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                    "typeDescriptions": {
                      "typeIdentifier": "t_tuple$_t_address_$_t_enum$_RecoverError_$13778_$",
                      "typeString": "tuple(address,enum ECDSA.RecoverError)"
                    }
                  },
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                  "src": "3758:69:26"
                },
                {
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                        "name": "error",
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                        "src": "3849:5:26",
                        "typeDescriptions": {
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                          "typeString": "enum ECDSA.RecoverError"
                        }
                      }
                    ],
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                        {
                          "typeIdentifier": "t_enum$_RecoverError_$13778",
                          "typeString": "enum ECDSA.RecoverError"
                        }
                      ],
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                      "name": "_throwError",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 13822,
                      "src": "3837:11:26",
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                        "typeString": "function (enum ECDSA.RecoverError) pure"
                      }
                    },
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                    "isPure": false,
                    "kind": "functionCall",
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                    "src": "3837:18:26",
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                      "typeString": "tuple()"
                    }
                  },
                  "id": 13891,
                  "nodeType": "ExpressionStatement",
                  "src": "3837:18:26"
                },
                {
                  "expression": {
                    "id": 13892,
                    "name": "recovered",
                    "nodeType": "Identifier",
                    "overloadedDeclarations": [],
                    "referencedDeclaration": 13879,
                    "src": "3872:9:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_address",
                      "typeString": "address"
                    }
                  },
                  "functionReturnParameters": 13877,
                  "id": 13893,
                  "nodeType": "Return",
                  "src": "3865:16:26"
                }
              ]
            },
            "documentation": {
              "id": 13869,
              "nodeType": "StructuredDocumentation",
              "src": "2881:775:26",
              "text": " @dev Returns the address that signed a hashed message (`hash`) with\n `signature`. This address can then be used for verification purposes.\n The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:\n this function rejects them by requiring the `s` value to be in the lower\n half order, and the `v` value to be either 27 or 28.\n IMPORTANT: `hash` _must_ be the result of a hash operation for the\n verification to be secure: it is possible to craft signatures that\n recover to arbitrary addresses for non-hashed data. A safe way to ensure\n this is by receiving a hash of the original message (which may otherwise\n be too long), and then calling {toEthSignedMessageHash} on it."
            },
            "id": 13895,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
            "name": "recover",
            "nameLocation": "3670:7:26",
            "nodeType": "FunctionDefinition",
            "parameters": {
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              "nodeType": "ParameterList",
              "parameters": [
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                  "constant": false,
                  "id": 13871,
                  "mutability": "mutable",
                  "name": "hash",
                  "nameLocation": "3686:4:26",
                  "nodeType": "VariableDeclaration",
                  "scope": 13895,
                  "src": "3678:12:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_bytes32",
                    "typeString": "bytes32"
                  },
                  "typeName": {
                    "id": 13870,
                    "name": "bytes32",
                    "nodeType": "ElementaryTypeName",
                    "src": "3678:7:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_bytes32",
                      "typeString": "bytes32"
                    }
                  },
                  "visibility": "internal"
                },
                {
                  "constant": false,
                  "id": 13873,
                  "mutability": "mutable",
                  "name": "signature",
                  "nameLocation": "3705:9:26",
                  "nodeType": "VariableDeclaration",
                  "scope": 13895,
                  "src": "3692:22:26",
                  "stateVariable": false,
                  "storageLocation": "memory",
                  "typeDescriptions": {
                    "typeIdentifier": "t_bytes_memory_ptr",
                    "typeString": "bytes"
                  },
                  "typeName": {
                    "id": 13872,
                    "name": "bytes",
                    "nodeType": "ElementaryTypeName",
                    "src": "3692:5:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_bytes_storage_ptr",
                      "typeString": "bytes"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "3677:38:26"
            },
            "returnParameters": {
              "id": 13877,
              "nodeType": "ParameterList",
              "parameters": [
                {
                  "constant": false,
                  "id": 13876,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 13895,
                  "src": "3739:7:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_address",
                    "typeString": "address"
                  },
                  "typeName": {
                    "id": 13875,
                    "name": "address",
                    "nodeType": "ElementaryTypeName",
                    "src": "3739:7:26",
                    "stateMutability": "nonpayable",
                    "typeDescriptions": {
                      "typeIdentifier": "t_address",
                      "typeString": "address"
                    }
                  },
                  "visibility": "internal"
                }
              ],
              "src": "3738:9:26"
            },
            "scope": 14129,
            "src": "3661:227:26",
            "stateMutability": "pure",
            "virtual": false,
            "visibility": "internal"
          },
          {
            "body": {
              "id": 13941,
              "nodeType": "Block",
              "src": "4275:203:26",
              "statements": [
                {
                  "assignments": [
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                  ],
                  "declarations": [
                    {
                      "constant": false,
                      "id": 13911,
                      "mutability": "mutable",
                      "name": "s",
                      "nameLocation": "4293:1:26",
                      "nodeType": "VariableDeclaration",
                      "scope": 13941,
                      "src": "4285:9:26",
                      "stateVariable": false,
                      "storageLocation": "default",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bytes32",
                        "typeString": "bytes32"
                      },
                      "typeName": {
                        "id": 13910,
                        "name": "bytes32",
                        "nodeType": "ElementaryTypeName",
                        "src": "4285:7:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_bytes32",
                          "typeString": "bytes32"
                        }
                      },
                      "visibility": "internal"
                    }
                  ],
                  "id": 13918,
                  "initialValue": {
                    "commonType": {
                      "typeIdentifier": "t_bytes32",
                      "typeString": "bytes32"
                    },
                    "id": 13917,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "lValueRequested": false,
                    "leftExpression": {
                      "id": 13912,
                      "name": "vs",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [],
                      "referencedDeclaration": 13902,
                      "src": "4297:2:26",
                      "typeDescriptions": {
                        "typeIdentifier": "t_bytes32",
                        "typeString": "bytes32"
                      }
                    },
                    "nodeType": "BinaryOperation",
                    "operator": "&",
                    "rightExpression": {
                      "arguments": [
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                          "id": 13915,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": true,
                          "kind": "number",
                          "lValueRequested": false,
                          "nodeType": "Literal",
                          "src": "4310:66:26",
                          "typeDescriptions": {
                            "typeIdentifier": "t_rational_57896044618658097711785492504343953926634992332820282019728792003956564819967_by_1",
                            "typeString": "int_const 5789...(69 digits omitted)...9967"
                          },
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                        }
                      ],
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                        "argumentTypes": [
                          {
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                        "lValueRequested": false,
                        "nodeType": "ElementaryTypeNameExpression",
                        "src": "4302:7:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_type$_t_bytes32_$",
                          "typeString": "type(bytes32)"
                        },
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                          "id": 13913,
                          "name": "bytes32",
                          "nodeType": "ElementaryTypeName",
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                        }
                      },
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                      "isConstant": false,
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                      "isPure": true,
                      "kind": "typeConversion",
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                      "names": [],
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                        "typeString": "bytes32"
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                      "typeString": "bytes32"
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                      "id": 13920,
                      "mutability": "mutable",
                      "name": "v",
                      "nameLocation": "4393:1:26",
                      "nodeType": "VariableDeclaration",
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                      "stateVariable": false,
                      "storageLocation": "default",
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                        "typeIdentifier": "t_uint8",
                        "typeString": "uint8"
                      },
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                        "id": 13919,
                        "name": "uint8",
                        "nodeType": "ElementaryTypeName",
                        "src": "4387:5:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint8",
                          "typeString": "uint8"
                        }
                      },
                      "visibility": "internal"
                    }
                  ],
                  "id": 13933,
                  "initialValue": {
                    "arguments": [
                      {
                        "commonType": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        },
                        "id": 13931,
                        "isConstant": false,
                        "isLValue": false,
                        "isPure": false,
                        "lValueRequested": false,
                        "leftExpression": {
                          "components": [
                            {
                              "commonType": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              },
                              "id": 13928,
                              "isConstant": false,
                              "isLValue": false,
                              "isPure": false,
                              "lValueRequested": false,
                              "leftExpression": {
                                "arguments": [
                                  {
                                    "id": 13925,
                                    "name": "vs",
                                    "nodeType": "Identifier",
                                    "overloadedDeclarations": [],
                                    "referencedDeclaration": 13902,
                                    "src": "4412:2:26",
                                    "typeDescriptions": {
                                      "typeIdentifier": "t_bytes32",
                                      "typeString": "bytes32"
                                    }
                                  }
                                ],
                                "expression": {
                                  "argumentTypes": [
                                    {
                                      "typeIdentifier": "t_bytes32",
                                      "typeString": "bytes32"
                                    }
                                  ],
                                  "id": 13924,
                                  "isConstant": false,
                                  "isLValue": false,
                                  "isPure": true,
                                  "lValueRequested": false,
                                  "nodeType": "ElementaryTypeNameExpression",
                                  "src": "4404:7:26",
                                  "typeDescriptions": {
                                    "typeIdentifier": "t_type$_t_uint256_$",
                                    "typeString": "type(uint256)"
                                  },
                                  "typeName": {
                                    "id": 13923,
                                    "name": "uint256",
                                    "nodeType": "ElementaryTypeName",
                                    "src": "4404:7:26",
                                    "typeDescriptions": {}
                                  }
                                },
                                "id": 13926,
                                "isConstant": false,
                                "isLValue": false,
                                "isPure": false,
                                "kind": "typeConversion",
                                "lValueRequested": false,
                                "nameLocations": [],
                                "names": [],
                                "nodeType": "FunctionCall",
                                "src": "4404:11:26",
                                "tryCall": false,
                                "typeDescriptions": {
                                  "typeIdentifier": "t_uint256",
                                  "typeString": "uint256"
                                }
                              },
                              "nodeType": "BinaryOperation",
                              "operator": ">>",
                              "rightExpression": {
                                "hexValue": "323535",
                                "id": 13927,
                                "isConstant": false,
                                "isLValue": false,
                                "isPure": true,
                                "kind": "number",
                                "lValueRequested": false,
                                "nodeType": "Literal",
                                "src": "4419:3:26",
                                "typeDescriptions": {
                                  "typeIdentifier": "t_rational_255_by_1",
                                  "typeString": "int_const 255"
                                },
                                "value": "255"
                              },
                              "src": "4404:18:26",
                              "typeDescriptions": {
                                "typeIdentifier": "t_uint256",
                                "typeString": "uint256"
                              }
                            }
                          ],
                          "id": 13929,
                          "isConstant": false,
                          "isInlineArray": false,
                          "isLValue": false,
                          "isPure": false,
                          "lValueRequested": false,
                          "nodeType": "TupleExpression",
                          "src": "4403:20:26",
                          "typeDescriptions": {
                            "typeIdentifier": "t_uint256",
                            "typeString": "uint256"
                          }
                        },
                        "nodeType": "BinaryOperation",
                        "operator": "+",
                        "rightExpression": {
                          "hexValue": "3237",
                          "id": 13930,
                          "isConstant": false,
                          "isLValue": false,
                          "isPure": true,
                          "kind": "number",
                          "lValueRequested": false,
                          "nodeType": "Literal",
                          "src": "4426:2:26",
                          "typeDescriptions": {
                            "typeIdentifier": "t_rational_27_by_1",
                            "typeString": "int_const 27"
                          },
                          "value": "27"
                        },
                        "src": "4403:25:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      }
                    ],
                    "expression": {
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                        {
                          "typeIdentifier": "t_uint256",
                          "typeString": "uint256"
                        }
                      ],
                      "id": 13922,
                      "isConstant": false,
                      "isLValue": false,
                      "isPure": true,
                      "lValueRequested": false,
                      "nodeType": "ElementaryTypeNameExpression",
                      "src": "4397:5:26",
                      "typeDescriptions": {
                        "typeIdentifier": "t_type$_t_uint8_$",
                        "typeString": "type(uint8)"
                      },
                      "typeName": {
                        "id": 13921,
                        "name": "uint8",
                        "nodeType": "ElementaryTypeName",
                        "src": "4397:5:26",
                        "typeDescriptions": {}
                      }
                    },
                    "id": 13932,
                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "kind": "typeConversion",
                    "lValueRequested": false,
                    "nameLocations": [],
                    "names": [],
                    "nodeType": "FunctionCall",
                    "src": "4397:32:26",
                    "tryCall": false,
                    "typeDescriptions": {
                      "typeIdentifier": "t_uint8",
                      "typeString": "uint8"
                    }
                  },
                  "nodeType": "VariableDeclarationStatement",
                  "src": "4387:42:26"
                },
                {
                  "expression": {
                    "arguments": [
                      {
                        "id": 13935,
                        "name": "hash",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 13898,
                        "src": "4457:4:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_bytes32",
                          "typeString": "bytes32"
                        }
                      },
                      {
                        "id": 13936,
                        "name": "v",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 13920,
                        "src": "4463:1:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_uint8",
                          "typeString": "uint8"
                        }
                      },
                      {
                        "id": 13937,
                        "name": "r",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 13900,
                        "src": "4466:1:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_bytes32",
                          "typeString": "bytes32"
                        }
                      },
                      {
                        "id": 13938,
                        "name": "s",
                        "nodeType": "Identifier",
                        "overloadedDeclarations": [],
                        "referencedDeclaration": 13911,
                        "src": "4469:1:26",
                        "typeDescriptions": {
                          "typeIdentifier": "t_bytes32",
                          "typeString": "bytes32"
                        }
                      }
                    ],
                    "expression": {
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                          "typeIdentifier": "t_bytes32",
                          "typeString": "bytes32"
                        },
                        {
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                          "typeString": "uint8"
                        },
                        {
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                          "typeString": "bytes32"
                        },
                        {
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                          "typeString": "bytes32"
                        }
                      ],
                      "id": 13934,
                      "name": "tryRecover",
                      "nodeType": "Identifier",
                      "overloadedDeclarations": [
                        13868,
                        13942,
                        14036
                      ],
                      "referencedDeclaration": 14036,
                      "src": "4446:10:26",
                      "typeDescriptions": {
                        "typeIdentifier": "t_function_internal_pure$_t_bytes32_$_t_uint8_$_t_bytes32_$_t_bytes32_$returns$_t_address_$_t_enum$_RecoverError_$13778_$",
                        "typeString": "function (bytes32,uint8,bytes32,bytes32) pure returns (address,enum ECDSA.RecoverError)"
                      }
                    },
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                    "isConstant": false,
                    "isLValue": false,
                    "isPure": false,
                    "kind": "functionCall",
                    "lValueRequested": false,
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                    "names": [],
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                    "tryCall": false,
                    "typeDescriptions": {
                      "typeIdentifier": "t_tuple$_t_address_$_t_enum$_RecoverError_$13778_$",
                      "typeString": "tuple(address,enum ECDSA.RecoverError)"
                    }
                  },
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                  "id": 13940,
                  "nodeType": "Return",
                  "src": "4439:32:26"
                }
              ]
            },
            "documentation": {
              "id": 13896,
              "nodeType": "StructuredDocumentation",
              "src": "3894:243:26",
              "text": " @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.\n See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]\n _Available since v4.3._"
            },
            "id": 13942,
            "implemented": true,
            "kind": "function",
            "modifiers": [],
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              "nodeType": "ParameterList",
              "parameters": [
                {
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                  "mutability": "mutable",
                  "name": "hash",
                  "nameLocation": "4179:4:26",
                  "nodeType": "VariableDeclaration",
                  "scope": 13942,
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                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
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                    "typeString": "bytes32"
                  },
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                    "nodeType": "ElementaryTypeName",
                    "src": "4171:7:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_bytes32",
                      "typeString": "bytes32"
                    }
                  },
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                },
                {
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                  "id": 13900,
                  "mutability": "mutable",
                  "name": "r",
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                  "nodeType": "VariableDeclaration",
                  "scope": 13942,
                  "src": "4193:9:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
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                    "typeString": "bytes32"
                  },
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                    "name": "bytes32",
                    "nodeType": "ElementaryTypeName",
                    "src": "4193:7:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_bytes32",
                      "typeString": "bytes32"
                    }
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                },
                {
                  "constant": false,
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                  "mutability": "mutable",
                  "name": "vs",
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                  "nodeType": "VariableDeclaration",
                  "scope": 13942,
                  "src": "4212:10:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_bytes32",
                    "typeString": "bytes32"
                  },
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                    "name": "bytes32",
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                    "src": "4212:7:26",
                    "typeDescriptions": {
                      "typeIdentifier": "t_bytes32",
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                  },
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                }
              ],
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            },
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                  "mutability": "mutable",
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                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 13942,
                  "src": "4252:7:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_address",
                    "typeString": "address"
                  },
                  "typeName": {
                    "id": 13904,
                    "name": "address",
                    "nodeType": "ElementaryTypeName",
                    "src": "4252:7:26",
                    "stateMutability": "nonpayable",
                    "typeDescriptions": {
                      "typeIdentifier": "t_address",
                      "typeString": "address"
                    }
                  },
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                },
                {
                  "constant": false,
                  "id": 13908,
                  "mutability": "mutable",
                  "name": "",
                  "nameLocation": "-1:-1:-1",
                  "nodeType": "VariableDeclaration",
                  "scope": 13942,
                  "src": "4261:12:26",
                  "stateVariable": false,
                  "storageLocation": "default",
                  "typeDescriptions": {
                    "typeIdentifier": "t_enum$_RecoverError_$13778",
                    "typeString": "enum ECDSA.RecoverError"
                  },
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  "source": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/ECDSA.sol)\n\npragma solidity ^0.8.0;\n\nimport \"../Strings.sol\";\n\n/**\n * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.\n *\n * These functions can be used to verify that a message was signed by the holder\n * of the private keys of a given address.\n */\nlibrary ECDSA {\n    enum RecoverError {\n        NoError,\n        InvalidSignature,\n        InvalidSignatureLength,\n        InvalidSignatureS,\n        InvalidSignatureV // Deprecated in v4.8\n    }\n\n    function _throwError(RecoverError error) private pure {\n        if (error == RecoverError.NoError) {\n            return; // no error: do nothing\n        } else if (error == RecoverError.InvalidSignature) {\n            revert(\"ECDSA: invalid signature\");\n        } else if (error == RecoverError.InvalidSignatureLength) {\n            revert(\"ECDSA: invalid signature length\");\n        } else if (error == RecoverError.InvalidSignatureS) {\n            revert(\"ECDSA: invalid signature 's' value\");\n        }\n    }\n\n    /**\n     * @dev Returns the address that signed a hashed message (`hash`) with\n     * `signature` or error string. This address can then be used for verification purposes.\n     *\n     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:\n     * this function rejects them by requiring the `s` value to be in the lower\n     * half order, and the `v` value to be either 27 or 28.\n     *\n     * IMPORTANT: `hash` _must_ be the result of a hash operation for the\n     * verification to be secure: it is possible to craft signatures that\n     * recover to arbitrary addresses for non-hashed data. A safe way to ensure\n     * this is by receiving a hash of the original message (which may otherwise\n     * be too long), and then calling {toEthSignedMessageHash} on it.\n     *\n     * Documentation for signature generation:\n     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]\n     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]\n     *\n     * _Available since v4.3._\n     */\n    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {\n        if (signature.length == 65) {\n            bytes32 r;\n            bytes32 s;\n            uint8 v;\n            // ecrecover takes the signature parameters, and the only way to get them\n            // currently is to use assembly.\n            /// @solidity memory-safe-assembly\n            assembly {\n                r := mload(add(signature, 0x20))\n                s := mload(add(signature, 0x40))\n                v := byte(0, mload(add(signature, 0x60)))\n            }\n            return tryRecover(hash, v, r, s);\n        } else {\n            return (address(0), RecoverError.InvalidSignatureLength);\n        }\n    }\n\n    /**\n     * @dev Returns the address that signed a hashed message (`hash`) with\n     * `signature`. This address can then be used for verification purposes.\n     *\n     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:\n     * this function rejects them by requiring the `s` value to be in the lower\n     * half order, and the `v` value to be either 27 or 28.\n     *\n     * IMPORTANT: `hash` _must_ be the result of a hash operation for the\n     * verification to be secure: it is possible to craft signatures that\n     * recover to arbitrary addresses for non-hashed data. A safe way to ensure\n     * this is by receiving a hash of the original message (which may otherwise\n     * be too long), and then calling {toEthSignedMessageHash} on it.\n     */\n    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {\n        (address recovered, RecoverError error) = tryRecover(hash, signature);\n        _throwError(error);\n        return recovered;\n    }\n\n    /**\n     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.\n     *\n     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]\n     *\n     * _Available since v4.3._\n     */\n    function tryRecover(\n        bytes32 hash,\n        bytes32 r,\n        bytes32 vs\n    ) internal pure returns (address, RecoverError) {\n        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);\n        uint8 v = uint8((uint256(vs) >> 255) + 27);\n        return tryRecover(hash, v, r, s);\n    }\n\n    /**\n     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.\n     *\n     * _Available since v4.2._\n     */\n    function recover(\n        bytes32 hash,\n        bytes32 r,\n        bytes32 vs\n    ) internal pure returns (address) {\n        (address recovered, RecoverError error) = tryRecover(hash, r, vs);\n        _throwError(error);\n        return recovered;\n    }\n\n    /**\n     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,\n     * `r` and `s` signature fields separately.\n     *\n     * _Available since v4.3._\n     */\n    function tryRecover(\n        bytes32 hash,\n        uint8 v,\n        bytes32 r,\n        bytes32 s\n    ) internal pure returns (address, RecoverError) {\n        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature\n        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines\n        // the valid range for s in (301): 0 < s < secp256k1n \u00f7 2 + 1, and for v in (302): v \u2208 {27, 28}. Most\n        // signatures from current libraries generate a unique signature with an s-value in the lower half order.\n        //\n        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value\n        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or\n        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept\n        // these malleable signatures as well.\n        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {\n            return (address(0), RecoverError.InvalidSignatureS);\n        }\n\n        // If the signature is valid (and not malleable), return the signer address\n        address signer = ecrecover(hash, v, r, s);\n        if (signer == address(0)) {\n            return (address(0), RecoverError.InvalidSignature);\n        }\n\n        return (signer, RecoverError.NoError);\n    }\n\n    /**\n     * @dev Overload of {ECDSA-recover} that receives the `v`,\n     * `r` and `s` signature fields separately.\n     */\n    function recover(\n        bytes32 hash,\n        uint8 v,\n        bytes32 r,\n        bytes32 s\n    ) internal pure returns (address) {\n        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);\n        _throwError(error);\n        return recovered;\n    }\n\n    /**\n     * @dev Returns an Ethereum Signed Message, created from a `hash`. This\n     * produces hash corresponding to the one signed with the\n     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]\n     * JSON-RPC method as part of EIP-191.\n     *\n     * See {recover}.\n     */\n    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32) {\n        // 32 is the length in bytes of hash,\n        // enforced by the type signature above\n        return keccak256(abi.encodePacked(\"\\x19Ethereum Signed Message:\\n32\", hash));\n    }\n\n    /**\n     * @dev Returns an Ethereum Signed Message, created from `s`. This\n     * produces hash corresponding to the one signed with the\n     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]\n     * JSON-RPC method as part of EIP-191.\n     *\n     * See {recover}.\n     */\n    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {\n        return keccak256(abi.encodePacked(\"\\x19Ethereum Signed Message:\\n\", Strings.toString(s.length), s));\n    }\n\n    /**\n     * @dev Returns an Ethereum Signed Typed Data, created from a\n     * `domainSeparator` and a `structHash`. This produces hash corresponding\n     * to the one signed with the\n     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]\n     * JSON-RPC method as part of EIP-712.\n     *\n     * See {recover}.\n     */\n    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {\n        return keccak256(abi.encodePacked(\"\\x19\\x01\", domainSeparator, structHash));\n    }\n}\n",
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