__ */ (() => gen(0x06, 104, 384 / 8))();\n/** SHA3-512 hash function. */\nexport const sha3_512: CHash = /* @__PURE__ */ (() => gen(0x06, 72, 512 / 8))();\n\n/** keccak-224 hash function. */\nexport const keccak_224: CHash = /* @__PURE__ */ (() => gen(0x01, 144, 224 / 8))();\n/** keccak-256 hash function. Different from SHA3-256. */\nexport const keccak_256: CHash = /* @__PURE__ */ (() => gen(0x01, 136, 256 / 8))();\n/** keccak-384 hash function. */\nexport const keccak_384: CHash = /* @__PURE__ */ (() => gen(0x01, 104, 384 / 8))();\n/** keccak-512 hash function. */\nexport const keccak_512: CHash = /* @__PURE__ */ (() => gen(0x01, 72, 512 / 8))();\n\nexport type ShakeOpts = { dkLen?: number };\n\nconst genShake = (suffix: number, blockLen: number, outputLen: number) =>\n  createXOFer<HashXOF<Keccak>, ShakeOpts>(\n    (opts: ShakeOpts = {}) =>\n      new Keccak(blockLen, suffix, opts.dkLen === undefined ? outputLen : opts.dkLen, true)\n  );\n\n/** SHAKE128 XOF with 128-bit security. */\nexport const shake128: CHashXO = /* @__PURE__ */ (() => genShake(0x1f, 168, 128 / 8))();\n/** SHAKE256 XOF with 256-bit security. */\nexport const shake256: CHashXO = /* @__PURE__ */ (() => genShake(0x1f, 136, 256 / 8))();\n", "import {ChainInfo, defaultChainOptions} from './index';\nimport HttpChainClient from './http-chain-client';\nimport HttpCachingChain from './http-caching-chain';\n\nexport const DEFAULT_CHAIN_URL = 'https://api.drand.sh'\n\nexport const DEFAULT_CHAIN_INFO = {\n    public_key: '868f005eb8e6e4ca0a47c8a77ceaa5309a47978a7c71bc5cce96366b5d7a569937c529eeda66c7293784a9402801af31',\n    period: 30,\n    genesis_time: 1595431050,\n    hash: '8990e7a9aaed2ffed73dbd7092123d6f289930540d7651336225dc172e51b2ce',\n    groupHash: '176f93498eac9ca337150b46d21dd58673ea4e3581185f869672e59fa4cb390a',\n    schemeID: 'pedersen-bls-chained',\n    metadata: {\n        'beaconID': 'default'\n    }\n}\nexport const QUICKNET_CHAIN_URL = 'https://api.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971'\n\nexport const QUICKNET_CHAIN_INFO = {\n    public_key: '83cf0f2896adee7eb8b5f01fcad3912212c437e0073e911fb90022d3e760183c8c4b450b6a0a6c3ac6a5776a2d1064510d1fec758c921cc22b0e17e63aaf4bcb5ed66304de9cf809bd274ca73bab4af5a6e9c76a4bc09e76eae8991ef5ece45a',\n    period: 3,\n    genesis_time: 1692803367,\n    hash: '52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971',\n    groupHash: 'f477d5c89f21a17c863a7f937c6a6d15859414d2be09cd448d4279af331c5d3e',\n    schemeID: 'bls-unchained-g1-rfc9380',\n    metadata: {\n        beaconID: 'quicknet'\n    }\n}\n\nexport const TESTNET_DEFAULT_CHAIN_URL = 'https://pl-us.testnet.drand.sh'\nexport const TESTNET_DEFAULT_CHAIN_INFO: ChainInfo = {\n    public_key: '922a2e93828ff83345bae533f5172669a26c02dc76d6bf59c80892e12ab1455c229211886f35bb56af6d5bea981024df',\n    period: 25,\n    genesis_time: 1590445175,\n    hash: '84b2234fb34e835dccd048255d7ad3194b81af7d978c3bf157e3469592ae4e02',\n    groupHash: '4dd408e5fdff9323c76a9b6f087ba8fdc5a6da907bd9217d9d10f2287d081957',\n    schemeID: 'pedersen-bls-chained',\n    metadata: {\n        beaconID: 'default'\n    }\n}\nexport const TESTNET_QUICKNET_CHAIN_URL = 'https://pl-us.testnet.drand.sh/cc9c398442737cbd141526600919edd69f1d6f9b4adb67e4d912fbc64341a9a5'\nexport const TESTNET_QUICKNET_CHAIN_INFO: ChainInfo = {\n    public_key: 'b15b65b46fb29104f6a4b5d1e11a8da6344463973d423661bb0804846a0ecd1ef93c25057f1c0baab2ac53e56c662b66072f6d84ee791a3382bfb055afab1e6a375538d8ffc451104ac971d2dc9b168e2d3246b0be2015969cbaac298f6502da',\n    period: 3,\n    genesis_time: 1689232296,\n    hash: 'cc9c398442737cbd141526600919edd69f1d6f9b4adb67e4d912fbc64341a9a5',\n    groupHash: '40d49d910472d4adb1d67f65db8332f11b4284eecf05c05c5eacd5eef7d40e2d',\n    schemeID: 'bls-unchained-g1-rfc9380',\n    metadata: {\n        beaconID: 'quicknet-t'\n    }\n}\nexport function defaultClient(): HttpChainClient {\n    const opts = {\n        ...defaultChainOptions,\n        chainVerificationParams: {\n            chainHash: DEFAULT_CHAIN_INFO.hash,\n            publicKey: DEFAULT_CHAIN_INFO.public_key\n        }\n    }\n    const chain = new HttpCachingChain(DEFAULT_CHAIN_URL, opts)\n    return new HttpChainClient(chain, opts)\n}\n\nexport function quicknetClient(): HttpChainClient {\n    const opts = {\n        ...defaultChainOptions,\n        chainVerificationParams: {\n            chainHash: QUICKNET_CHAIN_INFO.hash,\n            publicKey: QUICKNET_CHAIN_INFO.public_key\n        }\n    }\n    const chain = new HttpCachingChain(QUICKNET_CHAIN_URL, opts)\n    return new HttpChainClient(chain, opts)\n}\n\nexport function testnetDefaultClient(): HttpChainClient {\n    const opts = {\n        ...defaultChainOptions,\n        chainVerificationParams: {\n            chainHash: TESTNET_DEFAULT_CHAIN_INFO.hash,\n            publicKey: TESTNET_DEFAULT_CHAIN_INFO.public_key\n        }\n    }\n    const chain = new HttpCachingChain(TESTNET_DEFAULT_CHAIN_URL, opts)\n    return new HttpChainClient(chain, opts)\n}\n\nexport function testnetQuicknetClient(): HttpChainClient {\n    const opts = {\n        ...defaultChainOptions,\n        chainVerificationParams: {\n            chainHash: TESTNET_QUICKNET_CHAIN_INFO.hash,\n            publicKey: TESTNET_QUICKNET_CHAIN_INFO.public_key\n        }\n    }\n    const chain = new HttpCachingChain(TESTNET_QUICKNET_CHAIN_URL, opts)\n    return new HttpChainClient(chain, opts)\n}", "import HttpCachingChain from './http-caching-chain'\nimport {HttpChain} from './http-caching-chain'\nimport HttpChainClient from './http-chain-client'\nimport FastestNodeClient from './fastest-node-client'\nimport MultiBeaconNode from './multi-beacon-node'\nimport {retryOnError, roundAt, roundTime, sleep} from './util'\nimport {verifyBeacon} from './beacon-verification'\nimport {defaultClient, quicknetClient, testnetDefaultClient, testnetQuicknetClient} from './defaults'\n\n// functionality for inspecting a drand node\nexport interface DrandNode {\n    chains(): Promise<Array<Chain>>\n\n    health(): Promise<HealthCheckResponse>\n}\n\n// functionality for a given chain hosted by a node\nexport interface Chain {\n    baseUrl: string\n\n    info(): Promise<ChainInfo>\n}\n\nexport type ChainOptions = {\n    // setting this to true will skip validation of beacons signatures (not recommended)\n    disableBeaconVerification: boolean\n\n    // setting this will add a query param to requests to stop providers returning a cached version\n    noCache: boolean\n\n    // adding these params will verify that the chain info from the requested chain matches them, otherwise an error will be thrown.\n    // Leaving them out assumes that you are sure the `baseUrl` you are using for the chain client is the correct chain\n    chainVerificationParams?: ChainVerificationParams\n}\n\nexport const defaultChainOptions: ChainOptions = {\n    disableBeaconVerification: false,\n    noCache: false,\n}\n\n// these should correspond to `hash` and `public_key` in the `ChainInfo` below\nexport type ChainVerificationParams = {\n    chainHash: string\n    publicKey: string\n}\n\n// this is aggregation of information returned by the `/health` endpoint of a node\nexport type HealthCheckResponse = {\n    // the http status code returned from the node's healthcheck\n    status: number\n    // the current round this node has caught up to. -1 when the service cannot be contacted\n    current: number\n    // the expected current round. -1 when the service cannot be contacted\n    expected: number\n}\n\n// functionality for fetching individual beacons for a given `Chain`\n// you can implement this yourself to support protocols other than HTTP\nexport interface ChainClient {\n    options: ChainOptions\n\n    latest(): Promise<RandomnessBeacon>\n\n    get(roundNumber: number): Promise<RandomnessBeacon>\n\n    chain(): Chain\n}\n\n// fetch a beacon for a given `roundNumber` or get the latest beacon by omitting the `roundNumber`\nexport async function fetchBeacon(client: ChainClient, roundNumber?: number): Promise<RandomnessBeacon> {\n    if (!roundNumber) {\n        roundNumber = roundAt(Date.now(), await client.chain().info())\n    }\n\n    if (roundNumber < 1) {\n        throw Error('Cannot request lower than round number 1')\n    }\n    const beacon = await client.get(roundNumber)\n\n    return validatedBeacon(client, beacon, roundNumber)\n}\n\n// fetch the most recent beacon to have been emitted at a given `time` in epoch ms\nexport async function fetchBeaconByTime(client: ChainClient, time: number): Promise<RandomnessBeacon> {\n    const info = await client.chain().info()\n    const roundNumber = roundAt(time, info)\n    return fetchBeacon(client, roundNumber)\n}\n\n// an async generator emitting beacons from the latest round onwards\nexport async function* watch(\n    client: ChainClient,\n    abortController: AbortController,\n    options: WatchOptions = defaultWatchOptions,\n): AsyncGenerator<RandomnessBeacon> {\n    const info = await client.chain().info()\n    let currentRound = roundAt(Date.now(), info)\n\n    while (!abortController.signal.aborted) {\n        const now = Date.now()\n        await sleep(roundTime(info, currentRound) - now)\n\n        const beacon = await retryOnError(async () => client.get(currentRound), options.retriesOnFailure)\n        yield validatedBeacon(client, beacon, currentRound)\n        currentRound = currentRound + 1\n    }\n}\n\n// options for the async generator `watch` function\nexport type WatchOptions = {\n    // the number of retries to attempt for a failed response\n    // could be useful if e.g. the network does not generate a round perfectly on time\n    retriesOnFailure: number\n}\n\nconst defaultWatchOptions = {\n    retriesOnFailure: 3\n}\n\n// internal function for validating a beacon if validation has not been disabled in the client options\nasync function validatedBeacon(client: ChainClient, beacon: RandomnessBeacon, expectedRound: number): Promise<RandomnessBeacon> {\n    if (client.options.disableBeaconVerification) {\n        return beacon\n    }\n    const info = await client.chain().info()\n    if (!await verifyBeacon(info, beacon, expectedRound)) {\n        throw Error('The beacon retrieved was not valid!')\n    }\n\n    return beacon\n}\n\n// `ChainInfo` is returned by a node's `/info` endpoint\nexport type ChainInfo = {\n    public_key: string    // hex encoded BLS12-381 public key\n    period: number        // how often the network emits randomness (in seconds)\n    genesis_time: number  // the time of the round 0 of the network (in epoch seconds)\n    hash: string          // the hash identifying this specific chain of beacons\n    groupHash: string     // a hash of the group file containing details of all the nodes participating in the network\n    schemeID: string      // the version/format of cryptography\n    metadata: {\n        beaconID: string  // the ID of the beacon chain this `ChainInfo` corresponds to\n    }\n}\n\n// currently drand supports chained and unchained randomness - read more here: https://drand.love/docs/cryptography/#randomness\nexport type RandomnessBeacon = G2ChainedBeacon | G2UnchainedBeacon | G1UnchainedBeacon | G1RFC9380Beacon  | Bn254OnG1Beacon\n\nexport type G2ChainedBeacon = {\n    round: number\n    randomness: string\n    signature: string\n    previous_signature: string\n}\n\nexport type G2UnchainedBeacon = {\n    round: number\n    randomness: string\n    signature: string\n    // this is needed to distinguish it from the other unchained beacons so the type guard works correctly\n    _phantomg2?: never\n}\n\nexport type G1UnchainedBeacon = {\n    round: number\n    randomness: string\n    signature: string\n    // this distinguishes it from the other unchained beacons so the type guard works correctly\n    _phantomg1?: never\n}\n\nexport type G1RFC9380Beacon = {\n    round: number\n    randomness: string\n    signature: string\n    // this distinguishes it from the other unchained beacons so the type guard works correctly\n    _phantomg19380?: never\n}\n\nexport type Bn254OnG1Beacon = {\n    round: number\n    randomness: string\n    signature: string\n    // this distinguishes it from the other unchained beacons so the type guard works correctly\n    _phantombn254ong1?: never\n}\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport function isChainedBeacon(value: any, info: ChainInfo): value is G2ChainedBeacon {\n    return info.schemeID === 'pedersen-bls-chained' &&\n        !!value.previous_signature &&\n        !!value.randomness &&\n        !!value.signature &&\n        value.round > 0\n}\n\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport function isUnchainedBeacon(value: any, info: ChainInfo): value is G2UnchainedBeacon {\n    return info.schemeID === 'pedersen-bls-unchained' &&\n        !!value.randomness &&\n        !!value.signature &&\n        value.previous_signature === undefined &&\n        value.round > 0\n}\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport function isG1G2SwappedBeacon(value: any, info: ChainInfo): value is G1UnchainedBeacon {\n    return info.schemeID === 'bls-unchained-on-g1' &&\n        !!value.randomness &&\n        !!value.signature &&\n        value.previous_signature === undefined &&\n        value.round > 0\n}\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport function isG1Rfc9380(value: any, info: ChainInfo): value is G1RFC9380Beacon {\n    return info.schemeID === 'bls-unchained-g1-rfc9380' &&\n        !!value.randomness &&\n        !!value.signature &&\n        value.previous_signature === undefined &&\n        value.round > 0\n}\n\n// eslint-disable-next-line  @typescript-eslint/no-explicit-any\nexport function isBn254OnG1(value: any, info: ChainInfo): value is Bn254OnG1Beacon {\n    return info.schemeID === 'bls-bn254-unchained-on-g1' &&\n        !!value.randomness &&\n        !!value.signature &&\n        value.previous_signature === undefined &&\n        value.round > 0\n}\n\n// exports some default implementations of the above interfaces and other utility functions that could be used with them\nexport {\n    HttpChain,\n    HttpChainClient,\n    HttpCachingChain,\n    MultiBeaconNode,\n    FastestNodeClient,\n    roundAt,\n    roundTime,\n    defaultClient,\n    quicknetClient,\n    testnetDefaultClient,\n    testnetQuicknetClient,\n}\n", null, null, null, "export const ignoreOverride = Symbol(\"Let zodToJsonSchema decide on which parser to use\");\nexport const jsonDescription = (jsonSchema, def) => {\n    if (def.description) {\n        try {\n            return {\n                ...jsonSchema,\n                ...JSON.parse(def.description),\n            };\n        }\n        catch { }\n    }\n    return jsonSchema;\n};\nexport const defaultOptions = {\n    name: undefined,\n    $refStrategy: \"root\",\n    basePath: [\"#\"],\n    effectStrategy: \"input\",\n    pipeStrategy: \"all\",\n    dateStrategy: \"format:date-time\",\n    mapStrategy: \"entries\",\n    removeAdditionalStrategy: \"passthrough\",\n    allowedAdditionalProperties: true,\n    rejectedAdditionalProperties: false,\n    definitionPath: \"definitions\",\n    target: \"jsonSchema7\",\n    strictUnions: false,\n    definitions: {},\n    errorMessages: false,\n    markdownDescription: false,\n    patternStrategy: \"escape\",\n    applyRegexFlags: false,\n    emailStrategy: \"format:email\",\n    base64Strategy: \"contentEncoding:base64\",\n    nameStrategy: \"ref\",\n};\nexport const getDefaultOptions = (options) => (typeof options === \"string\"\n    ? {\n        ...defaultOptions,\n        name: options,\n    }\n    : {\n        ...defaultOptions,\n        ...options,\n    });\n", "import { getDefaultOptions } from \"./Options.js\";\nexport const getRefs = (options) => {\n    const _options = getDefaultOptions(options);\n    const currentPath = _options.name !== undefined\n        ? [..._options.basePath, _options.definitionPath, _options.name]\n        : _options.basePath;\n    return {\n        ..._options,\n        currentPath: currentPath,\n        propertyPath: undefined,\n        seen: new Map(Object.entries(_options.definitions).map(([name, def]) => [\n            def._def,\n            {\n                def: def._def,\n                path: [..._options.basePath, _options.definitionPath, name],\n                // Resolution of references will be forced even though seen, so it's ok that the schema is undefined here for now.\n                jsonSchema: undefined,\n            },\n        ])),\n    };\n};\n", "export function addErrorMessage(res, key, errorMessage, refs) {\n    if (!refs?.errorMessages)\n        return;\n    if (errorMessage) {\n        res.errorMessage = {\n            ...res.errorMessage,\n            [key]: errorMessage,\n        };\n    }\n}\nexport function setResponseValueAndErrors(res, key, value, errorMessage, refs) {\n    res[key] = value;\n    addErrorMessage(res, key, errorMessage, refs);\n}\n", "export function parseAnyDef() {\n    return {};\n}\n", "import { ZodFirstPartyTypeKind } from \"zod\";\nimport { setResponseValueAndErrors } from \"../errorMessages.js\";\nimport { parseDef } from \"../parseDef.js\";\nexport function parseArrayDef(def, refs) {\n    const res = {\n        type: \"array\",\n    };\n    if (def.type?._def &&\n        def.type?._def?.typeName !== ZodFirstPartyTypeKind.ZodAny) {\n        res.items = parseDef(def.type._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"items\"],\n        });\n    }\n    if (def.minLength) {\n        setResponseValueAndErrors(res, \"minItems\", def.minLength.value, def.minLength.message, refs);\n    }\n    if (def.maxLength) {\n        setResponseValueAndErrors(res, \"maxItems\", def.maxLength.value, def.maxLength.message, refs);\n    }\n    if (def.exactLength) {\n        setResponseValueAndErrors(res, \"minItems\", def.exactLength.value, def.exactLength.message, refs);\n        setResponseValueAndErrors(res, \"maxItems\", def.exactLength.value, def.exactLength.message, refs);\n    }\n    return res;\n}\n", "import { setResponseValueAndErrors } from \"../errorMessages.js\";\nexport function parseBigintDef(def, refs) {\n    const res = {\n        type: \"integer\",\n        format: \"int64\",\n    };\n    if (!def.checks)\n        return res;\n    for (const check of def.checks) {\n        switch (check.kind) {\n            case \"min\":\n                if (refs.target === \"jsonSchema7\") {\n                    if (check.inclusive) {\n                        setResponseValueAndErrors(res, \"minimum\", check.value, check.message, refs);\n                    }\n                    else {\n                        setResponseValueAndErrors(res, \"exclusiveMinimum\", check.value, check.message, refs);\n                    }\n                }\n                else {\n                    if (!check.inclusive) {\n                        res.exclusiveMinimum = true;\n                    }\n                    setResponseValueAndErrors(res, \"minimum\", check.value, check.message, refs);\n                }\n                break;\n            case \"max\":\n                if (refs.target === \"jsonSchema7\") {\n                    if (check.inclusive) {\n                        setResponseValueAndErrors(res, \"maximum\", check.value, check.message, refs);\n                    }\n                    else {\n                        setResponseValueAndErrors(res, \"exclusiveMaximum\", check.value, check.message, refs);\n                    }\n                }\n                else {\n                    if (!check.inclusive) {\n                        res.exclusiveMaximum = true;\n                    }\n                    setResponseValueAndErrors(res, \"maximum\", check.value, check.message, refs);\n                }\n                break;\n            case \"multipleOf\":\n                setResponseValueAndErrors(res, \"multipleOf\", check.value, check.message, refs);\n                break;\n        }\n    }\n    return res;\n}\n", "export function parseBooleanDef() {\n    return {\n        type: \"boolean\",\n    };\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport function parseBrandedDef(_def, refs) {\n    return parseDef(_def.type._def, refs);\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport const parseCatchDef = (def, refs) => {\n    return parseDef(def.innerType._def, refs);\n};\n", "import { setResponseValueAndErrors } from \"../errorMessages.js\";\nexport function parseDateDef(def, refs, overrideDateStrategy) {\n    const strategy = overrideDateStrategy ?? refs.dateStrategy;\n    if (Array.isArray(strategy)) {\n        return {\n            anyOf: strategy.map((item, i) => parseDateDef(def, refs, item)),\n        };\n    }\n    switch (strategy) {\n        case \"string\":\n        case \"format:date-time\":\n            return {\n                type: \"string\",\n                format: \"date-time\",\n            };\n        case \"format:date\":\n            return {\n                type: \"string\",\n                format: \"date\",\n            };\n        case \"integer\":\n            return integerDateParser(def, refs);\n    }\n}\nconst integerDateParser = (def, refs) => {\n    const res = {\n        type: \"integer\",\n        format: \"unix-time\",\n    };\n    if (refs.target === \"openApi3\") {\n        return res;\n    }\n    for (const check of def.checks) {\n        switch (check.kind) {\n            case \"min\":\n                setResponseValueAndErrors(res, \"minimum\", check.value, // This is in milliseconds\n                check.message, refs);\n                break;\n            case \"max\":\n                setResponseValueAndErrors(res, \"maximum\", check.value, // This is in milliseconds\n                check.message, refs);\n                break;\n        }\n    }\n    return res;\n};\n", "import { parseDef } from \"../parseDef.js\";\nexport function parseDefaultDef(_def, refs) {\n    return {\n        ...parseDef(_def.innerType._def, refs),\n        default: _def.defaultValue(),\n    };\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport function parseEffectsDef(_def, refs) {\n    return refs.effectStrategy === \"input\"\n        ? parseDef(_def.schema._def, refs)\n        : {};\n}\n", "export function parseEnumDef(def) {\n    return {\n        type: \"string\",\n        enum: Array.from(def.values),\n    };\n}\n", "import { parseDef } from \"../parseDef.js\";\nconst isJsonSchema7AllOfType = (type) => {\n    if (\"type\" in type && type.type === \"string\")\n        return false;\n    return \"allOf\" in type;\n};\nexport function parseIntersectionDef(def, refs) {\n    const allOf = [\n        parseDef(def.left._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"allOf\", \"0\"],\n        }),\n        parseDef(def.right._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"allOf\", \"1\"],\n        }),\n    ].filter((x) => !!x);\n    let unevaluatedProperties = refs.target === \"jsonSchema2019-09\"\n        ? { unevaluatedProperties: false }\n        : undefined;\n    const mergedAllOf = [];\n    // If either of the schemas is an allOf, merge them into a single allOf\n    allOf.forEach((schema) => {\n        if (isJsonSchema7AllOfType(schema)) {\n            mergedAllOf.push(...schema.allOf);\n            if (schema.unevaluatedProperties === undefined) {\n                // If one of the schemas has no unevaluatedProperties set,\n                // the merged schema should also have no unevaluatedProperties set\n                unevaluatedProperties = undefined;\n            }\n        }\n        else {\n            let nestedSchema = schema;\n            if (\"additionalProperties\" in schema &&\n                schema.additionalProperties === false) {\n                const { additionalProperties, ...rest } = schema;\n                nestedSchema = rest;\n            }\n            else {\n                // As soon as one of the schemas has additionalProperties set not to false, we allow unevaluatedProperties\n                unevaluatedProperties = undefined;\n            }\n            mergedAllOf.push(nestedSchema);\n        }\n    });\n    return mergedAllOf.length\n        ? {\n            allOf: mergedAllOf,\n            ...unevaluatedProperties,\n        }\n        : undefined;\n}\n", "export function parseLiteralDef(def, refs) {\n    const parsedType = typeof def.value;\n    if (parsedType !== \"bigint\" &&\n        parsedType !== \"number\" &&\n        parsedType !== \"boolean\" &&\n        parsedType !== \"string\") {\n        return {\n            type: Array.isArray(def.value) ? \"array\" : \"object\",\n        };\n    }\n    if (refs.target === \"openApi3\") {\n        return {\n            type: parsedType === \"bigint\" ? \"integer\" : parsedType,\n            enum: [def.value],\n        };\n    }\n    return {\n        type: parsedType === \"bigint\" ? \"integer\" : parsedType,\n        const: def.value,\n    };\n}\n", "import { setResponseValueAndErrors } from \"../errorMessages.js\";\nlet emojiRegex = undefined;\n/**\n * Generated from the regular expressions found here as of 2024-05-22:\n * https://github.com/colinhacks/zod/blob/master/src/types.ts.\n *\n * Expressions with /i flag have been changed accordingly.\n */\nexport const zodPatterns = {\n    /**\n     * `c` was changed to `[cC]` to replicate /i flag\n     */\n    cuid: /^[cC][^\\s-]{8,}$/,\n    cuid2: /^[0-9a-z]+$/,\n    ulid: /^[0-9A-HJKMNP-TV-Z]{26}$/,\n    /**\n     * `a-z` was added to replicate /i flag\n     */\n    email: /^(?!\\.)(?!.*\\.\\.)([a-zA-Z0-9_'+\\-\\.]*)[a-zA-Z0-9_+-]@([a-zA-Z0-9][a-zA-Z0-9\\-]*\\.)+[a-zA-Z]{2,}$/,\n    /**\n     * Constructed a valid Unicode RegExp\n     *\n     * Lazily instantiate since this type of regex isn't supported\n     * in all envs (e.g. React Native).\n     *\n     * See:\n     * https://github.com/colinhacks/zod/issues/2433\n     * Fix in Zod:\n     * https://github.com/colinhacks/zod/commit/9340fd51e48576a75adc919bff65dbc4a5d4c99b\n     */\n    emoji: () => {\n        if (emojiRegex === undefined) {\n            emojiRegex = RegExp(\"^(\\\\p{Extended_Pictographic}|\\\\p{Emoji_Component})+$\", \"u\");\n        }\n        return emojiRegex;\n    },\n    /**\n     * Unused\n     */\n    uuid: /^[0-9a-fA-F]{8}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{4}\\b-[0-9a-fA-F]{12}$/,\n    /**\n     * Unused\n     */\n    ipv4: /^(?:(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])$/,\n    ipv4Cidr: /^(?:(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}(?:25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\/(3[0-2]|[12]?[0-9])$/,\n    /**\n     * Unused\n     */\n    ipv6: /^(([a-f0-9]{1,4}:){7}|::([a-f0-9]{1,4}:){0,6}|([a-f0-9]{1,4}:){1}:([a-f0-9]{1,4}:){0,5}|([a-f0-9]{1,4}:){2}:([a-f0-9]{1,4}:){0,4}|([a-f0-9]{1,4}:){3}:([a-f0-9]{1,4}:){0,3}|([a-f0-9]{1,4}:){4}:([a-f0-9]{1,4}:){0,2}|([a-f0-9]{1,4}:){5}:([a-f0-9]{1,4}:){0,1})([a-f0-9]{1,4}|(((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2}))\\.){3}((25[0-5])|(2[0-4][0-9])|(1[0-9]{2})|([0-9]{1,2})))$/,\n    ipv6Cidr: /^(([0-9a-fA-F]{1,4}:){7,7}[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,7}:|([0-9a-fA-F]{1,4}:){1,6}:[0-9a-fA-F]{1,4}|([0-9a-fA-F]{1,4}:){1,5}(:[0-9a-fA-F]{1,4}){1,2}|([0-9a-fA-F]{1,4}:){1,4}(:[0-9a-fA-F]{1,4}){1,3}|([0-9a-fA-F]{1,4}:){1,3}(:[0-9a-fA-F]{1,4}){1,4}|([0-9a-fA-F]{1,4}:){1,2}(:[0-9a-fA-F]{1,4}){1,5}|[0-9a-fA-F]{1,4}:((:[0-9a-fA-F]{1,4}){1,6})|:((:[0-9a-fA-F]{1,4}){1,7}|:)|fe80:(:[0-9a-fA-F]{0,4}){0,4}%[0-9a-zA-Z]{1,}|::(ffff(:0{1,4}){0,1}:){0,1}((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])|([0-9a-fA-F]{1,4}:){1,4}:((25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9])\\.){3,3}(25[0-5]|(2[0-4]|1{0,1}[0-9]){0,1}[0-9]))\\/(12[0-8]|1[01][0-9]|[1-9]?[0-9])$/,\n    base64: /^([0-9a-zA-Z+/]{4})*(([0-9a-zA-Z+/]{2}==)|([0-9a-zA-Z+/]{3}=))?$/,\n    base64url: /^([0-9a-zA-Z-_]{4})*(([0-9a-zA-Z-_]{2}(==)?)|([0-9a-zA-Z-_]{3}(=)?))?$/,\n    nanoid: /^[a-zA-Z0-9_-]{21}$/,\n    jwt: /^[A-Za-z0-9-_]+\\.[A-Za-z0-9-_]+\\.[A-Za-z0-9-_]*$/,\n};\nexport function parseStringDef(def, refs) {\n    const res = {\n        type: \"string\",\n    };\n    if (def.checks) {\n        for (const check of def.checks) {\n            switch (check.kind) {\n                case \"min\":\n                    setResponseValueAndErrors(res, \"minLength\", typeof res.minLength === \"number\"\n                        ? Math.max(res.minLength, check.value)\n                        : check.value, check.message, refs);\n                    break;\n                case \"max\":\n                    setResponseValueAndErrors(res, \"maxLength\", typeof res.maxLength === \"number\"\n                        ? Math.min(res.maxLength, check.value)\n                        : check.value, check.message, refs);\n                    break;\n                case \"email\":\n                    switch (refs.emailStrategy) {\n                        case \"format:email\":\n                            addFormat(res, \"email\", check.message, refs);\n                            break;\n                        case \"format:idn-email\":\n                            addFormat(res, \"idn-email\", check.message, refs);\n                            break;\n                        case \"pattern:zod\":\n                            addPattern(res, zodPatterns.email, check.message, refs);\n                            break;\n                    }\n                    break;\n                case \"url\":\n                    addFormat(res, \"uri\", check.message, refs);\n                    break;\n                case \"uuid\":\n                    addFormat(res, \"uuid\", check.message, refs);\n                    break;\n                case \"regex\":\n                    addPattern(res, check.regex, check.message, refs);\n                    break;\n                case \"cuid\":\n                    addPattern(res, zodPatterns.cuid, check.message, refs);\n                    break;\n                case \"cuid2\":\n                    addPattern(res, zodPatterns.cuid2, check.message, refs);\n                    break;\n                case \"startsWith\":\n                    addPattern(res, RegExp(`^${escapeLiteralCheckValue(check.value, refs)}`), check.message, refs);\n                    break;\n                case \"endsWith\":\n                    addPattern(res, RegExp(`${escapeLiteralCheckValue(check.value, refs)}$`), check.message, refs);\n                    break;\n                case \"datetime\":\n                    addFormat(res, \"date-time\", check.message, refs);\n                    break;\n                case \"date\":\n                    addFormat(res, \"date\", check.message, refs);\n                    break;\n                case \"time\":\n                    addFormat(res, \"time\", check.message, refs);\n                    break;\n                case \"duration\":\n                    addFormat(res, \"duration\", check.message, refs);\n                    break;\n                case \"length\":\n                    setResponseValueAndErrors(res, \"minLength\", typeof res.minLength === \"number\"\n                        ? Math.max(res.minLength, check.value)\n                        : check.value, check.message, refs);\n                    setResponseValueAndErrors(res, \"maxLength\", typeof res.maxLength === \"number\"\n                        ? Math.min(res.maxLength, check.value)\n                        : check.value, check.message, refs);\n                    break;\n                case \"includes\": {\n                    addPattern(res, RegExp(escapeLiteralCheckValue(check.value, refs)), check.message, refs);\n                    break;\n                }\n                case \"ip\": {\n                    if (check.version !== \"v6\") {\n                        addFormat(res, \"ipv4\", check.message, refs);\n                    }\n                    if (check.version !== \"v4\") {\n                        addFormat(res, \"ipv6\", check.message, refs);\n                    }\n                    break;\n                }\n                case \"base64url\":\n                    addPattern(res, zodPatterns.base64url, check.message, refs);\n                    break;\n                case \"jwt\":\n                    addPattern(res, zodPatterns.jwt, check.message, refs);\n                    break;\n                case \"cidr\": {\n                    if (check.version !== \"v6\") {\n                        addPattern(res, zodPatterns.ipv4Cidr, check.message, refs);\n                    }\n                    if (check.version !== \"v4\") {\n                        addPattern(res, zodPatterns.ipv6Cidr, check.message, refs);\n                    }\n                    break;\n                }\n                case \"emoji\":\n                    addPattern(res, zodPatterns.emoji(), check.message, refs);\n                    break;\n                case \"ulid\": {\n                    addPattern(res, zodPatterns.ulid, check.message, refs);\n                    break;\n                }\n                case \"base64\": {\n                    switch (refs.base64Strategy) {\n                        case \"format:binary\": {\n                            addFormat(res, \"binary\", check.message, refs);\n                            break;\n                        }\n                        case \"contentEncoding:base64\": {\n                            setResponseValueAndErrors(res, \"contentEncoding\", \"base64\", check.message, refs);\n                            break;\n                        }\n                        case \"pattern:zod\": {\n                            addPattern(res, zodPatterns.base64, check.message, refs);\n                            break;\n                        }\n                    }\n                    break;\n                }\n                case \"nanoid\": {\n                    addPattern(res, zodPatterns.nanoid, check.message, refs);\n                }\n                case \"toLowerCase\":\n                case \"toUpperCase\":\n                case \"trim\":\n                    break;\n                default:\n                    /* c8 ignore next */\n                    ((_) => { })(check);\n            }\n        }\n    }\n    return res;\n}\nfunction escapeLiteralCheckValue(literal, refs) {\n    return refs.patternStrategy === \"escape\"\n        ? escapeNonAlphaNumeric(literal)\n        : literal;\n}\nconst ALPHA_NUMERIC = new Set(\"ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvxyz0123456789\");\nfunction escapeNonAlphaNumeric(source) {\n    let result = \"\";\n    for (let i = 0; i < source.length; i++) {\n        if (!ALPHA_NUMERIC.has(source[i])) {\n            result += \"\\\\\";\n        }\n        result += source[i];\n    }\n    return result;\n}\n// Adds a \"format\" keyword to the schema. If a format exists, both formats will be joined in an allOf-node, along with subsequent ones.\nfunction addFormat(schema, value, message, refs) {\n    if (schema.format || schema.anyOf?.some((x) => x.format)) {\n        if (!schema.anyOf) {\n            schema.anyOf = [];\n        }\n        if (schema.format) {\n            schema.anyOf.push({\n                format: schema.format,\n                ...(schema.errorMessage &&\n                    refs.errorMessages && {\n                    errorMessage: { format: schema.errorMessage.format },\n                }),\n            });\n            delete schema.format;\n            if (schema.errorMessage) {\n                delete schema.errorMessage.format;\n                if (Object.keys(schema.errorMessage).length === 0) {\n                    delete schema.errorMessage;\n                }\n            }\n        }\n        schema.anyOf.push({\n            format: value,\n            ...(message &&\n                refs.errorMessages && { errorMessage: { format: message } }),\n        });\n    }\n    else {\n        setResponseValueAndErrors(schema, \"format\", value, message, refs);\n    }\n}\n// Adds a \"pattern\" keyword to the schema. If a pattern exists, both patterns will be joined in an allOf-node, along with subsequent ones.\nfunction addPattern(schema, regex, message, refs) {\n    if (schema.pattern || schema.allOf?.some((x) => x.pattern)) {\n        if (!schema.allOf) {\n            schema.allOf = [];\n        }\n        if (schema.pattern) {\n            schema.allOf.push({\n                pattern: schema.pattern,\n                ...(schema.errorMessage &&\n                    refs.errorMessages && {\n                    errorMessage: { pattern: schema.errorMessage.pattern },\n                }),\n            });\n            delete schema.pattern;\n            if (schema.errorMessage) {\n                delete schema.errorMessage.pattern;\n                if (Object.keys(schema.errorMessage).length === 0) {\n                    delete schema.errorMessage;\n                }\n            }\n        }\n        schema.allOf.push({\n            pattern: stringifyRegExpWithFlags(regex, refs),\n            ...(message &&\n                refs.errorMessages && { errorMessage: { pattern: message } }),\n        });\n    }\n    else {\n        setResponseValueAndErrors(schema, \"pattern\", stringifyRegExpWithFlags(regex, refs), message, refs);\n    }\n}\n// Mutate z.string.regex() in a best attempt to accommodate for regex flags when applyRegexFlags is true\nfunction stringifyRegExpWithFlags(regex, refs) {\n    if (!refs.applyRegexFlags || !regex.flags) {\n        return regex.source;\n    }\n    // Currently handled flags\n    const flags = {\n        i: regex.flags.includes(\"i\"),\n        m: regex.flags.includes(\"m\"),\n        s: regex.flags.includes(\"s\"), // `.` matches newlines\n    };\n    // The general principle here is to step through each character, one at a time, applying mutations as flags require. We keep track when the current character is escaped, and when it's inside a group /like [this]/ or (also) a range like /[a-z]/. The following is fairly brittle imperative code; edit at your peril!\n    const source = flags.i ? regex.source.toLowerCase() : regex.source;\n    let pattern = \"\";\n    let isEscaped = false;\n    let inCharGroup = false;\n    let inCharRange = false;\n    for (let i = 0; i < source.length; i++) {\n        if (isEscaped) {\n            pattern += source[i];\n            isEscaped = false;\n            continue;\n        }\n        if (flags.i) {\n            if (inCharGroup) {\n                if (source[i].match(/[a-z]/)) {\n                    if (inCharRange) {\n                        pattern += source[i];\n                        pattern += `${source[i - 2]}-${source[i]}`.toUpperCase();\n                        inCharRange = false;\n                    }\n                    else if (source[i + 1] === \"-\" && source[i + 2]?.match(/[a-z]/)) {\n                        pattern += source[i];\n                        inCharRange = true;\n                    }\n                    else {\n                        pattern += `${source[i]}${source[i].toUpperCase()}`;\n                    }\n                    continue;\n                }\n            }\n            else if (source[i].match(/[a-z]/)) {\n                pattern += `[${source[i]}${source[i].toUpperCase()}]`;\n                continue;\n            }\n        }\n        if (flags.m) {\n            if (source[i] === \"^\") {\n                pattern += `(^|(?<=[\\r\\n]))`;\n                continue;\n            }\n            else if (source[i] === \"$\") {\n                pattern += `($|(?=[\\r\\n]))`;\n                continue;\n            }\n        }\n        if (flags.s && source[i] === \".\") {\n            pattern += inCharGroup ? `${source[i]}\\r\\n` : `[${source[i]}\\r\\n]`;\n            continue;\n        }\n        pattern += source[i];\n        if (source[i] === \"\\\\\") {\n            isEscaped = true;\n        }\n        else if (inCharGroup && source[i] === \"]\") {\n            inCharGroup = false;\n        }\n        else if (!inCharGroup && source[i] === \"[\") {\n            inCharGroup = true;\n        }\n    }\n    try {\n        new RegExp(pattern);\n    }\n    catch {\n        console.warn(`Could not convert regex pattern at ${refs.currentPath.join(\"/\")} to a flag-independent form! Falling back to the flag-ignorant source`);\n        return regex.source;\n    }\n    return pattern;\n}\n", "import { ZodFirstPartyTypeKind, } from \"zod\";\nimport { parseDef } from \"../parseDef.js\";\nimport { parseStringDef } from \"./string.js\";\nimport { parseBrandedDef } from \"./branded.js\";\nexport function parseRecordDef(def, refs) {\n    if (refs.target === \"openAi\") {\n        console.warn(\"Warning: OpenAI may not support records in schemas! Try an array of key-value pairs instead.\");\n    }\n    if (refs.target === \"openApi3\" &&\n        def.keyType?._def.typeName === ZodFirstPartyTypeKind.ZodEnum) {\n        return {\n            type: \"object\",\n            required: def.keyType._def.values,\n            properties: def.keyType._def.values.reduce((acc, key) => ({\n                ...acc,\n                [key]: parseDef(def.valueType._def, {\n                    ...refs,\n                    currentPath: [...refs.currentPath, \"properties\", key],\n                }) ?? {},\n            }), {}),\n            additionalProperties: refs.rejectedAdditionalProperties,\n        };\n    }\n    const schema = {\n        type: \"object\",\n        additionalProperties: parseDef(def.valueType._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"additionalProperties\"],\n        }) ?? refs.allowedAdditionalProperties,\n    };\n    if (refs.target === \"openApi3\") {\n        return schema;\n    }\n    if (def.keyType?._def.typeName === ZodFirstPartyTypeKind.ZodString &&\n        def.keyType._def.checks?.length) {\n        const { type, ...keyType } = parseStringDef(def.keyType._def, refs);\n        return {\n            ...schema,\n            propertyNames: keyType,\n        };\n    }\n    else if (def.keyType?._def.typeName === ZodFirstPartyTypeKind.ZodEnum) {\n        return {\n            ...schema,\n            propertyNames: {\n                enum: def.keyType._def.values,\n            },\n        };\n    }\n    else if (def.keyType?._def.typeName === ZodFirstPartyTypeKind.ZodBranded &&\n        def.keyType._def.type._def.typeName === ZodFirstPartyTypeKind.ZodString &&\n        def.keyType._def.type._def.checks?.length) {\n        const { type, ...keyType } = parseBrandedDef(def.keyType._def, refs);\n        return {\n            ...schema,\n            propertyNames: keyType,\n        };\n    }\n    return schema;\n}\n", "import { parseDef } from \"../parseDef.js\";\nimport { parseRecordDef } from \"./record.js\";\nexport function parseMapDef(def, refs) {\n    if (refs.mapStrategy === \"record\") {\n        return parseRecordDef(def, refs);\n    }\n    const keys = parseDef(def.keyType._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"items\", \"items\", \"0\"],\n    }) || {};\n    const values = parseDef(def.valueType._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"items\", \"items\", \"1\"],\n    }) || {};\n    return {\n        type: \"array\",\n        maxItems: 125,\n        items: {\n            type: \"array\",\n            items: [keys, values],\n            minItems: 2,\n            maxItems: 2,\n        },\n    };\n}\n", "export function parseNativeEnumDef(def) {\n    const object = def.values;\n    const actualKeys = Object.keys(def.values).filter((key) => {\n        return typeof object[object[key]] !== \"number\";\n    });\n    const actualValues = actualKeys.map((key) => object[key]);\n    const parsedTypes = Array.from(new Set(actualValues.map((values) => typeof values)));\n    return {\n        type: parsedTypes.length === 1\n            ? parsedTypes[0] === \"string\"\n                ? \"string\"\n                : \"number\"\n            : [\"string\", \"number\"],\n        enum: actualValues,\n    };\n}\n", "export function parseNeverDef() {\n    return {\n        not: {},\n    };\n}\n", "export function parseNullDef(refs) {\n    return refs.target === \"openApi3\"\n        ? {\n            enum: [\"null\"],\n            nullable: true,\n        }\n        : {\n            type: \"null\",\n        };\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport const primitiveMappings = {\n    ZodString: \"string\",\n    ZodNumber: \"number\",\n    ZodBigInt: \"integer\",\n    ZodBoolean: \"boolean\",\n    ZodNull: \"null\",\n};\nexport function parseUnionDef(def, refs) {\n    if (refs.target === \"openApi3\")\n        return asAnyOf(def, refs);\n    const options = def.options instanceof Map ? Array.from(def.options.values()) : def.options;\n    // This blocks tries to look ahead a bit to produce nicer looking schemas with type array instead of anyOf.\n    if (options.every((x) => x._def.typeName in primitiveMappings &&\n        (!x._def.checks || !x._def.checks.length))) {\n        // all types in union are primitive and lack checks, so might as well squash into {type: [...]}\n        const types = options.reduce((types, x) => {\n            const type = primitiveMappings[x._def.typeName]; //Can be safely casted due to row 43\n            return type && !types.includes(type) ? [...types, type] : types;\n        }, []);\n        return {\n            type: types.length > 1 ? types : types[0],\n        };\n    }\n    else if (options.every((x) => x._def.typeName === \"ZodLiteral\" && !x.description)) {\n        // all options literals\n        const types = options.reduce((acc, x) => {\n            const type = typeof x._def.value;\n            switch (type) {\n                case \"string\":\n                case \"number\":\n                case \"boolean\":\n                    return [...acc, type];\n                case \"bigint\":\n                    return [...acc, \"integer\"];\n                case \"object\":\n                    if (x._def.value === null)\n                        return [...acc, \"null\"];\n                case \"symbol\":\n                case \"undefined\":\n                case \"function\":\n                default:\n                    return acc;\n            }\n        }, []);\n        if (types.length === options.length) {\n            // all the literals are primitive, as far as null can be considered primitive\n            const uniqueTypes = types.filter((x, i, a) => a.indexOf(x) === i);\n            return {\n                type: uniqueTypes.length > 1 ? uniqueTypes : uniqueTypes[0],\n                enum: options.reduce((acc, x) => {\n                    return acc.includes(x._def.value) ? acc : [...acc, x._def.value];\n                }, []),\n            };\n        }\n    }\n    else if (options.every((x) => x._def.typeName === \"ZodEnum\")) {\n        return {\n            type: \"string\",\n            enum: options.reduce((acc, x) => [\n                ...acc,\n                ...x._def.values.filter((x) => !acc.includes(x)),\n            ], []),\n        };\n    }\n    return asAnyOf(def, refs);\n}\nconst asAnyOf = (def, refs) => {\n    const anyOf = (def.options instanceof Map\n        ? Array.from(def.options.values())\n        : def.options)\n        .map((x, i) => parseDef(x._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"anyOf\", `${i}`],\n    }))\n        .filter((x) => !!x &&\n        (!refs.strictUnions ||\n            (typeof x === \"object\" && Object.keys(x).length > 0)));\n    return anyOf.length ? { anyOf } : undefined;\n};\n", "import { parseDef } from \"../parseDef.js\";\nimport { primitiveMappings } from \"./union.js\";\nexport function parseNullableDef(def, refs) {\n    if ([\"ZodString\", \"ZodNumber\", \"ZodBigInt\", \"ZodBoolean\", \"ZodNull\"].includes(def.innerType._def.typeName) &&\n        (!def.innerType._def.checks || !def.innerType._def.checks.length)) {\n        if (refs.target === \"openApi3\") {\n            return {\n                type: primitiveMappings[def.innerType._def.typeName],\n                nullable: true,\n            };\n        }\n        return {\n            type: [\n                primitiveMappings[def.innerType._def.typeName],\n                \"null\",\n            ],\n        };\n    }\n    if (refs.target === \"openApi3\") {\n        const base = parseDef(def.innerType._def, {\n            ...refs,\n            currentPath: [...refs.currentPath],\n        });\n        if (base && \"$ref\" in base)\n            return { allOf: [base], nullable: true };\n        return base && { ...base, nullable: true };\n    }\n    const base = parseDef(def.innerType._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"anyOf\", \"0\"],\n    });\n    return base && { anyOf: [base, { type: \"null\" }] };\n}\n", "import { addErrorMessage, setResponseValueAndErrors, } from \"../errorMessages.js\";\nexport function parseNumberDef(def, refs) {\n    const res = {\n        type: \"number\",\n    };\n    if (!def.checks)\n        return res;\n    for (const check of def.checks) {\n        switch (check.kind) {\n            case \"int\":\n                res.type = \"integer\";\n                addErrorMessage(res, \"type\", check.message, refs);\n                break;\n            case \"min\":\n                if (refs.target === \"jsonSchema7\") {\n                    if (check.inclusive) {\n                        setResponseValueAndErrors(res, \"minimum\", check.value, check.message, refs);\n                    }\n                    else {\n                        setResponseValueAndErrors(res, \"exclusiveMinimum\", check.value, check.message, refs);\n                    }\n                }\n                else {\n                    if (!check.inclusive) {\n                        res.exclusiveMinimum = true;\n                    }\n                    setResponseValueAndErrors(res, \"minimum\", check.value, check.message, refs);\n                }\n                break;\n            case \"max\":\n                if (refs.target === \"jsonSchema7\") {\n                    if (check.inclusive) {\n                        setResponseValueAndErrors(res, \"maximum\", check.value, check.message, refs);\n                    }\n                    else {\n                        setResponseValueAndErrors(res, \"exclusiveMaximum\", check.value, check.message, refs);\n                    }\n                }\n                else {\n                    if (!check.inclusive) {\n                        res.exclusiveMaximum = true;\n                    }\n                    setResponseValueAndErrors(res, \"maximum\", check.value, check.message, refs);\n                }\n                break;\n            case \"multipleOf\":\n                setResponseValueAndErrors(res, \"multipleOf\", check.value, check.message, refs);\n                break;\n        }\n    }\n    return res;\n}\n", "import { ZodOptional } from \"zod\";\nimport { parseDef } from \"../parseDef.js\";\nexport function parseObjectDef(def, refs) {\n    const forceOptionalIntoNullable = refs.target === \"openAi\";\n    const result = {\n        type: \"object\",\n        properties: {},\n    };\n    const required = [];\n    const shape = def.shape();\n    for (const propName in shape) {\n        let propDef = shape[propName];\n        if (propDef === undefined || propDef._def === undefined) {\n            continue;\n        }\n        let propOptional = safeIsOptional(propDef);\n        if (propOptional && forceOptionalIntoNullable) {\n            if (propDef instanceof ZodOptional) {\n                propDef = propDef._def.innerType;\n            }\n            if (!propDef.isNullable()) {\n                propDef = propDef.nullable();\n            }\n            propOptional = false;\n        }\n        const parsedDef = parseDef(propDef._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"properties\", propName],\n            propertyPath: [...refs.currentPath, \"properties\", propName],\n        });\n        if (parsedDef === undefined) {\n            continue;\n        }\n        result.properties[propName] = parsedDef;\n        if (!propOptional) {\n            required.push(propName);\n        }\n    }\n    if (required.length) {\n        result.required = required;\n    }\n    const additionalProperties = decideAdditionalProperties(def, refs);\n    if (additionalProperties !== undefined) {\n        result.additionalProperties = additionalProperties;\n    }\n    return result;\n}\nfunction decideAdditionalProperties(def, refs) {\n    if (def.catchall._def.typeName !== \"ZodNever\") {\n        return parseDef(def.catchall._def, {\n            ...refs,\n            currentPath: [...refs.currentPath, \"additionalProperties\"],\n        });\n    }\n    switch (def.unknownKeys) {\n        case \"passthrough\":\n            return refs.allowedAdditionalProperties;\n        case \"strict\":\n            return refs.rejectedAdditionalProperties;\n        case \"strip\":\n            return refs.removeAdditionalStrategy === \"strict\"\n                ? refs.allowedAdditionalProperties\n                : refs.rejectedAdditionalProperties;\n    }\n}\nfunction safeIsOptional(schema) {\n    try {\n        return schema.isOptional();\n    }\n    catch {\n        return true;\n    }\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport const parseOptionalDef = (def, refs) => {\n    if (refs.currentPath.toString() === refs.propertyPath?.toString()) {\n        return parseDef(def.innerType._def, refs);\n    }\n    const innerSchema = parseDef(def.innerType._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"anyOf\", \"1\"],\n    });\n    return innerSchema\n        ? {\n            anyOf: [\n                {\n                    not: {},\n                },\n                innerSchema,\n            ],\n        }\n        : {};\n};\n", "import { parseDef } from \"../parseDef.js\";\nexport const parsePipelineDef = (def, refs) => {\n    if (refs.pipeStrategy === \"input\") {\n        return parseDef(def.in._def, refs);\n    }\n    else if (refs.pipeStrategy === \"output\") {\n        return parseDef(def.out._def, refs);\n    }\n    const a = parseDef(def.in._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"allOf\", \"0\"],\n    });\n    const b = parseDef(def.out._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"allOf\", a ? \"1\" : \"0\"],\n    });\n    return {\n        allOf: [a, b].filter((x) => x !== undefined),\n    };\n};\n", "import { parseDef } from \"../parseDef.js\";\nexport function parsePromiseDef(def, refs) {\n    return parseDef(def.type._def, refs);\n}\n", "import { setResponseValueAndErrors } from \"../errorMessages.js\";\nimport { parseDef } from \"../parseDef.js\";\nexport function parseSetDef(def, refs) {\n    const items = parseDef(def.valueType._def, {\n        ...refs,\n        currentPath: [...refs.currentPath, \"items\"],\n    });\n    const schema = {\n        type: \"array\",\n        uniqueItems: true,\n        items,\n    };\n    if (def.minSize) {\n        setResponseValueAndErrors(schema, \"minItems\", def.minSize.value, def.minSize.message, refs);\n    }\n    if (def.maxSize) {\n        setResponseValueAndErrors(schema, \"maxItems\", def.maxSize.value, def.maxSize.message, refs);\n    }\n    return schema;\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport function parseTupleDef(def, refs) {\n    if (def.rest) {\n        return {\n            type: \"array\",\n            minItems: def.items.length,\n            items: def.items\n                .map((x, i) => parseDef(x._def, {\n                ...refs,\n                currentPath: [...refs.currentPath, \"items\", `${i}`],\n            }))\n                .reduce((acc, x) => (x === undefined ? acc : [...acc, x]), []),\n            additionalItems: parseDef(def.rest._def, {\n                ...refs,\n                currentPath: [...refs.currentPath, \"additionalItems\"],\n            }),\n        };\n    }\n    else {\n        return {\n            type: \"array\",\n            minItems: def.items.length,\n            maxItems: def.items.length,\n            items: def.items\n                .map((x, i) => parseDef(x._def, {\n                ...refs,\n                currentPath: [...refs.currentPath, \"items\", `${i}`],\n            }))\n                .reduce((acc, x) => (x === undefined ? acc : [...acc, x]), []),\n        };\n    }\n}\n", "export function parseUndefinedDef() {\n    return {\n        not: {},\n    };\n}\n", "export function parseUnknownDef() {\n    return {};\n}\n", "import { parseDef } from \"../parseDef.js\";\nexport const parseReadonlyDef = (def, refs) => {\n    return parseDef(def.innerType._def, refs);\n};\n", "import { ZodFirstPartyTypeKind } from \"zod\";\nimport { parseAnyDef } from \"./parsers/any.js\";\nimport { parseArrayDef } from \"./parsers/array.js\";\nimport { parseBigintDef } from \"./parsers/bigint.js\";\nimport { parseBooleanDef } from \"./parsers/boolean.js\";\nimport { parseBrandedDef } from \"./parsers/branded.js\";\nimport { parseCatchDef } from \"./parsers/catch.js\";\nimport { parseDateDef } from \"./parsers/date.js\";\nimport { parseDefaultDef } from \"./parsers/default.js\";\nimport { parseEffectsDef } from \"./parsers/effects.js\";\nimport { parseEnumDef } from \"./parsers/enum.js\";\nimport { parseIntersectionDef } from \"./parsers/intersection.js\";\nimport { parseLiteralDef } from \"./parsers/literal.js\";\nimport { parseMapDef } from \"./parsers/map.js\";\nimport { parseNativeEnumDef } from \"./parsers/nativeEnum.js\";\nimport { parseNeverDef } from \"./parsers/never.js\";\nimport { parseNullDef } from \"./parsers/null.js\";\nimport { parseNullableDef } from \"./parsers/nullable.js\";\nimport { parseNumberDef } from \"./parsers/number.js\";\nimport { parseObjectDef } from \"./parsers/object.js\";\nimport { parseOptionalDef } from \"./parsers/optional.js\";\nimport { parsePipelineDef } from \"./parsers/pipeline.js\";\nimport { parsePromiseDef } from \"./parsers/promise.js\";\nimport { parseRecordDef } from \"./parsers/record.js\";\nimport { parseSetDef } from \"./parsers/set.js\";\nimport { parseStringDef } from \"./parsers/string.js\";\nimport { parseTupleDef } from \"./parsers/tuple.js\";\nimport { parseUndefinedDef } from \"./parsers/undefined.js\";\nimport { parseUnionDef } from \"./parsers/union.js\";\nimport { parseUnknownDef } from \"./parsers/unknown.js\";\nimport { parseReadonlyDef } from \"./parsers/readonly.js\";\nexport const selectParser = (def, typeName, refs) => {\n    switch (typeName) {\n        case ZodFirstPartyTypeKind.ZodString:\n            return parseStringDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodNumber:\n            return parseNumberDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodObject:\n            return parseObjectDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodBigInt:\n            return parseBigintDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodBoolean:\n            return parseBooleanDef();\n        case ZodFirstPartyTypeKind.ZodDate:\n            return parseDateDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodUndefined:\n            return parseUndefinedDef();\n        case ZodFirstPartyTypeKind.ZodNull:\n            return parseNullDef(refs);\n        case ZodFirstPartyTypeKind.ZodArray:\n            return parseArrayDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodUnion:\n        case ZodFirstPartyTypeKind.ZodDiscriminatedUnion:\n            return parseUnionDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodIntersection:\n            return parseIntersectionDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodTuple:\n            return parseTupleDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodRecord:\n            return parseRecordDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodLiteral:\n            return parseLiteralDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodEnum:\n            return parseEnumDef(def);\n        case ZodFirstPartyTypeKind.ZodNativeEnum:\n            return parseNativeEnumDef(def);\n        case ZodFirstPartyTypeKind.ZodNullable:\n            return parseNullableDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodOptional:\n            return parseOptionalDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodMap:\n            return parseMapDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodSet:\n            return parseSetDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodLazy:\n            return () => def.getter()._def;\n        case ZodFirstPartyTypeKind.ZodPromise:\n            return parsePromiseDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodNaN:\n        case ZodFirstPartyTypeKind.ZodNever:\n            return parseNeverDef();\n        case ZodFirstPartyTypeKind.ZodEffects:\n            return parseEffectsDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodAny:\n            return parseAnyDef();\n        case ZodFirstPartyTypeKind.ZodUnknown:\n            return parseUnknownDef();\n        case ZodFirstPartyTypeKind.ZodDefault:\n            return parseDefaultDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodBranded:\n            return parseBrandedDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodReadonly:\n            return parseReadonlyDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodCatch:\n            return parseCatchDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodPipeline:\n            return parsePipelineDef(def, refs);\n        case ZodFirstPartyTypeKind.ZodFunction:\n        case ZodFirstPartyTypeKind.ZodVoid:\n        case ZodFirstPartyTypeKind.ZodSymbol:\n            return undefined;\n        default:\n            /* c8 ignore next */\n            return ((_) => undefined)(typeName);\n    }\n};\n", "import { ignoreOverride } from \"./Options.js\";\nimport { selectParser } from \"./selectParser.js\";\nexport function parseDef(def, refs, forceResolution = false) {\n    const seenItem = refs.seen.get(def);\n    if (refs.override) {\n        const overrideResult = refs.override?.(def, refs, seenItem, forceResolution);\n        if (overrideResult !== ignoreOverride) {\n            return overrideResult;\n        }\n    }\n    if (seenItem && !forceResolution) {\n        const seenSchema = get$ref(seenItem, refs);\n        if (seenSchema !== undefined) {\n            return seenSchema;\n        }\n    }\n    const newItem = { def, path: refs.currentPath, jsonSchema: undefined };\n    refs.seen.set(def, newItem);\n    const jsonSchemaOrGetter = selectParser(def, def.typeName, refs);\n    // If the return was a function, then the inner definition needs to be extracted before a call to parseDef (recursive)\n    const jsonSchema = typeof jsonSchemaOrGetter === \"function\"\n        ? parseDef(jsonSchemaOrGetter(), refs)\n        : jsonSchemaOrGetter;\n    if (jsonSchema) {\n        addMeta(def, refs, jsonSchema);\n    }\n    if (refs.postProcess) {\n        const postProcessResult = refs.postProcess(jsonSchema, def, refs);\n        newItem.jsonSchema = jsonSchema;\n        return postProcessResult;\n    }\n    newItem.jsonSchema = jsonSchema;\n    return jsonSchema;\n}\nconst get$ref = (item, refs) => {\n    switch (refs.$refStrategy) {\n        case \"root\":\n            return { $ref: item.path.join(\"/\") };\n        case \"relative\":\n            return { $ref: getRelativePath(refs.currentPath, item.path) };\n        case \"none\":\n        case \"seen\": {\n            if (item.path.length < refs.currentPath.length &&\n                item.path.every((value, index) => refs.currentPath[index] === value)) {\n                console.warn(`Recursive reference detected at ${refs.currentPath.join(\"/\")}! Defaulting to any`);\n                return {};\n            }\n            return refs.$refStrategy === \"seen\" ? {} : undefined;\n        }\n    }\n};\nconst getRelativePath = (pathA, pathB) => {\n    let i = 0;\n    for (; i < pathA.length && i < pathB.length; i++) {\n        if (pathA[i] !== pathB[i])\n            break;\n    }\n    return [(pathA.length - i).toString(), ...pathB.slice(i)].join(\"/\");\n};\nconst addMeta = (def, refs, jsonSchema) => {\n    if (def.description) {\n        jsonSchema.description = def.description;\n        if (refs.markdownDescription) {\n            jsonSchema.markdownDescription = def.description;\n        }\n    }\n    return jsonSchema;\n};\n", "import { parseDef } from \"./parseDef.js\";\nimport { getRefs } from \"./Refs.js\";\nconst zodToJsonSchema = (schema, options) => {\n    const refs = getRefs(options);\n    const definitions = typeof options === \"object\" && options.definitions\n        ? Object.entries(options.definitions).reduce((acc, [name, schema]) => ({\n            ...acc,\n            [name]: parseDef(schema._def, {\n                ...refs,\n                currentPath: [...refs.basePath, refs.definitionPath, name],\n            }, true) ?? {},\n        }), {})\n        : undefined;\n    const name = typeof options === \"string\"\n        ? options\n        : options?.nameStrategy === \"title\"\n            ? undefined\n            : options?.name;\n    const main = parseDef(schema._def, name === undefined\n        ? refs\n        : {\n            ...refs,\n            currentPath: [...refs.basePath, refs.definitionPath, name],\n        }, false) ?? {};\n    const title = typeof options === \"object\" &&\n        options.name !== undefined &&\n        options.nameStrategy === \"title\"\n        ? options.name\n        : undefined;\n    if (title !== undefined) {\n        main.title = title;\n    }\n    const combined = name === undefined\n        ? definitions\n            ? {\n                ...main,\n                [refs.definitionPath]: definitions,\n            }\n            : main\n        : {\n            $ref: [\n                ...(refs.$refStrategy === \"relative\" ? [] : refs.basePath),\n                refs.definitionPath,\n                name,\n            ].join(\"/\"),\n            [refs.definitionPath]: {\n                ...definitions,\n                [name]: main,\n            },\n        };\n    if (refs.target === \"jsonSchema7\") {\n        combined.$schema = \"http://json-schema.org/draft-07/schema#\";\n    }\n    else if (refs.target === \"jsonSchema2019-09\" || refs.target === \"openAi\") {\n        combined.$schema = \"https://json-schema.org/draft/2019-09/schema#\";\n    }\n    if (refs.target === \"openAi\" &&\n        (\"anyOf\" in combined ||\n            \"oneOf\" in combined ||\n            \"allOf\" in combined ||\n            (\"type\" in combined && Array.isArray(combined.type)))) {\n        console.warn(\"Warning: OpenAI may not support schemas with unions as roots! Try wrapping it in an object property.\");\n    }\n    return combined;\n};\nexport { zodToJsonSchema };\n", null, null, null, null, "import {z} from \"zod\"\nimport {FastestNodeClient, fetchBeacon, fetchBeaconByTime} from \"drand-client\"\nimport {McpServer} from \"@modelcontextprotocol/sdk/server/mcp.js\"\nimport {StdioServerTransport} from \"@modelcontextprotocol/sdk/server/stdio.js\"\n\nconst server = new McpServer({\n    name: \"drand\",\n    version: \"0.0.1\",\n    capabilities: {\n        resources: {},\n        tools: {}\n    }\n})\n\nconst drandClient = new FastestNodeClient([\"https://api.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971\", \"https://api3.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971\", \"https://api2.drand.sh/52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971\"], {\n    disableBeaconVerification: false,\n    noCache: false,\n    chainVerificationParams: {\n        chainHash: \"52db9ba70e0cc0f6eaf7803dd07447a1f5477735fd3f661792ba94600c84e971\",\n        publicKey: \"83cf0f2896adee7eb8b5f01fcad3912212c437e0073e911fb90022d3e760183c8c4b450b6a0a6c3ac6a5776a2d1064510d1fec758c921cc22b0e17e63aaf4bcb5ed66304de9cf809bd274ca73bab4af5a6e9c76a4bc09e76eae8991ef5ece45a\"\n    }\n}, 5000)\ndrandClient.start()\n\nserver.tool(\n    \"get-randomness-latest\",\n    \"Get the latest random value from drand quicknet\",\n    {},\n    async ()  => {\n        const response = await fetchBeaconByTime(drandClient, Date.now())\n        return {\n            content: [{\n                type: \"text\",\n                text: `0x${response.randomness}`\n            }]\n        }\n    }\n)\n\ntype RoundParams = {\n    round: number\n}\nserver.tool(\n    \"get-randomness-by-round\",\n    \"Get the random value associated with a specfic round from drand quicknet\",\n    {round: z.number()},\n    async ({round}: RoundParams) => {\n        const response = await fetchBeacon(drandClient, round)\n        return {\n            content: [{\n                type: \"text\",\n                text: `0x${response.randomness}`\n            }]\n        }\n    }\n)\n\ntype TimeParams = {\n    time: number\n}\nserver.tool(\n    \"get-randomness-by-time\",\n    \"Get the random value associated with a specific time from drand quicknet\",\n    {time: z.number()},\n    async ({time}: TimeParams) => {\n        const response = await fetchBeaconByTime(drandClient, time)\n        return {\n            content: [{\n                type: \"text\",\n                text: `0x${response.randomness}`\n            }]\n        }\n    }\n)\n\nasync function main() {\n    const transport = new StdioServerTransport()\n    await server.connect(transport)\n}\n\nmain().catch(err => {\n    console.error(\"fatal error running drand server\", err)\n    process.exit(1)\n})"],
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}