creation_sourcecode: {{
    "language": "Solidity",
    "sources": {
      "contracts/RunaPreSale.sol": {
        "content": "// SPDX-License-Identifier: MIT\npragma solidity ^0.8.0;\nimport \"@openzeppelin/contracts/access/Ownable.sol\";\nimport \"@openzeppelin/contracts/security/ReentrancyGuard.sol\";\nimport \"@openzeppelin/contracts/utils/cryptography/ECDSA.sol\";\n\ncontract RunaPreSale is Ownable, ReentrancyGuard {\n    using ECDSA for bytes32;\n    uint256 public currentPrice;\n    uint256 public totalSupply;\n    uint256 public totalReserved;\n    address public signer;\n    bool public isSaleActive;\n    uint16 public constant maxPerCode = 2;\n\n    mapping(bytes => bool) private signatures;\n    mapping(bytes32 => uint256) private codeNFTReservations;\n    mapping(address => uint256) public addressNFTReservations;\n\n    event SaleStateUpdated(bool indexed isActive);\n    event PriceAndSupplySet(uint256 indexed price, uint256 indexed supply);\n    event NFTReserved(\n        address indexed user,\n        uint256 indexed quantity,\n        string indexed code\n    );\n    event FundsWithdrawn(uint256 indexed amount, address indexed to);\n\n    constructor(address _signer) {\n        signer = _signer;\n        isSaleActive = false;\n    }\n\n    function toggleSaleState() public onlyOwner {\n        isSaleActive = !isSaleActive;\n        emit SaleStateUpdated(isSaleActive);\n    }\n\n    function setPriceAndSupply(\n        uint256 _price,\n        uint256 _supply\n    ) public onlyOwner {\n        require(!isSaleActive, \"Cannot change during active sale\");\n        currentPrice = _price;\n        totalSupply = _supply;\n        totalReserved = 0; // Optionally reset totalReserved if starting a new sale phase\n        emit PriceAndSupplySet(_price, _supply);\n    }\n\n    function reserveNFT(\n        string memory code,\n        uint256 quantity,\n        uint256 _salt,\n        bytes32 _msgHash,\n        bytes memory _signature\n    ) external payable nonReentrant {\n        require(isSaleActive, \"Sale is not active\");\n        require(totalReserved < totalSupply, \"All NFTs reserved\");\n        require(msg.value == currentPrice * quantity, \"Incorrect ETH amount\");\n        require(!signatures[_signature], \"Contract: Signature already used!\");\n        require(\n            addressNFTReservations[msg.sender] + quantity <= 2,\n            \"Cannot mint more than two NFTs\"\n        );\n\n        // Convert string code to bytes32\n        bytes32 codeHash = keccak256(abi.encodePacked(code));\n        uint256 reservedByCode = codeNFTReservations[codeHash];\n        // Ensure valid reservation\n        require(\n            quantity > 0 && quantity <= maxPerCode - reservedByCode,\n            \"Invalid quantity or code fully reserved\"\n        );\n\n        // create msghash with address and a number\n        bytes32 msgHash = keccak256(\n            abi.encodePacked(msg.sender, code, quantity, _salt)\n        );\n        bytes32 signedMsgHash = msgHash.toEthSignedMessageHash();\n\n        require(signedMsgHash == _msgHash, \"Invalid message hash!\");\n        require(_msgHash.recover(_signature) == signer, \"Invalid signer!\");\n        signatures[_signature] = true;\n\n        // Update totalReserved and user's reservation count for the code\n        totalReserved += quantity;\n        codeNFTReservations[codeHash] += quantity;\n        addressNFTReservations[msg.sender] += quantity;\n\n        emit NFTReserved(msg.sender, quantity, code);\n    }\n\n    function updateSigner(address _signer) public onlyOwner {\n        require(_signer != address(0), \"Invalid Address\");\n        require(_signer != signer, \"Signer already set\");\n        signer = _signer;\n    }\n\n    function withdrawFunds(address payable _to) public onlyOwner {\n        uint256 balance = address(this).balance;\n        _to.transfer(balance);\n        emit FundsWithdrawn(balance, _to);\n    }\n\n    function getReservationByCode(\n        string memory code\n    ) public view returns (uint256) {\n        bytes32 codeHash = keccak256(abi.encodePacked(code));\n        return codeNFTReservations[codeHash];\n    }\n}\n"
      },
      "@openzeppelin/contracts/utils/cryptography/ECDSA.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (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(bytes32 hash, bytes32 r, bytes32 vs) 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(bytes32 hash, bytes32 r, bytes32 vs) 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(bytes32 hash, uint8 v, bytes32 r, bytes32 s) 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 ÷ 2 + 1, and for v in (302): v ∈ {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(bytes32 hash, uint8 v, bytes32 r, bytes32 s) 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 message) {\n        // 32 is the length in bytes of hash,\n        // enforced by the type signature above\n        /// @solidity memory-safe-assembly\n        assembly {\n            mstore(0x00, \"\\x19Ethereum Signed Message:\\n32\")\n            mstore(0x1c, hash)\n            message := keccak256(0x00, 0x3c)\n        }\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 data) {\n        /// @solidity memory-safe-assembly\n        assembly {\n            let ptr := mload(0x40)\n            mstore(ptr, \"\\x19\\x01\")\n            mstore(add(ptr, 0x02), domainSeparator)\n            mstore(add(ptr, 0x22), structHash)\n            data := keccak256(ptr, 0x42)\n        }\n    }\n\n    /**\n     * @dev Returns an Ethereum Signed Data with intended validator, created from a\n     * `validator` and `data` according to the version 0 of EIP-191.\n     *\n     * See {recover}.\n     */\n    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {\n        return keccak256(abi.encodePacked(\"\\x19\\x00\", validator, data));\n    }\n}\n"
      },
      "@openzeppelin/contracts/security/ReentrancyGuard.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Contract module that helps prevent reentrant calls to a function.\n *\n * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier\n * available, which can be applied to functions to make sure there are no nested\n * (reentrant) calls to them.\n *\n * Note that because there is a single `nonReentrant` guard, functions marked as\n * `nonReentrant` may not call one another. This can be worked around by making\n * those functions `private`, and then adding `external` `nonReentrant` entry\n * points to them.\n *\n * TIP: If you would like to learn more about reentrancy and alternative ways\n * to protect against it, check out our blog post\n * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].\n */\nabstract contract ReentrancyGuard {\n    // Booleans are more expensive than uint256 or any type that takes up a full\n    // word because each write operation emits an extra SLOAD to first read the\n    // slot's contents, replace the bits taken up by the boolean, and then write\n    // back. This is the compiler's defense against contract upgrades and\n    // pointer aliasing, and it cannot be disabled.\n\n    // The values being non-zero value makes deployment a bit more expensive,\n    // but in exchange the refund on every call to nonReentrant will be lower in\n    // amount. Since refunds are capped to a percentage of the total\n    // transaction's gas, it is best to keep them low in cases like this one, to\n    // increase the likelihood of the full refund coming into effect.\n    uint256 private constant _NOT_ENTERED = 1;\n    uint256 private constant _ENTERED = 2;\n\n    uint256 private _status;\n\n    constructor() {\n        _status = _NOT_ENTERED;\n    }\n\n    /**\n     * @dev Prevents a contract from calling itself, directly or indirectly.\n     * Calling a `nonReentrant` function from another `nonReentrant`\n     * function is not supported. It is possible to prevent this from happening\n     * by making the `nonReentrant` function external, and making it call a\n     * `private` function that does the actual work.\n     */\n    modifier nonReentrant() {\n        _nonReentrantBefore();\n        _;\n        _nonReentrantAfter();\n    }\n\n    function _nonReentrantBefore() private {\n        // On the first call to nonReentrant, _status will be _NOT_ENTERED\n        require(_status != _ENTERED, \"ReentrancyGuard: reentrant call\");\n\n        // Any calls to nonReentrant after this point will fail\n        _status = _ENTERED;\n    }\n\n    function _nonReentrantAfter() private {\n        // By storing the original value once again, a refund is triggered (see\n        // https://eips.ethereum.org/EIPS/eip-2200)\n        _status = _NOT_ENTERED;\n    }\n\n    /**\n     * @dev Returns true if the reentrancy guard is currently set to \"entered\", which indicates there is a\n     * `nonReentrant` function in the call stack.\n     */\n    function _reentrancyGuardEntered() internal view returns (bool) {\n        return _status == _ENTERED;\n    }\n}\n"
      },
      "@openzeppelin/contracts/access/Ownable.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)\n\npragma solidity ^0.8.0;\n\nimport \"../utils/Context.sol\";\n\n/**\n * @dev Contract module which provides a basic access control mechanism, where\n * there is an account (an owner) that can be granted exclusive access to\n * specific functions.\n *\n * By default, the owner account will be the one that deploys the contract. This\n * can later be changed with {transferOwnership}.\n *\n * This module is used through inheritance. It will make available the modifier\n * `onlyOwner`, which can be applied to your functions to restrict their use to\n * the owner.\n */\nabstract contract Ownable is Context {\n    address private _owner;\n\n    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);\n\n    /**\n     * @dev Initializes the contract setting the deployer as the initial owner.\n     */\n    constructor() {\n        _transferOwnership(_msgSender());\n    }\n\n    /**\n     * @dev Throws if called by any account other than the owner.\n     */\n    modifier onlyOwner() {\n        _checkOwner();\n        _;\n    }\n\n    /**\n     * @dev Returns the address of the current owner.\n     */\n    function owner() public view virtual returns (address) {\n        return _owner;\n    }\n\n    /**\n     * @dev Throws if the sender is not the owner.\n     */\n    function _checkOwner() internal view virtual {\n        require(owner() == _msgSender(), \"Ownable: caller is not the owner\");\n    }\n\n    /**\n     * @dev Leaves the contract without owner. It will not be possible to call\n     * `onlyOwner` functions. Can only be called by the current owner.\n     *\n     * NOTE: Renouncing ownership will leave the contract without an owner,\n     * thereby disabling any functionality that is only available to the owner.\n     */\n    function renounceOwnership() public virtual onlyOwner {\n        _transferOwnership(address(0));\n    }\n\n    /**\n     * @dev Transfers ownership of the contract to a new account (`newOwner`).\n     * Can only be called by the current owner.\n     */\n    function transferOwnership(address newOwner) public virtual onlyOwner {\n        require(newOwner != address(0), \"Ownable: new owner is the zero address\");\n        _transferOwnership(newOwner);\n    }\n\n    /**\n     * @dev Transfers ownership of the contract to a new account (`newOwner`).\n     * Internal function without access restriction.\n     */\n    function _transferOwnership(address newOwner) internal virtual {\n        address oldOwner = _owner;\n        _owner = newOwner;\n        emit OwnershipTransferred(oldOwner, newOwner);\n    }\n}\n"
      },
      "@openzeppelin/contracts/utils/Strings.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)\n\npragma solidity ^0.8.0;\n\nimport \"./math/Math.sol\";\nimport \"./math/SignedMath.sol\";\n\n/**\n * @dev String operations.\n */\nlibrary Strings {\n    bytes16 private constant _SYMBOLS = \"0123456789abcdef\";\n    uint8 private constant _ADDRESS_LENGTH = 20;\n\n    /**\n     * @dev Converts a `uint256` to its ASCII `string` decimal representation.\n     */\n    function toString(uint256 value) internal pure returns (string memory) {\n        unchecked {\n            uint256 length = Math.log10(value) + 1;\n            string memory buffer = new string(length);\n            uint256 ptr;\n            /// @solidity memory-safe-assembly\n            assembly {\n                ptr := add(buffer, add(32, length))\n            }\n            while (true) {\n                ptr--;\n                /// @solidity memory-safe-assembly\n                assembly {\n                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))\n                }\n                value /= 10;\n                if (value == 0) break;\n            }\n            return buffer;\n        }\n    }\n\n    /**\n     * @dev Converts a `int256` to its ASCII `string` decimal representation.\n     */\n    function toString(int256 value) internal pure returns (string memory) {\n        return string(abi.encodePacked(value < 0 ? \"-\" : \"\", toString(SignedMath.abs(value))));\n    }\n\n    /**\n     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.\n     */\n    function toHexString(uint256 value) internal pure returns (string memory) {\n        unchecked {\n            return toHexString(value, Math.log256(value) + 1);\n        }\n    }\n\n    /**\n     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.\n     */\n    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {\n        bytes memory buffer = new bytes(2 * length + 2);\n        buffer[0] = \"0\";\n        buffer[1] = \"x\";\n        for (uint256 i = 2 * length + 1; i > 1; --i) {\n            buffer[i] = _SYMBOLS[value & 0xf];\n            value >>= 4;\n        }\n        require(value == 0, \"Strings: hex length insufficient\");\n        return string(buffer);\n    }\n\n    /**\n     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.\n     */\n    function toHexString(address addr) internal pure returns (string memory) {\n        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);\n    }\n\n    /**\n     * @dev Returns true if the two strings are equal.\n     */\n    function equal(string memory a, string memory b) internal pure returns (bool) {\n        return keccak256(bytes(a)) == keccak256(bytes(b));\n    }\n}\n"
      },
      "@openzeppelin/contracts/utils/Context.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.4) (utils/Context.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Provides information about the current execution context, including the\n * sender of the transaction and its data. While these are generally available\n * via msg.sender and msg.data, they should not be accessed in such a direct\n * manner, since when dealing with meta-transactions the account sending and\n * paying for execution may not be the actual sender (as far as an application\n * is concerned).\n *\n * This contract is only required for intermediate, library-like contracts.\n */\nabstract contract Context {\n    function _msgSender() internal view virtual returns (address) {\n        return msg.sender;\n    }\n\n    function _msgData() internal view virtual returns (bytes calldata) {\n        return msg.data;\n    }\n\n    function _contextSuffixLength() internal view virtual returns (uint256) {\n        return 0;\n    }\n}\n"
      },
      "@openzeppelin/contracts/utils/math/SignedMath.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev Standard signed math utilities missing in the Solidity language.\n */\nlibrary SignedMath {\n    /**\n     * @dev Returns the largest of two signed numbers.\n     */\n    function max(int256 a, int256 b) internal pure returns (int256) {\n        return a > b ? a : b;\n    }\n\n    /**\n     * @dev Returns the smallest of two signed numbers.\n     */\n    function min(int256 a, int256 b) internal pure returns (int256) {\n        return a < b ? a : b;\n    }\n\n    /**\n     * @dev Returns the average of two signed numbers without overflow.\n     * The result is rounded towards zero.\n     */\n    function average(int256 a, int256 b) internal pure returns (int256) {\n        // Formula from the book \"Hacker's Delight\"\n        int256 x = (a & b) + ((a ^ b) >> 1);\n        return x + (int256(uint256(x) >> 255) & (a ^ b));\n    }\n\n    /**\n     * @dev Returns the absolute unsigned value of a signed value.\n     */\n    function abs(int256 n) internal pure returns (uint256) {\n        unchecked {\n            // must be unchecked in order to support `n = type(int256).min`\n            return uint256(n >= 0 ? n : -n);\n        }\n    }\n}\n"
      },
      "@openzeppelin/contracts/utils/math/Math.sol": {
        "content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.9.0) (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    enum Rounding {\n        Down, // Toward negative infinity\n        Up, // Toward infinity\n        Zero // Toward zero\n    }\n\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 == 0 ? 0 : (a - 1) / b + 1;\n    }\n\n    /**\n     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0\n     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)\n     * with further edits by Uniswap Labs also under MIT license.\n     */\n    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {\n        unchecked {\n            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use\n            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256\n            // variables such that product = prod1 * 2^256 + prod0.\n            uint256 prod0; // Least significant 256 bits of the product\n            uint256 prod1; // Most significant 256 bits of the product\n            assembly {\n                let mm := mulmod(x, y, not(0))\n                prod0 := mul(x, y)\n                prod1 := sub(sub(mm, prod0), lt(mm, prod0))\n            }\n\n            // Handle non-overflow cases, 256 by 256 division.\n            if (prod1 == 0) {\n                // Solidity will revert if denominator == 0, unlike the div opcode on its own.\n                // The surrounding unchecked block does not change this fact.\n                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.\n                return prod0 / denominator;\n            }\n\n            // Make sure the result is less than 2^256. Also prevents denominator == 0.\n            require(denominator > prod1, \"Math: mulDiv overflow\");\n\n            ///////////////////////////////////////////////\n            // 512 by 256 division.\n            ///////////////////////////////////////////////\n\n            // Make division exact by subtracting the remainder from [prod1 prod0].\n            uint256 remainder;\n            assembly {\n                // Compute remainder using mulmod.\n                remainder := mulmod(x, y, denominator)\n\n                // Subtract 256 bit number from 512 bit number.\n                prod1 := sub(prod1, gt(remainder, prod0))\n                prod0 := sub(prod0, remainder)\n            }\n\n            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.\n            // See https://cs.stackexchange.com/q/138556/92363.\n\n            // Does not overflow because the denominator cannot be zero at this stage in the function.\n            uint256 twos = denominator & (~denominator + 1);\n            assembly {\n                // Divide denominator by twos.\n                denominator := div(denominator, twos)\n\n                // Divide [prod1 prod0] by twos.\n                prod0 := div(prod0, twos)\n\n                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.\n                twos := add(div(sub(0, twos), twos), 1)\n            }\n\n            // Shift in bits from prod1 into prod0.\n            prod0 |= prod1 * twos;\n\n            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such\n            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for\n            // four bits. That is, denominator * inv = 1 mod 2^4.\n            uint256 inverse = (3 * denominator) ^ 2;\n\n            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works\n            // in modular arithmetic, doubling the correct bits in each step.\n            inverse *= 2 - denominator * inverse; // inverse mod 2^8\n            inverse *= 2 - denominator * inverse; // inverse mod 2^16\n            inverse *= 2 - denominator * inverse; // inverse mod 2^32\n            inverse *= 2 - denominator * inverse; // inverse mod 2^64\n            inverse *= 2 - denominator * inverse; // inverse mod 2^128\n            inverse *= 2 - denominator * inverse; // inverse mod 2^256\n\n            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.\n            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is\n            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1\n            // is no longer required.\n            result = prod0 * inverse;\n            return result;\n        }\n    }\n\n    /**\n     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.\n     */\n    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {\n        uint256 result = mulDiv(x, y, denominator);\n        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {\n            result += 1;\n        }\n        return result;\n    }\n\n    /**\n     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.\n     *\n     * Inspired by Henry S. Warren, Jr.'s \"Hacker's Delight\" (Chapter 11).\n     */\n    function sqrt(uint256 a) internal pure returns (uint256) {\n        if (a == 0) {\n            return 0;\n        }\n\n        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.\n        //\n        // We know that the \"msb\" (most significant bit) of our target number `a` is a power of 2 such that we have\n        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.\n        //\n        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`\n        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`\n        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`\n        //\n        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.\n        uint256 result = 1 << (log2(a) >> 1);\n\n        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,\n        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at\n        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision\n        // into the expected uint128 result.\n        unchecked {\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            result = (result + a / result) >> 1;\n            return min(result, a / result);\n        }\n    }\n\n    /**\n     * @notice Calculates sqrt(a), following the selected rounding direction.\n     */\n    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {\n        unchecked {\n            uint256 result = sqrt(a);\n            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);\n        }\n    }\n\n    /**\n     * @dev Return the log in base 2, rounded down, of a positive value.\n     * Returns 0 if given 0.\n     */\n    function log2(uint256 value) internal pure returns (uint256) {\n        uint256 result = 0;\n        unchecked {\n            if (value >> 128 > 0) {\n                value >>= 128;\n                result += 128;\n            }\n            if (value >> 64 > 0) {\n                value >>= 64;\n                result += 64;\n            }\n            if (value >> 32 > 0) {\n                value >>= 32;\n                result += 32;\n            }\n            if (value >> 16 > 0) {\n                value >>= 16;\n                result += 16;\n            }\n            if (value >> 8 > 0) {\n                value >>= 8;\n                result += 8;\n            }\n            if (value >> 4 > 0) {\n                value >>= 4;\n                result += 4;\n            }\n            if (value >> 2 > 0) {\n                value >>= 2;\n                result += 2;\n            }\n            if (value >> 1 > 0) {\n                result += 1;\n            }\n        }\n        return result;\n    }\n\n    /**\n     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.\n     * Returns 0 if given 0.\n     */\n    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {\n        unchecked {\n            uint256 result = log2(value);\n            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);\n        }\n    }\n\n    /**\n     * @dev Return the log in base 10, rounded down, of a positive value.\n     * Returns 0 if given 0.\n     */\n    function log10(uint256 value) internal pure returns (uint256) {\n        uint256 result = 0;\n        unchecked {\n            if (value >= 10 ** 64) {\n                value /= 10 ** 64;\n                result += 64;\n            }\n            if (value >= 10 ** 32) {\n                value /= 10 ** 32;\n                result += 32;\n            }\n            if (value >= 10 ** 16) {\n                value /= 10 ** 16;\n                result += 16;\n            }\n            if (value >= 10 ** 8) {\n                value /= 10 ** 8;\n                result += 8;\n            }\n            if (value >= 10 ** 4) {\n                value /= 10 ** 4;\n                result += 4;\n            }\n            if (value >= 10 ** 2) {\n                value /= 10 ** 2;\n                result += 2;\n            }\n            if (value >= 10 ** 1) {\n                result += 1;\n            }\n        }\n        return result;\n    }\n\n    /**\n     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.\n     * Returns 0 if given 0.\n     */\n    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {\n        unchecked {\n            uint256 result = log10(value);\n            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);\n        }\n    }\n\n    /**\n     * @dev Return the log in base 256, rounded down, of a positive value.\n     * Returns 0 if given 0.\n     *\n     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.\n     */\n    function log256(uint256 value) internal pure returns (uint256) {\n        uint256 result = 0;\n        unchecked {\n            if (value >> 128 > 0) {\n                value >>= 128;\n                result += 16;\n            }\n            if (value >> 64 > 0) {\n                value >>= 64;\n                result += 8;\n            }\n            if (value >> 32 > 0) {\n                value >>= 32;\n                result += 4;\n            }\n            if (value >> 16 > 0) {\n                value >>= 16;\n                result += 2;\n            }\n            if (value >> 8 > 0) {\n                result += 1;\n            }\n        }\n        return result;\n    }\n\n    /**\n     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.\n     * Returns 0 if given 0.\n     */\n    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {\n        unchecked {\n            uint256 result = log256(value);\n            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);\n        }\n    }\n}\n"
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