// File: @openzeppelin/contracts/security/ReentrancyGuard.sol



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

pragma solidity ^0.8.0;

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == _ENTERED;
    }
}

// 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: contracts/deca-posters/PosterMinter.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.17;

import {ECDSA} from "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/security/ReentrancyGuard.sol";

import {IPosters} from "../interfaces/internal/IPosters.sol";
import {IPosterInfo} from "../interfaces/internal/IPosterInfo.sol";
import {IPosterMinter} from "../interfaces/internal/IPosterMinter.sol";
import {IRoleAuthority} from "../interfaces/internal/IRoleAuthority.sol";

/**
 * @title PosterMinter contract.
 * @notice The contract that mints Deca Posters.
 * @author j6i, 0x-jj
 */
contract PosterMinter is IPosterMinter, ReentrancyGuard {
  /*//////////////////////////////////////////////////////////////
                              STORAGE
    //////////////////////////////////////////////////////////////*/

  /**
   * @notice The address of the RoleAuthority used to determine whether an address has some admin role.
   */
  IRoleAuthority public immutable roleAuthority;

  /**
   * @notice The address of the Posters contract.
   */
  IPosters public immutable posters;

  /**
   * @notice The address of the PosterInfo contract.
   */
  IPosterInfo public immutable posterInfo;

  /*//////////////////////////////////////////////////////////////
                              CONSTRUCTOR
    //////////////////////////////////////////////////////////////*/

  constructor(address _roleAuthority, address _posters, address _posterInfo) {
    if (_roleAuthority == address(0) || _posters == address(0) || _posterInfo == address(0)) revert ZeroAddress();

    roleAuthority = IRoleAuthority(_roleAuthority);
    posters = IPosters(_posters);
    posterInfo = IPosterInfo(_posterInfo);
  }

  /*//////////////////////////////////////////////////////////////
                                 EXTERNAL
    //////////////////////////////////////////////////////////////*/

  /**
   * @notice The mint function that sets up the custom mint period. Setting the mint period is idempotent.
   * @param mintPosterInfo The information required to mint a poster.
   * @param mintEndsAt When the mint ends.
   * @param signature The signature of the mint info.
   * @param signer The signer of the mint info.
   */
  function mintFirst(
    MintPosterInfo calldata mintPosterInfo,
    uint256 mintEndsAt,
    bytes calldata signature,
    address signer
  ) external payable nonReentrant {
    // Check arguments and signature validity then store poster info
    {
      bytes32 computedHash = _hashWithMintPeriod(mintPosterInfo, mintEndsAt);
      // Ensure the arguments are valid
      _verifyArguments(
        computedHash,
        mintPosterInfo.expiry,
        mintPosterInfo.amount,
        mintPosterInfo.totalCost,
        mintPosterInfo.feeRecipients.length,
        mintPosterInfo.shares.length,
        signer
      );
      // Ensure the signature is valid
      if (!_verifySignature(computedHash, signature, signer)) revert ProofInvalid();
      // Store poster info in posterInfo
      posterInfo.setPosterInfoWithMintPeriod(
        computedHash,
        mintPosterInfo.tokenId,
        mintPosterInfo.ownerMint,
        mintEndsAt
      );
      // Ensure the poster mint period has not elapsed
      if (!posterInfo.isMintActive(mintPosterInfo.tokenId)) revert PosterMintingClosed();
    }

    // Perform mint and fee split
    {
      // Send ETH to recipients
      _splitFee(
        mintPosterInfo.totalCost,
        mintPosterInfo.shares,
        mintPosterInfo.feeRecipients,
        mintPosterInfo.ownerMint
      );
      // Mint poster to buyer
      posters.mint(mintPosterInfo.buyer, mintPosterInfo.tokenId, mintPosterInfo.amount);
    }
  }

  /**
   * @notice The mint function for posters.
   * @param mintPosterInfo The information required to mint a poster.
   * @param signature The signature of the mint info.
   * @param signer The signer of the mint info.
   */
  function mint(
    MintPosterInfo calldata mintPosterInfo,
    bytes calldata signature,
    address signer
  ) external payable nonReentrant {
    // Check arguments and signature validity then store poster info
    {
      bytes32 computedHash = _hash(mintPosterInfo);
      // Ensure the arguments are valid
      _verifyArguments(
        computedHash,
        mintPosterInfo.expiry,
        mintPosterInfo.amount,
        mintPosterInfo.totalCost,
        mintPosterInfo.feeRecipients.length,
        mintPosterInfo.shares.length,
        signer
      );
      // Ensure the signature is valid
      if (!_verifySignature(computedHash, signature, signer)) revert ProofInvalid();

      // Store poster info in posterInfo
      posterInfo.setPosterInfo(computedHash, mintPosterInfo.tokenId, mintPosterInfo.ownerMint);

      // Ensure the poster mint period has not elapsed
      if (!posterInfo.isMintActive(mintPosterInfo.tokenId)) revert PosterMintingClosed();
    }

    // Perform mint and fee split
    {
      // Send ETH to recipients
      _splitFee(
        mintPosterInfo.totalCost,
        mintPosterInfo.shares,
        mintPosterInfo.feeRecipients,
        mintPosterInfo.ownerMint
      );
      // Mint poster to buyer
      posters.mint(mintPosterInfo.buyer, mintPosterInfo.tokenId, mintPosterInfo.amount);
    }
  }

  /*//////////////////////////////////////////////////////////////
                                 INTERNAL
    //////////////////////////////////////////////////////////////*/

  /**
   * @notice Used to split the fee between the fee recipients.
   * @param totalCost The total cost of the mint.
   * @param shares The shares for each fee recipient.
   * @param feeRecipients The addresses of the fee recipients.
   * @param ownerMint Whether the owner is minting.
   */
  function _splitFee(
    uint256 totalCost,
    uint256[] calldata shares,
    address[] calldata feeRecipients,
    bool ownerMint
  ) internal {
    // Send ETH to recipients
    if (!ownerMint) {
      uint256 total = 0;
      uint256 i = 0;
      while (i < feeRecipients.length) {
        total += shares[i];
        (bool suceeded, ) = feeRecipients[i].call{value: shares[i]}("");
        if (!suceeded) revert TransferFailed();
        unchecked {
          i++;
        }
      }
      // Ensure total shares is equal to totalCost
      if (total != totalCost) revert CostMismatch();
    }
    // Return excess ETH
    uint256 excess = msg.value - totalCost;
    if (excess > 0) {
      (bool successfullyReturned, ) = msg.sender.call{value: excess}("");
      if (!successfullyReturned) revert TransferFailed();
    }
  }

  /**
   * @notice Used to verify the arguments passed to the mint functions.
   * @param computedHash The computed hash of the mint info.
   * @param expiry The expiry of the mint info signature.
   * @param amount The amount of posters to mint.
   * @param totalCost The total cost of the mint.
   * @param feeRecipientsLength The length of the fee recipients array.
   * @param sharesLength The length of the shares array.
   * @param signer The signer of the mint info.
   */
  function _verifyArguments(
    bytes32 computedHash,
    uint256 expiry,
    uint256 amount,
    uint256 totalCost,
    uint256 feeRecipientsLength,
    uint256 sharesLength,
    address signer
  ) internal view {
    // Ensure signature is not expired
    if (expiry < block.timestamp) {
      revert SignatureExpired();
    }
    // Ensure the amount is greater than 0
    if (amount == 0) {
      revert CannotMintZeroAmount();
    }
    // Ensure enough ETH is received
    if (totalCost > msg.value) {
      revert NotEnoughEth();
    }
    // Ensure the signer has the correct role
    if (!roleAuthority.isPosterSigner(signer)) {
      revert NotSigner();
    }
    // Confirm shares and fee recipients are valid
    if (feeRecipientsLength != sharesLength || feeRecipientsLength == 0) {
      revert MissingShares();
    }
    // Ensure signature has not already been used
    if (posterInfo.isPosterHashUsed(computedHash)) revert HashRepeated();
  }

  /**
   * @notice Used to compute the digest, and verify the signature.
   * @param messageHash The hash of the message.
   * @param signature The signature of the message.
   * @param signer The signer of the message.
   */
  function _verifySignature(
    bytes32 messageHash,
    bytes calldata signature,
    address signer
  ) internal pure returns (bool) {
    return signer == ECDSA.recover(ECDSA.toEthSignedMessageHash(messageHash), signature);
  }

  /**
   * @notice Used to compute the hash of the mint info for the first time.
   * @param mintPosterInfo The information required to mint a poster.
   * @param mintEndsAt The custom mint period of the poster.
   */
  function _hashWithMintPeriod(
    MintPosterInfo calldata mintPosterInfo,
    uint256 mintEndsAt
  ) internal pure returns (bytes32) {
    return
      keccak256(
        abi.encodePacked(
          mintPosterInfo.tokenId,
          mintEndsAt,
          mintPosterInfo.amount,
          mintPosterInfo.ownerMint,
          mintPosterInfo.totalCost,
          mintPosterInfo.shares,
          mintPosterInfo.feeRecipients,
          mintPosterInfo.buyer,
          mintPosterInfo.nonce,
          mintPosterInfo.expiry
        )
      );
  }

  /**
   * @notice Used to compute the hash of the mint info.
   * @param mintPosterInfo The information required to mint a poster.
   */
  function _hash(MintPosterInfo calldata mintPosterInfo) internal pure returns (bytes32) {
    return
      keccak256(
        abi.encodePacked(
          mintPosterInfo.tokenId,
          mintPosterInfo.amount,
          mintPosterInfo.ownerMint,
          mintPosterInfo.totalCost,
          mintPosterInfo.shares,
          mintPosterInfo.feeRecipients,
          mintPosterInfo.buyer,
          mintPosterInfo.nonce,
          mintPosterInfo.expiry
        )
      );
  }
}

// File: contracts/interfaces/internal/IPosterInfo.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.17;

interface IPosterInfo {
  error NotPosterMinter();
  error OwnerAlreadyMinted();

  /**
   * @notice Emitted when the poster info is set for the first time.
   */
  event FirstPosterMinted(uint256 indexed tokenId, uint256 expiry);

  function setPosterInfoWithMintPeriod(
    bytes32 _mintHash,
    uint256 _tokenId,
    bool _ownerMint,
    uint256 mintEndsAt
  ) external;

  function setPosterInfo(bytes32 _mintHash, uint256 _tokenId, bool _ownerMint) external;

  function isPosterHashUsed(bytes32 mintHash) external view returns (bool);

  function posterExpiryTimestamp(uint256 tokenId) external view returns (uint256);

  function isMintActive(uint256 tokenId) external view returns (bool);

  function ownerMinted(uint256 tokenId) external view returns (bool);
}

// File: contracts/interfaces/internal/IPosterMinter.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.17;

interface IPosterMinter {
  error NotSigner();
  error NotEnoughEth();
  error CostMismatch();
  error PosterMintingClosed();
  error HashRepeated();
  error TransferFailed();
  error MissingShares();
  error CannotMintZeroAmount();
  error ZeroAddress();
  error ProofInvalid();
  error SignatureExpired();

  /**
   * @notice The information required to mint a poster.
   * @param tokenId The id of the token to mint.
   * @param amount The amount of the tokens to mint.
   * @param ownerMint Whether the owner is minting.
   * @param totalCost The total cost of the poster/posters being minted.
   * @param shares The shares for each fee recipient.
   * @param feeRecipients The addresses of the fee recipients.
   * @param buyer The address of the buyer.
   * @param nonce The nonce of the poster info.
   * @param expiry The expiry date of the poster info.
   */
  struct MintPosterInfo {
    uint256 tokenId;
    uint256 amount;
    bool ownerMint;
    uint256 totalCost;
    uint256[] shares;
    address[] feeRecipients;
    address buyer;
    uint256 nonce;
    uint256 expiry;
  }

  function mint(MintPosterInfo calldata mintPosterInfo, bytes calldata signature, address signer) external payable;

  function mintFirst(
    MintPosterInfo calldata mintPosterInfo,
    uint256 mintEndsAt,
    bytes calldata signature,
    address signer
  ) external payable;
}

// File: contracts/interfaces/internal/IPosters.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.17;

interface IPosters {
  error NotPosterMinter();

  /**
   * @dev Emitted when a poster is minted.
   * @param to The address of the poster owner.
   * @param id The token id of the poster.
   * @param amount The amount of posters minted.
   */
  event PosterMinted(address indexed to, uint256 indexed id, uint256 amount);

  /**
   * @dev Emitted when the base uri is set.
   * @param baseUri The base uri of the poster.
   */
  event BaseUriSet(string baseUri);

  function mint(address _to, uint256 _id, uint256 _amount) external;

  function setBaseUri(string calldata _baseUri) external;

  function uri(uint256 _id) external view returns (string memory);
}

// File: contracts/interfaces/internal/IRoleAuthority.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.17;

interface IRoleAuthority {
  function isOperator(address _address) external view returns (bool);

  function is721Minter(address _address) external view returns (bool);

  function isMintPassSigner(address _address) external view returns (bool);

  function isPosterMinter(address _address) external view returns (bool);

  function isPosterSigner(address _address) external view returns (bool);
}