// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 message) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32")
            mstore(0x1c, hash)
            message := keccak256(0x00, 0x3c)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 data) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, "\x19\x01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            data := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Data with intended validator, created from a
     * `validator` and `data` according to the version 0 of EIP-191.
     *
     * See {recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x00", validator, data));
    }
}

// File: @openzeppelin/contracts/utils/math/Math.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

// File: @openzeppelin/contracts/utils/math/SignedMath.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

// File: @openzeppelin/contracts/utils/Strings.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// File: @unlock-protocol/contracts/dist/PublicLock/IPublicLockV12.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.5.17 <0.9.0;
pragma experimental ABIEncoderV2;

/**
* @title The PublicLock Interface
*/


interface IPublicLockV12
{

  /// Functions
  function initialize(
    address _lockCreator,
    uint _expirationDuration,
    address _tokenAddress,
    uint _keyPrice,
    uint _maxNumberOfKeys,
    string calldata _lockName
  ) external;


  // roles
  function DEFAULT_ADMIN_ROLE() external view returns (bytes32 role);
  function KEY_GRANTER_ROLE() external view returns (bytes32 role);
  function LOCK_MANAGER_ROLE() external view returns (bytes32 role);

  /**
  * @notice The version number of the current implementation on this network.
  * @return The current version number.
  */
  function publicLockVersion() external pure returns (uint16);

  /**
   * @dev Called by lock manager to withdraw all funds from the lock
   * @param _tokenAddress specifies the token address to withdraw or 0 for ETH. This is usually
   * the same as `tokenAddress` in MixinFunds.
   * @param _recipient specifies the address that will receive the tokens
   * @param _amount specifies the max amount to withdraw, which may be reduced when
   * considering the available balance. Set to 0 or MAX_UINT to withdraw everything. 
   * -- however be wary of draining funds as it breaks the `cancelAndRefund` and `expireAndRefundFor` use cases.
   */
  function withdraw(
    address _tokenAddress,
    address payable _recipient,
    uint _amount
  ) external;

  /**
   * A function which lets a Lock manager of the lock to change the price for future purchases.
   * @dev Throws if called by other than a Lock manager
   * @dev Throws if lock has been disabled
   * @dev Throws if _tokenAddress is not a valid token
   * @param _keyPrice The new price to set for keys
   * @param _tokenAddress The address of the erc20 token to use for pricing the keys,
   * or 0 to use ETH
   */
  function updateKeyPricing( uint _keyPrice, address _tokenAddress ) external;

  /**
   * Update the main key properties for the entire lock: 
   * 
   * - default duration of each key
   * - the maximum number of keys the lock can edit
   * - the maximum number of keys a single address can hold
   *
   * @notice keys previously bought are unaffected by this changes in expiration duration (i.e.
   * existing keys timestamps are not recalculated/updated)
   * @param _newExpirationDuration the new amount of time for each key purchased or type(uint).max for a non-expiring key
   * @param _maxKeysPerAcccount the maximum amount of key a single user can own
   * @param _maxNumberOfKeys uint the maximum number of keys
   * @dev _maxNumberOfKeys Can't be smaller than the existing supply 
   */
   function updateLockConfig(
    uint _newExpirationDuration,
    uint _maxNumberOfKeys,
    uint _maxKeysPerAcccount
  ) external;

  /**
   * Checks if the user has a non-expired key.
   * @param _user The address of the key owner
   */
  function getHasValidKey(
    address _user
  ) external view returns (bool);

  /**
  * @dev Returns the key's ExpirationTimestamp field for a given owner.
  * @param _tokenId the id of the key
  * @dev Returns 0 if the owner has never owned a key for this lock
  */
  function keyExpirationTimestampFor(
    uint _tokenId
  ) external view returns (uint timestamp);
  
  /**
   * Public function which returns the total number of unique owners (both expired
   * and valid).  This may be larger than totalSupply.
   */
  function numberOfOwners() external view returns (uint);

  /**
   * Allows the Lock owner to assign 
   * @param _lockName a descriptive name for this Lock.
   * @param _lockSymbol a Symbol for this Lock (default to KEY).
   * @param _baseTokenURI the baseTokenURI for this Lock
   */
  function setLockMetadata(
    string calldata _lockName,
    string calldata _lockSymbol,
    string calldata _baseTokenURI
  ) external;

  /**
   * @dev Gets the token symbol
   * @return string representing the token symbol
   */
  function symbol() external view returns(string memory);


  /**  @notice A distinct Uniform Resource Identifier (URI) for a given asset.
   * @dev Throws if `_tokenId` is not a valid NFT. URIs are defined in RFC
   *  3986. The URI may point to a JSON file that conforms to the "ERC721
   *  Metadata JSON Schema".
   * https://github.com/ethereum/EIPs/blob/master/EIPS/eip-721.md
   * @param _tokenId The tokenID we're inquiring about
   * @return String representing the URI for the requested token
   */
  function tokenURI(
    uint256 _tokenId
  ) external view returns(string memory);

  /**
   * Allows a Lock manager to add or remove an event hook
   * @param _onKeyPurchaseHook Hook called when the `purchase` function is called
   * @param _onKeyCancelHook Hook called when the internal `_cancelAndRefund` function is called
   * @param _onValidKeyHook Hook called to determine if the contract should overide the status for a given address
   * @param _onTokenURIHook Hook called to generate a data URI used for NFT metadata
   * @param _onKeyTransferHook Hook called when a key is transfered
   * @param _onKeyExtendHook Hook called when a key is extended or renewed
   * @param _onKeyGrantHook Hook called when a key is granted
   */
  function setEventHooks(
    address _onKeyPurchaseHook,
    address _onKeyCancelHook,
    address _onValidKeyHook,
    address _onTokenURIHook,
    address _onKeyTransferHook,
    address _onKeyExtendHook,
    address _onKeyGrantHook
  ) external;

  /**
   * Allows a Lock manager to give a collection of users a key with no charge.
   * Each key may be assigned a different expiration date.
   * @dev Throws if called by other than a Lock manager
   * @param _recipients An array of receiving addresses
   * @param _expirationTimestamps An array of expiration Timestamps for the keys being granted
   * @return the ids of the granted tokens
   */
  function grantKeys(
    address[] calldata _recipients,
    uint[] calldata _expirationTimestamps,
    address[] calldata _keyManagers
  ) external returns (uint256[] memory);

  /**
   * Allows the Lock owner to extend an existing keys with no charge.
   * @param _tokenId The id of the token to extend
   * @param _duration The duration in secondes to add ot the key
   * @dev set `_duration` to 0 to use the default duration of the lock
   */
  function grantKeyExtension(uint _tokenId, uint _duration) external;

  /**
  * @dev Purchase function
  * @param _values array of tokens amount to pay for this purchase >= the current keyPrice - any applicable discount
  * (_values is ignored when using ETH)
  * @param _recipients array of addresses of the recipients of the purchased key
  * @param _referrers array of addresses of the users making the referral
  * @param _keyManagers optional array of addresses to grant managing rights to a specific address on creation
  * @param _data array of arbitrary data populated by the front-end which initiated the sale
  * @notice when called for an existing and non-expired key, the `_keyManager` param will be ignored 
  * @dev Setting _value to keyPrice exactly doubles as a security feature. That way if the lock owner increases the
  * price while my transaction is pending I can't be charged more than I expected (only applicable to ERC-20 when more
  * than keyPrice is approved for spending).
  * @return tokenIds the ids of the created tokens 
  */
  function purchase(
    uint256[] calldata _values,
    address[] calldata _recipients,
    address[] calldata _referrers,
    address[] calldata _keyManagers,
    bytes[] calldata _data
  ) external payable returns (uint256[] memory tokenIds);
  
  /**
  * @dev Extend function
  * @param _value the number of tokens to pay for this purchase >= the current keyPrice - any applicable discount
  * (_value is ignored when using ETH)
  * @param _tokenId the id of the key to extend
  * @param _referrer address of the user making the referral
  * @param _data arbitrary data populated by the front-end which initiated the sale
  * @dev Throws if lock is disabled or key does not exist for _recipient. Throws if _recipient == address(0).
  */
  function extend(
    uint _value,
    uint _tokenId,
    address _referrer,
    bytes calldata _data
  ) external payable;


  /**
  * Returns the percentage of the keyPrice to be sent to the referrer (in basis points)
  * @param _referrer the address of the referrer
  * @return referrerFee the percentage of the keyPrice to be sent to the referrer (in basis points)
  */
  function referrerFees(address _referrer) external view returns (uint referrerFee);
  
  /**
  * Set a specific percentage of the keyPrice to be sent to the referrer while purchasing, 
  * extending or renewing a key. 
  * @param _referrer the address of the referrer
  * @param _feeBasisPoint the percentage of the price to be used for this 
  * specific referrer (in basis points)
  * @dev To send a fixed percentage of the key price to all referrers, sett a percentage to `address(0)`
  */
  function setReferrerFee(address _referrer, uint _feeBasisPoint) external;

  /**
   * Merge existing keys
   * @param _tokenIdFrom the id of the token to substract time from
   * @param _tokenIdTo the id of the destination token  to add time
   * @param _amount the amount of time to transfer (in seconds)
   */
  function mergeKeys(uint _tokenIdFrom, uint _tokenIdTo, uint _amount) external;

  /**
   * Deactivate an existing key
   * @param _tokenId the id of token to burn
   * @notice the key will be expired and ownership records will be destroyed
   */
  function burn(uint _tokenId) external;

  /**
  * @param _gasRefundValue price in wei or token in smallest price unit
  * @dev Set the value to be refunded to the sender on purchase
  */
  function setGasRefundValue(uint256 _gasRefundValue) external;
  
  /**
  * _gasRefundValue price in wei or token in smallest price unit
  * @dev Returns the value/rpice to be refunded to the sender on purchase
  */
  function gasRefundValue() external view returns (uint256 _gasRefundValue);

  /**
   * @notice returns the minimum price paid for a purchase with these params.
   * @dev this considers any discount from Unlock or the OnKeyPurchase hook.
   */
  function purchasePriceFor(
    address _recipient,
    address _referrer,
    bytes calldata _data
  ) external view
    returns (uint);

  /**
   * Allow a Lock manager to change the transfer fee.
   * @dev Throws if called by other than a Lock manager
   * @param _transferFeeBasisPoints The new transfer fee in basis-points(bps).
   * Ex: 200 bps = 2%
   */
  function updateTransferFee(
    uint _transferFeeBasisPoints
  ) external;

  /**
   * Determines how much of a fee would need to be paid in order to
   * transfer to another account.  This is pro-rated so the fee goes 
   * down overtime.
   * @dev Throws if _tokenId does not have a valid key
   * @param _tokenId The id of the key check the transfer fee for.
   * @param _time The amount of time to calculate the fee for.
   * @return The transfer fee in seconds.
   */
  function getTransferFee(
    uint _tokenId,
    uint _time
  ) external view returns (uint);

  /**
   * @dev Invoked by a Lock manager to expire the user's key 
   * and perform a refund and cancellation of the key
   * @param _tokenId The key id we wish to refund to
   * @param _amount The amount to refund to the key-owner
   * @dev Throws if called by other than a Lock manager
   * @dev Throws if _keyOwner does not have a valid key
   */
  function expireAndRefundFor(
    uint _tokenId,
    uint _amount
  ) external;

   /**
   * @dev allows the key manager to expire a given tokenId
   * and send a refund to the keyOwner based on the amount of time remaining.
   * @param _tokenId The id of the key to cancel.
   */
  function cancelAndRefund(uint _tokenId) external;

  /**
   * Allow a Lock manager to change the refund penalty.
   * @dev Throws if called by other than a Lock manager
   * @param _freeTrialLength The new duration of free trials for this lock
   * @param _refundPenaltyBasisPoints The new refund penaly in basis-points(bps)
   */
  function updateRefundPenalty(
    uint _freeTrialLength,
    uint _refundPenaltyBasisPoints
  ) external;

  /**
   * @dev Determines how much of a refund a key owner would receive if they issued
   * @param _tokenId the id of the token to get the refund value for.
   * @notice Due to the time required to mine a tx, the actual refund amount will be lower
   * than what the user reads from this call.
   * @return refund the amount of tokens refunded
   */
  function getCancelAndRefundValue(
    uint _tokenId
  ) external view returns (uint refund);

  function addKeyGranter(address account) external;

  function addLockManager(address account) external;

  function isKeyGranter(address account) external view returns (bool);

  function isLockManager(address account) external view returns (bool);

  
 /**
   * Returns the address of the `onKeyPurchaseHook` hook.
   * @return hookAddress address of the hook
   */  
  function onKeyPurchaseHook() external view returns(address hookAddress);

  /**
   * Returns the address of the `onKeyCancelHook` hook.
   * @return hookAddress address of the hook
   */  
  function onKeyCancelHook() external view returns(address hookAddress);

  /**
   * Returns the address of the `onValidKeyHook` hook.
   * @return hookAddress address of the hook
   */  
  function onValidKeyHook() external view returns(address hookAddress);

  /**
   * Returns the address of the `onTokenURIHook` hook.
   * @return hookAddress address of the hook
   */
  function onTokenURIHook() external view returns(address hookAddress);
  
  /**
   * Returns the address of the `onKeyTransferHook` hook.
   * @return hookAddress address of the hook
   */
  function onKeyTransferHook() external view returns(address hookAddress);
  
  /**
   * Returns the address of the `onKeyExtendHook` hook.
  * @return hookAddress the address ok the hook
  */
  function onKeyExtendHook() external view returns(address hookAddress);

  /**
  * Returns the address of the `onKeyGrantHook` hook.
  * @return hookAddress the address ok the hook
  */
  function onKeyGrantHook() external view returns(address hookAddress);

  function revokeKeyGranter(address _granter) external;

  function renounceLockManager() external;

  /**
   * @return the maximum number of key allowed for a single address
   */
  function maxKeysPerAddress() external view returns (uint);

  function expirationDuration() external view returns (uint256 );

  function freeTrialLength() external view returns (uint256 );

  function keyPrice() external view returns (uint256 );

  function maxNumberOfKeys() external view returns (uint256 );

  function refundPenaltyBasisPoints() external view returns (uint256 );

  function tokenAddress() external view returns (address );

  function transferFeeBasisPoints() external view returns (uint256 );

  function unlockProtocol() external view returns (address );

  function keyManagerOf(uint) external view returns (address );

  ///===================================================================

  /**
  * @notice Allows the key owner to safely share their key (parent key) by
  * transferring a portion of the remaining time to a new key (child key).
  * @dev Throws if key is not valid.
  * @dev Throws if `_to` is the zero address
  * @param _to The recipient of the shared key
  * @param _tokenId the key to share
  * @param _timeShared The amount of time shared
  * checks if `_to` is a smart contract (code size > 0). If so, it calls
  * `onERC721Received` on `_to` and throws if the return value is not
  * `bytes4(keccak256('onERC721Received(address,address,uint,bytes)'))`.
  * @dev Emit Transfer event
  */
  function shareKey(
    address _to,
    uint _tokenId,
    uint _timeShared
  ) external;

  /**
  * @notice Update transfer and cancel rights for a given key
  * @param _tokenId The id of the key to assign rights for
  * @param _keyManager The address to assign the rights to for the given key
  */
  function setKeyManagerOf(
    uint _tokenId,
    address _keyManager
  ) external;
  
  /**
  * Check if a certain key is valid
  * @param _tokenId the id of the key to check validity
  * @notice this makes use of the onValidKeyHook if it is set
  */
  function isValidKey(
    uint _tokenId
  )
    external
    view
    returns (bool);
  
  /**
   * Returns the number of keys owned by `_keyOwner` (expired or not)
   * @param _keyOwner address for which we are retrieving the total number of keys
   * @return numberOfKeys total number of keys owned by the address
   */
  function totalKeys(address _keyOwner) external view returns (uint numberOfKeys);
  
  /// @notice A descriptive name for a collection of NFTs in this contract
  function name() external view returns (string memory _name);
  ///===================================================================

  /// From ERC165.sol
  function supportsInterface(bytes4 interfaceId) external view returns (bool);
  ///===================================================================

  /// From ERC-721
  /**
   * In the specific case of a Lock, `balanceOf` returns only the tokens with a valid expiration timerange
   * @return balance The number of valid keys owned by `_keyOwner`
  */
  function balanceOf(address _owner) external view returns (uint256 balance);

  /**
    * @dev Returns the owner of the NFT specified by `tokenId`.
    */
  function ownerOf(uint256 tokenId) external view returns (address _owner);

  /**
    * @dev Transfers a specific NFT (`tokenId`) from one account (`from`) to
    * another (`to`).
    *
    * Requirements:
    * - `from`, `to` cannot be zero.
    * - `tokenId` must be owned by `from`.
    * - If the caller is not `from`, it must be have been allowed to move this
    * NFT by either {approve} or {setApprovalForAll}.
    */
  function safeTransferFrom(address from, address to, uint256 tokenId) external;
  
  /** 
  * an ERC721-like function to transfer a token from one account to another. 
  * @param from the owner of token to transfer
  * @param to the address that will receive the token
  * @param tokenId the id of the token
  * @dev Requirements: if the caller is not `from`, it must be approved to move this token by
  * either {approve} or {setApprovalForAll}. 
  * The key manager will be reset to address zero after the transfer
  */
  function transferFrom(address from, address to, uint256 tokenId) external;

  /** 
  * Lending a key allows you to transfer the token while retaining the
  * ownerships right by setting yourself as a key manager first. 
  * @param from the owner of token to transfer
  * @param to the address that will receive the token
  * @param tokenId the id of the token
  * @notice This function can only be called by 1) the key owner when no key manager is set or 2) the key manager.
  * After calling the function, the `_recipent` will be the new owner, and the sender of the tx
  * will become the key manager.
  */
  function lendKey(address from, address to, uint tokenId) external;

  /** 
  * Unlend is called when you have lent a key and want to claim its full ownership back. 
  * @param _recipient the address that will receive the token ownership
  * @param _tokenId the id of the token
  * @dev Only the key manager of the token can call this function
  */
  function unlendKey(address _recipient, uint _tokenId) external;

  function approve(address to, uint256 tokenId) external;

  /**
  * @notice Get the approved address for a single NFT
  * @dev Throws if `_tokenId` is not a valid NFT.
  * @param _tokenId The NFT to find the approved address for
  * @return operator The approved address for this NFT, or the zero address if there is none
  */
  function getApproved(uint256 _tokenId) external view returns (address operator);

   /**
   * @dev Sets or unsets the approval of a given operator
   * An operator is allowed to transfer all tokens of the sender on their behalf
   * @param _operator operator address to set the approval
   * @param _approved representing the status of the approval to be set
   * @notice disabled when transfers are disabled
   */
  function setApprovalForAll(address _operator, bool _approved) external;

   /**
   * @dev Tells whether an operator is approved by a given keyManager
   * @param _owner owner address which you want to query the approval of
   * @param _operator operator address which you want to query the approval of
   * @return bool whether the given operator is approved by the given owner
   */
  function isApprovedForAll(address _owner, address _operator) external view returns (bool);

  function safeTransferFrom(address from, address to, uint256 tokenId, bytes calldata data) external;

  function totalSupply() external view returns (uint256);
  function tokenOfOwnerByIndex(address _owner, uint256 index) external view returns (uint256 tokenId);

  function tokenByIndex(uint256 index) external view returns (uint256);

  /**
    * Innherited from Open Zeppelin AccessControl.sol
    */
  function getRoleAdmin(bytes32 role) external view returns (bytes32);
  function grantRole(bytes32 role, address account) external;
  function revokeRole(bytes32 role, address account) external;
  function renounceRole(bytes32 role, address account) external;
  function hasRole(bytes32 role, address account) external view returns (bool);

  /**
    * @param _tokenId the id of the token to transfer time from
    * @param _to the recipient of the new token with time
    * @param _value sends a token with _value * expirationDuration (the amount of time remaining on a standard purchase).
    * @dev The typical use case would be to call this with _value 1, which is on par with calling `transferFrom`. If the user
    * has more than `expirationDuration` time remaining this may use the `shareKey` function to send some but not all of the token.
    * @return success the result of the transfer operation
    */
  function transfer(
    uint _tokenId,
    address _to,
    uint _value
  ) external
    returns (bool success);

  /** `owner()` is provided as an helper to mimick the `Ownable` contract ABI.
    * The `Ownable` logic is used by many 3rd party services to determine
    * contract ownership - e.g. who is allowed to edit metadata on Opensea.
    * 
    * @notice This logic is NOT used internally by the Unlock Protocol and is made 
    * available only as a convenience helper.
    */
  function owner() external view returns (address owner);
  function setOwner(address account) external;
  function isOwner(address account) view external returns (bool isOwner);

  /**
  * Migrate data from the previous single owner => key mapping to 
  * the new data structure w multiple tokens.
  * @param _calldata an ABI-encoded representation of the params (v10: the number of records to migrate as `uint`)
  * @dev when all record schemas are sucessfully upgraded, this function will update the `schemaVersion`
  * variable to the latest/current lock version
  */
  function migrate(bytes calldata _calldata) external;

  /**
  * Returns the version number of the data schema currently used by the lock
  * @notice if this is different from `publicLockVersion`, then the ability to purchase, grant
  * or extend keys is disabled.
  * @dev will return 0 if no ;igration has ever been run
  */
  function schemaVersion() external view returns (uint);

  /**
   * Set the schema version to the latest
   * @notice only lock manager call call this
   */
  function updateSchemaVersion() external;

    /**
  * Renew a given token
  * @notice only works for non-free, expiring, ERC20 locks
  * @param _tokenId the ID fo the token to renew
  * @param _referrer the address of the person to be granted UDT
  */
  function renewMembershipFor(
    uint _tokenId,
    address _referrer
  ) external;
}

// File: contracts/PurchaseHook.sol



//SPDX-License-Identifier: Unlicense
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "@unlock-protocol/contracts/dist/PublicLock/IPublicLockV12.sol";
import "@openzeppelin/contracts/access/Ownable.sol";

contract PurchaseHook is Ownable {
    mapping(address => bool) public signers;

    constructor() {}

    function addSigner(address signer) public onlyOwner {
        signers[signer] = true;
    }

    function removeSigner(address signer) public onlyOwner {
        signers[signer] = false;
    }

    /**
     * Price is the same for everyone... but we fail if signature by Unlock Lab's backend service (sent as signature) does not match!
     */
    function keyPurchasePrice(
        address /* from */,
        address recipient,
        address /* referrer */,
        bytes calldata signature /* data */
    ) external view returns (uint256 minKeyPrice) {
        string memory message = toString(recipient);
        require(checkIsSigner(message, signature), "WRONG_SIGNATURE");
        if (address(msg.sender).code.length > 0) {
            return IPublicLockV12(msg.sender).keyPrice();
        }
        return 0;
    }

    /**
     * Debug function
     */
    function checkIsSigner(
        string memory message,
        bytes calldata signature /* data */
    ) public view returns (bool isSigner) {
        bytes memory encoded = abi.encodePacked(message);
        bytes32 messageHash = keccak256(encoded);
        bytes32 hash = ECDSA.toEthSignedMessageHash(messageHash);
        address recoveredAddress = ECDSA.recover(hash, signature);
        return signers[recoveredAddress];
    }

    /**
     * Helper functions to turn addrerss into string so we can verify the signature (address is signed as string on the client)
     */
    function toString(address account) public pure returns (string memory) {
        return toString(abi.encodePacked(account));
    }

    function toString(uint256 value) public pure returns (string memory) {
        return toString(abi.encodePacked(value));
    }

    function toString(bytes32 value) public pure returns (string memory) {
        return toString(abi.encodePacked(value));
    }

    function toString(bytes memory data) public pure returns (string memory) {
        bytes memory alphabet = "0123456789abcdef";

        bytes memory str = new bytes(2 + data.length * 2);
        str[0] = "0";
        str[1] = "x";
        for (uint256 i = 0; i < data.length; i++) {
            str[2 + i * 2] = alphabet[uint256(uint8(data[i] >> 4))];
            str[3 + i * 2] = alphabet[uint256(uint8(data[i] & 0x0f))];
        }
        return string(str);
    }

    /**
     * No-op but required
     */
    function onKeyPurchase(
        uint256 /* tokenId */,
        address /*from*/,
        address /*recipient*/,
        address /*referrer*/,
        bytes calldata /*data*/,
        uint256 /*minKeyPrice*/,
        uint256 /*pricePaid*/
    ) external {}
}