{
  "contractName": "Math",
  "abi": [],
  "metadata": "{\"compiler\":{\"version\":\"0.8.11+commit.d7f03943\"},\"language\":\"Solidity\",\"output\":{\"abi\":[],\"devdoc\":{\"details\":\"Standard math utilities missing in the Solidity language.\",\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"@openzeppelin/contracts/utils/math/Math.sol\":\"Math\"},\"evmVersion\":\"london\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[]},\"sources\":{\"@openzeppelin/contracts/utils/math/Math.sol\":{\"keccak256\":\"0xc995bddbca1ae19788db9f8b61e63385edd3fddf89693b612d5abd1a275974d2\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://ab84f13e6e6e0823854a0cddd49e96df052092d5919f95587607f0ed28a64cb6\",\"dweb:/ipfs/QmbNtqAq23ZDjCzHukQaa7B3y6rcobscm6FZF5PMQXcnVr\"]}},\"version\":1}",
  "bytecode": "0x60566037600b82828239805160001a607314602a57634e487b7160e01b600052600060045260246000fd5b30600052607381538281f3fe73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220d281b8166fa31ee00cff179ad3f4c54b43ea3fc95114303959d9d4a6cb0a73e764736f6c634300080b0033",
  "deployedBytecode": "0x73000000000000000000000000000000000000000030146080604052600080fdfea2646970667358221220d281b8166fa31ee00cff179ad3f4c54b43ea3fc95114303959d9d4a6cb0a73e764736f6c634300080b0033",
  "immutableReferences": {},
  "generatedSources": [],
  "deployedGeneratedSources": [],
  "sourceMap": "202:1024:35:-:0;;;;;;;;;;;;;;;-1:-1:-1;;;202:1024:35;;;;;;;;;;;;;;;;;",
  "deployedSourceMap": "202:1024:35:-:0;;;;;;;;",
  "source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/Math.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard math utilities missing in the Solidity language.\n */\nlibrary Math {\n    /**\n     * @dev Returns the largest of two numbers.\n     */\n    function max(uint256 a, uint256 b) internal pure returns (uint256) {\n        return a >= b ? a : b;\n    }\n\n    /**\n     * @dev Returns the smallest of two numbers.\n     */\n    function min(uint256 a, uint256 b) internal pure returns (uint256) {\n        return a < b ? a : b;\n    }\n\n    /**\n     * @dev Returns the average of two numbers. The result is rounded towards\n     * zero.\n     */\n    function average(uint256 a, uint256 b) internal pure returns (uint256) {\n        // (a + b) / 2 can overflow.\n        return (a & b) + (a ^ b) / 2;\n    }\n\n    /**\n     * @dev Returns the ceiling of the division of two numbers.\n     *\n     * This differs from standard division with `/` in that it rounds up instead\n     * of rounding down.\n     */\n    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {\n        // (a + b - 1) / b can overflow on addition, so we distribute.\n        return a / b + (a % b == 0 ? 0 : 1);\n    }\n}\n",
  "sourcePath": "@openzeppelin/contracts/utils/math/Math.sol",
  "ast": {
    "absolutePath": "@openzeppelin/contracts/utils/math/Math.sol",
    "exportedSymbols": {
      "Math": [
        6352
      ]
    },
    "id": 6353,
    "license": "MIT",
    "nodeType": "SourceUnit",
    "nodes": [
      {
        "id": 6266,
        "literals": [
          "solidity",
          "^",
          "0.8",
          ".0"
        ],
        "nodeType": "PragmaDirective",
        "src": "103:23:35"
      },
      {
        "abstract": false,
        "baseContracts": [],
        "canonicalName": "Math",
        "contractDependencies": [],
        "contractKind": "library",
        "documentation": {
          "id": 6267,
          "nodeType": "StructuredDocumentation",
          "src": "128:73:35",
          "text": " @dev Standard math utilities missing in the Solidity language."
        },
        "fullyImplemented": true,
        "id": 6352,
        "linearizedBaseContracts": [
          6352
        ],
        "name": "Math",
        "nameLocation": "210:4:35",
        "nodeType": "ContractDefinition",
        "nodes": [
          {
            "body": {
              "id": 6284,
              "nodeType": "Block",
              "src": "352:38:35",
              "statements": [
                {
                  "expression": {
                    "condition": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6279,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6277,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6270,
                        "src": "369:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": ">=",
                      "rightExpression": {
                        "id": 6278,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6272,
                        "src": "374:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "369:6:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bool",
                        "typeString": "bool"
                      }
                    },
                    "falseExpression": {
                      "id": 6281,
                      "name": "b",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6272,
                      "src": "382:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "id": 6282,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "nodeType": "Conditional",
                    "src": "369:14:35",
                    "trueExpression": {
                      "id": 6280,
                      "name": "a",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6270,
                      "src": "378:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6276,
                  "id": 6283,
                  "nodeType": "Return",
                  "src": "362:21:35"
                }
              ]
            },
            "documentation": {
              "id": 6268,
              "nodeType": "StructuredDocumentation",
              "src": "221:59:35",
              "text": " @dev Returns the largest of two numbers."
            },
            "id": 6285,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "max",
            "nameLocation": "294:3:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6273,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6270,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "306:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "298:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6269,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "298:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6272,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "317:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "309:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6271,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "309:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "297:22:35"
            },
            "returnParameters": {
              "id": 6276,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6275,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "343:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6274,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "343:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "342:9:35"
            },
            "scope": 6352,
            "src": "285:105:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6302,
              "nodeType": "Block",
              "src": "528:37:35",
              "statements": [
                {
                  "expression": {
                    "condition": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6297,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6295,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6288,
                        "src": "545:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "<",
                      "rightExpression": {
                        "id": 6296,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6290,
                        "src": "549:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "545:5:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bool",
                        "typeString": "bool"
                      }
                    },
                    "falseExpression": {
                      "id": 6299,
                      "name": "b",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6290,
                      "src": "557:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "id": 6300,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "nodeType": "Conditional",
                    "src": "545:13:35",
                    "trueExpression": {
                      "id": 6298,
                      "name": "a",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6288,
                      "src": "553:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6294,
                  "id": 6301,
                  "nodeType": "Return",
                  "src": "538:20:35"
                }
              ]
            },
            "documentation": {
              "id": 6286,
              "nodeType": "StructuredDocumentation",
              "src": "396:60:35",
              "text": " @dev Returns the smallest of two numbers."
            },
            "id": 6303,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "min",
            "nameLocation": "470:3:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6291,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6288,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "482:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "474:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6287,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "474:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6290,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "493:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "485:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6289,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "485:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "473:22:35"
            },
            "returnParameters": {
              "id": 6294,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6293,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "519:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6292,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "519:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "518:9:35"
            },
            "scope": 6352,
            "src": "461:104:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6325,
              "nodeType": "Block",
              "src": "749:82:35",
              "statements": [
                {
                  "expression": {
                    "commonType": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    },
                    "id": 6323,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "leftExpression": {
                      "components": [
                        {
                          "commonType": {
                            "typeIdentifier": "t_uint256",
                            "typeString": "uint256"
                          },
                          "id": 6315,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": false,
                          "lValueRequested": false,
                          "leftExpression": {
                            "id": 6313,
                            "name": "a",
                            "nodeType": "Identifier",
                            "overloadedDeclarations": [],
                            "referencedDeclaration": 6306,
                            "src": "804:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          },
                          "nodeType": "BinaryOperation",
                          "operator": "&",
                          "rightExpression": {
                            "id": 6314,
                            "name": "b",
                            "nodeType": "Identifier",
                            "overloadedDeclarations": [],
                            "referencedDeclaration": 6308,
                            "src": "808:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          },
                          "src": "804:5:35",
                          "typeDescriptions": {
                            "typeIdentifier": "t_uint256",
                            "typeString": "uint256"
                          }
                        }
                      ],
                      "id": 6316,
                      "isConstant": false,
                      "isInlineArray": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "nodeType": "TupleExpression",
                      "src": "803:7:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "nodeType": "BinaryOperation",
                    "operator": "+",
                    "rightExpression": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6322,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "components": [
                          {
                            "commonType": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            },
                            "id": 6319,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": false,
                            "lValueRequested": false,
                            "leftExpression": {
                              "id": 6317,
                              "name": "a",
                              "nodeType": "Identifier",
                              "overloadedDeclarations": [],
                              "referencedDeclaration": 6306,
                              "src": "814:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "nodeType": "BinaryOperation",
                            "operator": "^",
                            "rightExpression": {
                              "id": 6318,
                              "name": "b",
                              "nodeType": "Identifier",
                              "overloadedDeclarations": [],
                              "referencedDeclaration": 6308,
                              "src": "818:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "src": "814:5:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          }
                        ],
                        "id": 6320,
                        "isConstant": false,
                        "isInlineArray": false,
                        "isLValue": false,
                        "isPure": false,
                        "lValueRequested": false,
                        "nodeType": "TupleExpression",
                        "src": "813:7:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "/",
                      "rightExpression": {
                        "hexValue": "32",
                        "id": 6321,
                        "isConstant": false,
                        "isLValue": false,
                        "isPure": true,
                        "kind": "number",
                        "lValueRequested": false,
                        "nodeType": "Literal",
                        "src": "823:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_rational_2_by_1",
                          "typeString": "int_const 2"
                        },
                        "value": "2"
                      },
                      "src": "813:11:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "src": "803:21:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6312,
                  "id": 6324,
                  "nodeType": "Return",
                  "src": "796:28:35"
                }
              ]
            },
            "documentation": {
              "id": 6304,
              "nodeType": "StructuredDocumentation",
              "src": "571:102:35",
              "text": " @dev Returns the average of two numbers. The result is rounded towards\n zero."
            },
            "id": 6326,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "average",
            "nameLocation": "687:7:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6309,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6306,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "703:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "695:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6305,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "695:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6308,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "714:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "706:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6307,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "706:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "694:22:35"
            },
            "returnParameters": {
              "id": 6312,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6311,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "740:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6310,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "740:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "739:9:35"
            },
            "scope": 6352,
            "src": "678:153:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6350,
              "nodeType": "Block",
              "src": "1101:123:35",
              "statements": [
                {
                  "expression": {
                    "commonType": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    },
                    "id": 6348,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "leftExpression": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6338,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6336,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6329,
                        "src": "1189:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "/",
                      "rightExpression": {
                        "id": 6337,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6331,
                        "src": "1193:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "1189:5:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "nodeType": "BinaryOperation",
                    "operator": "+",
                    "rightExpression": {
                      "components": [
                        {
                          "condition": {
                            "commonType": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            },
                            "id": 6343,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": false,
                            "lValueRequested": false,
                            "leftExpression": {
                              "commonType": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              },
                              "id": 6341,
                              "isConstant": false,
                              "isLValue": false,
                              "isPure": false,
                              "lValueRequested": false,
                              "leftExpression": {
                                "id": 6339,
                                "name": "a",
                                "nodeType": "Identifier",
                                "overloadedDeclarations": [],
                                "referencedDeclaration": 6329,
                                "src": "1198:1:35",
                                "typeDescriptions": {
                                  "typeIdentifier": "t_uint256",
                                  "typeString": "uint256"
                                }
                              },
                              "nodeType": "BinaryOperation",
                              "operator": "%",
                              "rightExpression": {
                                "id": 6340,
                                "name": "b",
                                "nodeType": "Identifier",
                                "overloadedDeclarations": [],
                                "referencedDeclaration": 6331,
                                "src": "1202:1:35",
                                "typeDescriptions": {
                                  "typeIdentifier": "t_uint256",
                                  "typeString": "uint256"
                                }
                              },
                              "src": "1198:5:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "nodeType": "BinaryOperation",
                            "operator": "==",
                            "rightExpression": {
                              "hexValue": "30",
                              "id": 6342,
                              "isConstant": false,
                              "isLValue": false,
                              "isPure": true,
                              "kind": "number",
                              "lValueRequested": false,
                              "nodeType": "Literal",
                              "src": "1207:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_rational_0_by_1",
                                "typeString": "int_const 0"
                              },
                              "value": "0"
                            },
                            "src": "1198:10:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_bool",
                              "typeString": "bool"
                            }
                          },
                          "falseExpression": {
                            "hexValue": "31",
                            "id": 6345,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": true,
                            "kind": "number",
                            "lValueRequested": false,
                            "nodeType": "Literal",
                            "src": "1215:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_rational_1_by_1",
                              "typeString": "int_const 1"
                            },
                            "value": "1"
                          },
                          "id": 6346,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": false,
                          "lValueRequested": false,
                          "nodeType": "Conditional",
                          "src": "1198:18:35",
                          "trueExpression": {
                            "hexValue": "30",
                            "id": 6344,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": true,
                            "kind": "number",
                            "lValueRequested": false,
                            "nodeType": "Literal",
                            "src": "1211:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_rational_0_by_1",
                              "typeString": "int_const 0"
                            },
                            "value": "0"
                          },
                          "typeDescriptions": {
                            "typeIdentifier": "t_uint8",
                            "typeString": "uint8"
                          }
                        }
                      ],
                      "id": 6347,
                      "isConstant": false,
                      "isInlineArray": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "nodeType": "TupleExpression",
                      "src": "1197:20:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint8",
                        "typeString": "uint8"
                      }
                    },
                    "src": "1189:28:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6335,
                  "id": 6349,
                  "nodeType": "Return",
                  "src": "1182:35:35"
                }
              ]
            },
            "documentation": {
              "id": 6327,
              "nodeType": "StructuredDocumentation",
              "src": "837:188:35",
              "text": " @dev Returns the ceiling of the division of two numbers.\n This differs from standard division with `/` in that it rounds up instead\n of rounding down."
            },
            "id": 6351,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "ceilDiv",
            "nameLocation": "1039:7:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6332,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6329,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "1055:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1047:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6328,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1047:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6331,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "1066:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1058:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6330,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1058:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "1046:22:35"
            },
            "returnParameters": {
              "id": 6335,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6334,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1092:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6333,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1092:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "1091:9:35"
            },
            "scope": 6352,
            "src": "1030:194:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          }
        ],
        "scope": 6353,
        "src": "202:1024:35",
        "usedErrors": []
      }
    ],
    "src": "103:1124:35"
  },
  "legacyAST": {
    "absolutePath": "@openzeppelin/contracts/utils/math/Math.sol",
    "exportedSymbols": {
      "Math": [
        6352
      ]
    },
    "id": 6353,
    "license": "MIT",
    "nodeType": "SourceUnit",
    "nodes": [
      {
        "id": 6266,
        "literals": [
          "solidity",
          "^",
          "0.8",
          ".0"
        ],
        "nodeType": "PragmaDirective",
        "src": "103:23:35"
      },
      {
        "abstract": false,
        "baseContracts": [],
        "canonicalName": "Math",
        "contractDependencies": [],
        "contractKind": "library",
        "documentation": {
          "id": 6267,
          "nodeType": "StructuredDocumentation",
          "src": "128:73:35",
          "text": " @dev Standard math utilities missing in the Solidity language."
        },
        "fullyImplemented": true,
        "id": 6352,
        "linearizedBaseContracts": [
          6352
        ],
        "name": "Math",
        "nameLocation": "210:4:35",
        "nodeType": "ContractDefinition",
        "nodes": [
          {
            "body": {
              "id": 6284,
              "nodeType": "Block",
              "src": "352:38:35",
              "statements": [
                {
                  "expression": {
                    "condition": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6279,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6277,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6270,
                        "src": "369:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": ">=",
                      "rightExpression": {
                        "id": 6278,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6272,
                        "src": "374:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "369:6:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bool",
                        "typeString": "bool"
                      }
                    },
                    "falseExpression": {
                      "id": 6281,
                      "name": "b",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6272,
                      "src": "382:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "id": 6282,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "nodeType": "Conditional",
                    "src": "369:14:35",
                    "trueExpression": {
                      "id": 6280,
                      "name": "a",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6270,
                      "src": "378:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6276,
                  "id": 6283,
                  "nodeType": "Return",
                  "src": "362:21:35"
                }
              ]
            },
            "documentation": {
              "id": 6268,
              "nodeType": "StructuredDocumentation",
              "src": "221:59:35",
              "text": " @dev Returns the largest of two numbers."
            },
            "id": 6285,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "max",
            "nameLocation": "294:3:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6273,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6270,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "306:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "298:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6269,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "298:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6272,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "317:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "309:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6271,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "309:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "297:22:35"
            },
            "returnParameters": {
              "id": 6276,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6275,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6285,
                  "src": "343:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6274,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "343:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "342:9:35"
            },
            "scope": 6352,
            "src": "285:105:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6302,
              "nodeType": "Block",
              "src": "528:37:35",
              "statements": [
                {
                  "expression": {
                    "condition": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6297,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6295,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6288,
                        "src": "545:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "<",
                      "rightExpression": {
                        "id": 6296,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6290,
                        "src": "549:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "545:5:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bool",
                        "typeString": "bool"
                      }
                    },
                    "falseExpression": {
                      "id": 6299,
                      "name": "b",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6290,
                      "src": "557:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "id": 6300,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "nodeType": "Conditional",
                    "src": "545:13:35",
                    "trueExpression": {
                      "id": 6298,
                      "name": "a",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 6288,
                      "src": "553:1:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6294,
                  "id": 6301,
                  "nodeType": "Return",
                  "src": "538:20:35"
                }
              ]
            },
            "documentation": {
              "id": 6286,
              "nodeType": "StructuredDocumentation",
              "src": "396:60:35",
              "text": " @dev Returns the smallest of two numbers."
            },
            "id": 6303,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "min",
            "nameLocation": "470:3:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6291,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6288,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "482:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "474:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6287,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "474:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6290,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "493:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "485:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6289,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "485:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "473:22:35"
            },
            "returnParameters": {
              "id": 6294,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6293,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6303,
                  "src": "519:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6292,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "519:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "518:9:35"
            },
            "scope": 6352,
            "src": "461:104:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6325,
              "nodeType": "Block",
              "src": "749:82:35",
              "statements": [
                {
                  "expression": {
                    "commonType": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    },
                    "id": 6323,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "leftExpression": {
                      "components": [
                        {
                          "commonType": {
                            "typeIdentifier": "t_uint256",
                            "typeString": "uint256"
                          },
                          "id": 6315,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": false,
                          "lValueRequested": false,
                          "leftExpression": {
                            "id": 6313,
                            "name": "a",
                            "nodeType": "Identifier",
                            "overloadedDeclarations": [],
                            "referencedDeclaration": 6306,
                            "src": "804:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          },
                          "nodeType": "BinaryOperation",
                          "operator": "&",
                          "rightExpression": {
                            "id": 6314,
                            "name": "b",
                            "nodeType": "Identifier",
                            "overloadedDeclarations": [],
                            "referencedDeclaration": 6308,
                            "src": "808:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          },
                          "src": "804:5:35",
                          "typeDescriptions": {
                            "typeIdentifier": "t_uint256",
                            "typeString": "uint256"
                          }
                        }
                      ],
                      "id": 6316,
                      "isConstant": false,
                      "isInlineArray": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "nodeType": "TupleExpression",
                      "src": "803:7:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "nodeType": "BinaryOperation",
                    "operator": "+",
                    "rightExpression": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6322,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "components": [
                          {
                            "commonType": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            },
                            "id": 6319,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": false,
                            "lValueRequested": false,
                            "leftExpression": {
                              "id": 6317,
                              "name": "a",
                              "nodeType": "Identifier",
                              "overloadedDeclarations": [],
                              "referencedDeclaration": 6306,
                              "src": "814:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "nodeType": "BinaryOperation",
                            "operator": "^",
                            "rightExpression": {
                              "id": 6318,
                              "name": "b",
                              "nodeType": "Identifier",
                              "overloadedDeclarations": [],
                              "referencedDeclaration": 6308,
                              "src": "818:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "src": "814:5:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            }
                          }
                        ],
                        "id": 6320,
                        "isConstant": false,
                        "isInlineArray": false,
                        "isLValue": false,
                        "isPure": false,
                        "lValueRequested": false,
                        "nodeType": "TupleExpression",
                        "src": "813:7:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "/",
                      "rightExpression": {
                        "hexValue": "32",
                        "id": 6321,
                        "isConstant": false,
                        "isLValue": false,
                        "isPure": true,
                        "kind": "number",
                        "lValueRequested": false,
                        "nodeType": "Literal",
                        "src": "823:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_rational_2_by_1",
                          "typeString": "int_const 2"
                        },
                        "value": "2"
                      },
                      "src": "813:11:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "src": "803:21:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6312,
                  "id": 6324,
                  "nodeType": "Return",
                  "src": "796:28:35"
                }
              ]
            },
            "documentation": {
              "id": 6304,
              "nodeType": "StructuredDocumentation",
              "src": "571:102:35",
              "text": " @dev Returns the average of two numbers. The result is rounded towards\n zero."
            },
            "id": 6326,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "average",
            "nameLocation": "687:7:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6309,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6306,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "703:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "695:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6305,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "695:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6308,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "714:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "706:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6307,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "706:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "694:22:35"
            },
            "returnParameters": {
              "id": 6312,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6311,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6326,
                  "src": "740:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6310,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "740:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "739:9:35"
            },
            "scope": 6352,
            "src": "678:153:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 6350,
              "nodeType": "Block",
              "src": "1101:123:35",
              "statements": [
                {
                  "expression": {
                    "commonType": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    },
                    "id": 6348,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "leftExpression": {
                      "commonType": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      },
                      "id": 6338,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "leftExpression": {
                        "id": 6336,
                        "name": "a",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6329,
                        "src": "1189:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "nodeType": "BinaryOperation",
                      "operator": "/",
                      "rightExpression": {
                        "id": 6337,
                        "name": "b",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 6331,
                        "src": "1193:1:35",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      },
                      "src": "1189:5:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint256",
                        "typeString": "uint256"
                      }
                    },
                    "nodeType": "BinaryOperation",
                    "operator": "+",
                    "rightExpression": {
                      "components": [
                        {
                          "condition": {
                            "commonType": {
                              "typeIdentifier": "t_uint256",
                              "typeString": "uint256"
                            },
                            "id": 6343,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": false,
                            "lValueRequested": false,
                            "leftExpression": {
                              "commonType": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              },
                              "id": 6341,
                              "isConstant": false,
                              "isLValue": false,
                              "isPure": false,
                              "lValueRequested": false,
                              "leftExpression": {
                                "id": 6339,
                                "name": "a",
                                "nodeType": "Identifier",
                                "overloadedDeclarations": [],
                                "referencedDeclaration": 6329,
                                "src": "1198:1:35",
                                "typeDescriptions": {
                                  "typeIdentifier": "t_uint256",
                                  "typeString": "uint256"
                                }
                              },
                              "nodeType": "BinaryOperation",
                              "operator": "%",
                              "rightExpression": {
                                "id": 6340,
                                "name": "b",
                                "nodeType": "Identifier",
                                "overloadedDeclarations": [],
                                "referencedDeclaration": 6331,
                                "src": "1202:1:35",
                                "typeDescriptions": {
                                  "typeIdentifier": "t_uint256",
                                  "typeString": "uint256"
                                }
                              },
                              "src": "1198:5:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            },
                            "nodeType": "BinaryOperation",
                            "operator": "==",
                            "rightExpression": {
                              "hexValue": "30",
                              "id": 6342,
                              "isConstant": false,
                              "isLValue": false,
                              "isPure": true,
                              "kind": "number",
                              "lValueRequested": false,
                              "nodeType": "Literal",
                              "src": "1207:1:35",
                              "typeDescriptions": {
                                "typeIdentifier": "t_rational_0_by_1",
                                "typeString": "int_const 0"
                              },
                              "value": "0"
                            },
                            "src": "1198:10:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_bool",
                              "typeString": "bool"
                            }
                          },
                          "falseExpression": {
                            "hexValue": "31",
                            "id": 6345,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": true,
                            "kind": "number",
                            "lValueRequested": false,
                            "nodeType": "Literal",
                            "src": "1215:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_rational_1_by_1",
                              "typeString": "int_const 1"
                            },
                            "value": "1"
                          },
                          "id": 6346,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": false,
                          "lValueRequested": false,
                          "nodeType": "Conditional",
                          "src": "1198:18:35",
                          "trueExpression": {
                            "hexValue": "30",
                            "id": 6344,
                            "isConstant": false,
                            "isLValue": false,
                            "isPure": true,
                            "kind": "number",
                            "lValueRequested": false,
                            "nodeType": "Literal",
                            "src": "1211:1:35",
                            "typeDescriptions": {
                              "typeIdentifier": "t_rational_0_by_1",
                              "typeString": "int_const 0"
                            },
                            "value": "0"
                          },
                          "typeDescriptions": {
                            "typeIdentifier": "t_uint8",
                            "typeString": "uint8"
                          }
                        }
                      ],
                      "id": 6347,
                      "isConstant": false,
                      "isInlineArray": false,
                      "isLValue": false,
                      "isPure": false,
                      "lValueRequested": false,
                      "nodeType": "TupleExpression",
                      "src": "1197:20:35",
                      "typeDescriptions": {
                        "typeIdentifier": "t_uint8",
                        "typeString": "uint8"
                      }
                    },
                    "src": "1189:28:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "functionReturnParameters": 6335,
                  "id": 6349,
                  "nodeType": "Return",
                  "src": "1182:35:35"
                }
              ]
            },
            "documentation": {
              "id": 6327,
              "nodeType": "StructuredDocumentation",
              "src": "837:188:35",
              "text": " @dev Returns the ceiling of the division of two numbers.\n This differs from standard division with `/` in that it rounds up instead\n of rounding down."
            },
            "id": 6351,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "ceilDiv",
            "nameLocation": "1039:7:35",
            "nodeType": "FunctionDefinition",
            "parameters": {
              "id": 6332,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6329,
                  "mutability": "mutable",
                  "name": "a",
                  "nameLocation": "1055:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1047:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6328,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1047:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 6331,
                  "mutability": "mutable",
                  "name": "b",
                  "nameLocation": "1066:1:35",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1058:9:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6330,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1058:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "1046:22:35"
            },
            "returnParameters": {
              "id": 6335,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 6334,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 6351,
                  "src": "1092:7:35",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_uint256",
                    "typeString": "uint256"
                  },
                  "typeName": {
                    "id": 6333,
                    "name": "uint256",
                    "nodeType": "ElementaryTypeName",
                    "src": "1092:7:35",
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint256",
                      "typeString": "uint256"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "1091:9:35"
            },
            "scope": 6352,
            "src": "1030:194:35",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          }
        ],
        "scope": 6353,
        "src": "202:1024:35",
        "usedErrors": []
      }
    ],
    "src": "103:1124:35"
  },
  "compiler": {
    "name": "solc",
    "version": "0.8.11+commit.d7f03943.Emscripten.clang"
  },
  "networks": {},
  "schemaVersion": "3.4.4",
  "updatedAt": "2022-03-06T23:47:11.068Z",
  "devdoc": {
    "details": "Standard math utilities missing in the Solidity language.",
    "kind": "dev",
    "methods": {},
    "version": 1
  },
  "userdoc": {
    "kind": "user",
    "methods": {},
    "version": 1
  }
}