Contract

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/Bytes.sol)

pragma solidity ^0.8.24;

import {Math} from "./math/Math.sol";

/**
 * @dev Bytes operations.
 */
library Bytes {
    /**
     * @dev Forward search for `s` in `buffer`
     * * If `s` is present in the buffer, returns the index of the first instance
     * * If `s` is not present in the buffer, returns type(uint256).max
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/indexOf[Javascript's `Array.indexOf`]
     */
    function indexOf(bytes memory buffer, bytes1 s) internal pure returns (uint256) {
        return indexOf(buffer, s, 0);
    }

    /**
     * @dev Forward search for `s` in `buffer` starting at position `pos`
     * * If `s` is present in the buffer (at or after `pos`), returns the index of the next instance
     * * If `s` is not present in the buffer (at or after `pos`), returns type(uint256).max
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/indexOf[Javascript's `Array.indexOf`]
     */
    function indexOf(bytes memory buffer, bytes1 s, uint256 pos) internal pure returns (uint256) {
        uint256 length = buffer.length;
        for (uint256 i = pos; i < length; ++i) {
            if (bytes1(_unsafeReadBytesOffset(buffer, i)) == s) {
                return i;
            }
        }
        return type(uint256).max;
    }

    /**
     * @dev Backward search for `s` in `buffer`
     * * If `s` is present in the buffer, returns the index of the last instance
     * * If `s` is not present in the buffer, returns type(uint256).max
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/lastIndexOf[Javascript's `Array.lastIndexOf`]
     */
    function lastIndexOf(bytes memory buffer, bytes1 s) internal pure returns (uint256) {
        return lastIndexOf(buffer, s, type(uint256).max);
    }

    /**
     * @dev Backward search for `s` in `buffer` starting at position `pos`
     * * If `s` is present in the buffer (at or before `pos`), returns the index of the previous instance
     * * If `s` is not present in the buffer (at or before `pos`), returns type(uint256).max
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/lastIndexOf[Javascript's `Array.lastIndexOf`]
     */
    function lastIndexOf(bytes memory buffer, bytes1 s, uint256 pos) internal pure returns (uint256) {
        unchecked {
            uint256 length = buffer.length;
            for (uint256 i = Math.min(Math.saturatingAdd(pos, 1), length); i > 0; --i) {
                if (bytes1(_unsafeReadBytesOffset(buffer, i - 1)) == s) {
                    return i - 1;
                }
            }
            return type(uint256).max;
        }
    }

    /**
     * @dev Copies the content of `buffer`, from `start` (included) to the end of `buffer` into a new bytes object in
     * memory.
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/slice[Javascript's `Array.slice`]
     */
    function slice(bytes memory buffer, uint256 start) internal pure returns (bytes memory) {
        return slice(buffer, start, buffer.length);
    }

    /**
     * @dev Copies the content of `buffer`, from `start` (included) to `end` (excluded) into a new bytes object in
     * memory. The `end` argument is truncated to the length of the `buffer`.
     *
     * NOTE: replicates the behavior of https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/slice[Javascript's `Array.slice`]
     */
    function slice(bytes memory buffer, uint256 start, uint256 end) internal pure returns (bytes memory) {
        // sanitize
        end = Math.min(end, buffer.length);
        start = Math.min(start, end);

        // allocate and copy
        bytes memory result = new bytes(end - start);
        assembly ("memory-safe") {
            mcopy(add(result, 0x20), add(add(buffer, 0x20), start), sub(end, start))
        }

        return result;
    }

    /**
     * @dev Moves the content of `buffer`, from `start` (included) to the end of `buffer` to the start of that buffer,
     * and shrinks the buffer length accordingly, effectively overriding the content of buffer with buffer[start:].
     *
     * NOTE: This function modifies the provided buffer in place. If you need to preserve the original buffer, use {slice} instead
     */
    function splice(bytes memory buffer, uint256 start) internal pure returns (bytes memory) {
        return splice(buffer, start, buffer.length);
    }

    /**
     * @dev Moves the content of `buffer`, from `start` (included) to `end` (excluded) to the start of that buffer,
     * and shrinks the buffer length accordingly, effectively overriding the content of buffer with buffer[start:end].
     * The `end` argument is truncated to the length of the `buffer`.
     *
     * NOTE: This function modifies the provided buffer in place. If you need to preserve the original buffer, use {slice} instead
     */
    function splice(bytes memory buffer, uint256 start, uint256 end) internal pure returns (bytes memory) {
        // sanitize
        end = Math.min(end, buffer.length);
        start = Math.min(start, end);

        // move and resize
        assembly ("memory-safe") {
            mcopy(add(buffer, 0x20), add(add(buffer, 0x20), start), sub(end, start))
            mstore(buffer, sub(end, start))
        }

        return buffer;
    }

    /**
     * @dev Replaces bytes in `buffer` starting at `pos` with all bytes from `replacement`.
     *
     * Parameters are clamped to valid ranges (i.e. `pos` is clamped to `[0, buffer.length]`).
     * If `pos >= buffer.length`, no replacement occurs and the buffer is returned unchanged.
     *
     * NOTE: This function modifies the provided buffer in place.
     */
    function replace(bytes memory buffer, uint256 pos, bytes memory replacement) internal pure returns (bytes memory) {
        return replace(buffer, pos, replacement, 0, replacement.length);
    }

    /**
     * @dev Replaces bytes in `buffer` starting at `pos` with bytes from `replacement` starting at `offset`.
     * Copies at most `length` bytes from `replacement` to `buffer`.
     *
     * Parameters are clamped to valid ranges (i.e. `pos` is clamped to `[0, buffer.length]`, `offset` is
     * clamped to `[0, replacement.length]`, and `length` is clamped to `min(length, replacement.length - offset,
     * buffer.length - pos))`. If `pos >= buffer.length` or `offset >= replacement.length`, no replacement occurs
     * and the buffer is returned unchanged.
     *
     * NOTE: This function modifies the provided buffer in place.
     */
    function replace(
        bytes memory buffer,
        uint256 pos,
        bytes memory replacement,
        uint256 offset,
        uint256 length
    ) internal pure returns (bytes memory) {
        // sanitize
        pos = Math.min(pos, buffer.length);
        offset = Math.min(offset, replacement.length);
        length = Math.min(length, Math.min(replacement.length - offset, buffer.length - pos));

        // replace
        assembly ("memory-safe") {
            mcopy(add(add(buffer, 0x20), pos), add(add(replacement, 0x20), offset), length)
        }

        return buffer;
    }

    /**
     * @dev Concatenate an array of bytes into a single bytes object.
     *
     * For fixed bytes types, we recommend using the solidity built-in `bytes.concat` or (equivalent)
     * `abi.encodePacked`.
     *
     * NOTE: this could be done in assembly with a single loop that expands starting at the FMP, but that would be
     * significantly less readable. It might be worth benchmarking the savings of the full-assembly approach.
     */
    function concat(bytes[] memory buffers) internal pure returns (bytes memory) {
        uint256 length = 0;
        for (uint256 i = 0; i < buffers.length; ++i) {
            length += buffers[i].length;
        }

        bytes memory result = new bytes(length);

        uint256 offset = 0x20;
        for (uint256 i = 0; i < buffers.length; ++i) {
            bytes memory input = buffers[i];
            assembly ("memory-safe") {
                mcopy(add(result, offset), add(input, 0x20), mload(input))
            }
            unchecked {
                offset += input.length;
            }
        }

        return result;
    }

    /**
     * @dev Split each byte in `input` into two nibbles (4 bits each)
     *
     * Example: hex"01234567" → hex"0001020304050607"
     */
    function toNibbles(bytes memory input) internal pure returns (bytes memory output) {
        assembly ("memory-safe") {
            let length := mload(input)
            output := mload(0x40)
            mstore(0x40, add(add(output, 0x20), mul(length, 2)))
            mstore(output, mul(length, 2))
            for {
                let i := 0
            } lt(i, length) {
                i := add(i, 0x10)
            } {
                let chunk := shr(128, mload(add(add(input, 0x20), i)))
                chunk := and(
                    0x0000000000000000ffffffffffffffff0000000000000000ffffffffffffffff,
                    or(shl(64, chunk), chunk)
                )
                chunk := and(
                    0x00000000ffffffff00000000ffffffff00000000ffffffff00000000ffffffff,
                    or(shl(32, chunk), chunk)
                )
                chunk := and(
                    0x0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff,
                    or(shl(16, chunk), chunk)
                )
                chunk := and(
                    0x00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff,
                    or(shl(8, chunk), chunk)
                )
                chunk := and(
                    0x0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f,
                    or(shl(4, chunk), chunk)
                )
                mstore(add(add(output, 0x20), mul(i, 2)), chunk)
            }
        }
    }

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

    /**
     * @dev Reverses the byte order of a bytes32 value, converting between little-endian and big-endian.
     * Inspired by https://graphics.stanford.edu/~seander/bithacks.html#ReverseParallel[Reverse Parallel]
     */
    function reverseBytes32(bytes32 value) internal pure returns (bytes32) {
        value = // swap bytes
            ((value >> 8) & 0x00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF) |
            ((value & 0x00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF00FF) << 8);
        value = // swap 2-byte long pairs
            ((value >> 16) & 0x0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF) |
            ((value & 0x0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF0000FFFF) << 16);
        value = // swap 4-byte long pairs
            ((value >> 32) & 0x00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFF) |
            ((value & 0x00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFF00000000FFFFFFFF) << 32);
        value = // swap 8-byte long pairs
            ((value >> 64) & 0x0000000000000000FFFFFFFFFFFFFFFF0000000000000000FFFFFFFFFFFFFFFF) |
            ((value & 0x0000000000000000FFFFFFFFFFFFFFFF0000000000000000FFFFFFFFFFFFFFFF) << 64);
        return (value >> 128) | (value << 128); // swap 16-byte long pairs
    }

    /// @dev Same as {reverseBytes32} but optimized for 128-bit values.
    function reverseBytes16(bytes16 value) internal pure returns (bytes16) {
        value = // swap bytes
            ((value & 0xFF00FF00FF00FF00FF00FF00FF00FF00) >> 8) |
            ((value & 0x00FF00FF00FF00FF00FF00FF00FF00FF) << 8);
        value = // swap 2-byte long pairs
            ((value & 0xFFFF0000FFFF0000FFFF0000FFFF0000) >> 16) |
            ((value & 0x0000FFFF0000FFFF0000FFFF0000FFFF) << 16);
        value = // swap 4-byte long pairs
            ((value & 0xFFFFFFFF00000000FFFFFFFF00000000) >> 32) |
            ((value & 0x00000000FFFFFFFF00000000FFFFFFFF) << 32);
        return (value >> 64) | (value << 64); // swap 8-byte long pairs
    }

    /// @dev Same as {reverseBytes32} but optimized for 64-bit values.
    function reverseBytes8(bytes8 value) internal pure returns (bytes8) {
        value = ((value & 0xFF00FF00FF00FF00) >> 8) | ((value & 0x00FF00FF00FF00FF) << 8); // swap bytes
        value = ((value & 0xFFFF0000FFFF0000) >> 16) | ((value & 0x0000FFFF0000FFFF) << 16); // swap 2-byte long pairs
        return (value >> 32) | (value << 32); // swap 4-byte long pairs
    }

    /// @dev Same as {reverseBytes32} but optimized for 32-bit values.
    function reverseBytes4(bytes4 value) internal pure returns (bytes4) {
        value = ((value & 0xFF00FF00) >> 8) | ((value & 0x00FF00FF) << 8); // swap bytes
        return (value >> 16) | (value << 16); // swap 2-byte long pairs
    }

    /// @dev Same as {reverseBytes32} but optimized for 16-bit values.
    function reverseBytes2(bytes2 value) internal pure returns (bytes2) {
        return (value >> 8) | (value << 8);
    }

    /**
     * @dev Counts the number of leading zero bits a bytes array. Returns `8 * buffer.length`
     * if the buffer is all zeros.
     */
    function clz(bytes memory buffer) internal pure returns (uint256) {
        for (uint256 i = 0; i < buffer.length; i += 0x20) {
            bytes32 chunk = _unsafeReadBytesOffset(buffer, i);
            if (chunk != bytes32(0)) {
                return Math.min(8 * i + Math.clz(uint256(chunk)), 8 * buffer.length);
            }
        }
        return 8 * buffer.length;
    }

    /**
     * @dev Reads a bytes32 from a bytes array without bounds checking.
     *
     * NOTE: making this function internal would mean it could be used with memory unsafe offset, and marking the
     * assembly block as such would prevent some optimizations.
     */
    function _unsafeReadBytesOffset(bytes memory buffer, uint256 offset) private pure returns (bytes32 value) {
        // This is not memory safe in the general case, but all calls to this private function are within bounds.
        assembly ("memory-safe") {
            value := mload(add(add(buffer, 0x20), offset))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.5.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.20;

import {IERC20} from "../IERC20.sol";
import {IERC1363} from "../../../interfaces/IERC1363.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC-20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    /**
     * @dev An operation with an ERC-20 token failed.
     */
    error SafeERC20FailedOperation(address token);

    /**
     * @dev Indicates a failed `decreaseAllowance` request.
     */
    error SafeERC20FailedDecreaseAllowance(address spender, uint256 currentAllowance, uint256 requestedDecrease);

    /**
     * @dev Transfer `value` amount of `token` from the calling contract to `to`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        if (!_safeTransfer(token, to, value, true)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Transfer `value` amount of `token` from `from` to `to`, spending the approval given by `from` to the
     * calling contract. If `token` returns no value, non-reverting calls are assumed to be successful.
     */
    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        if (!_safeTransferFrom(token, from, to, value, true)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Variant of {safeTransfer} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransfer(IERC20 token, address to, uint256 value) internal returns (bool) {
        return _safeTransfer(token, to, value, false);
    }

    /**
     * @dev Variant of {safeTransferFrom} that returns a bool instead of reverting if the operation is not successful.
     */
    function trySafeTransferFrom(IERC20 token, address from, address to, uint256 value) internal returns (bool) {
        return _safeTransferFrom(token, from, to, value, false);
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        forceApprove(token, spender, oldAllowance + value);
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `requestedDecrease`. If `token` returns no
     * value, non-reverting calls are assumed to be successful.
     *
     * IMPORTANT: If the token implements ERC-7674 (ERC-20 with temporary allowance), and if the "client"
     * smart contract uses ERC-7674 to set temporary allowances, then the "client" smart contract should avoid using
     * this function. Performing a {safeIncreaseAllowance} or {safeDecreaseAllowance} operation on a token contract
     * that has a non-zero temporary allowance (for that particular owner-spender) will result in unexpected behavior.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 requestedDecrease) internal {
        unchecked {
            uint256 currentAllowance = token.allowance(address(this), spender);
            if (currentAllowance < requestedDecrease) {
                revert SafeERC20FailedDecreaseAllowance(spender, currentAllowance, requestedDecrease);
            }
            forceApprove(token, spender, currentAllowance - requestedDecrease);
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Meant to be used with tokens that require the approval
     * to be set to zero before setting it to a non-zero value, such as USDT.
     *
     * NOTE: If the token implements ERC-7674, this function will not modify any temporary allowance. This function
     * only sets the "standard" allowance. Any temporary allowance will remain active, in addition to the value being
     * set here.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        if (!_safeApprove(token, spender, value, false)) {
            if (!_safeApprove(token, spender, 0, true)) revert SafeERC20FailedOperation(address(token));
            if (!_safeApprove(token, spender, value, true)) revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferAndCall, with a fallback to the simple {ERC20} transfer if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that relies on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            safeTransfer(token, to, value);
        } else if (!token.transferAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} transferFromAndCall, with a fallback to the simple {ERC20} transferFrom if the target
     * has no code. This can be used to implement an {ERC721}-like safe transfer that relies on {ERC1363} checks when
     * targeting contracts.
     *
     * Reverts if the returned value is other than `true`.
     */
    function transferFromAndCallRelaxed(
        IERC1363 token,
        address from,
        address to,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length == 0) {
            safeTransferFrom(token, from, to, value);
        } else if (!token.transferFromAndCall(from, to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Performs an {ERC1363} approveAndCall, with a fallback to the simple {ERC20} approve if the target has no
     * code. This can be used to implement an {ERC721}-like safe transfer that rely on {ERC1363} checks when
     * targeting contracts.
     *
     * NOTE: When the recipient address (`to`) has no code (i.e. is an EOA), this function behaves as {forceApprove}.
     * Oppositely, when the recipient address (`to`) has code, this function only attempts to call {ERC1363-approveAndCall}
     * once without retrying, and relies on the returned value to be true.
     *
     * Reverts if the returned value is other than `true`.
     */
    function approveAndCallRelaxed(IERC1363 token, address to, uint256 value, bytes memory data) internal {
        if (to.code.length == 0) {
            forceApprove(token, to, value);
        } else if (!token.approveAndCall(to, value, data)) {
            revert SafeERC20FailedOperation(address(token));
        }
    }

    /**
     * @dev Imitates a Solidity `token.transfer(to, value)` call, relaxing the requirement on the return value: the
     * return value is optional (but if data is returned, it must not be false).
     *
     * @param token The token targeted by the call.
     * @param to The recipient of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeTransfer(IERC20 token, address to, uint256 value, bool bubble) private returns (bool success) {
        bytes4 selector = IERC20.transfer.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(to, shr(96, not(0))))
            mstore(0x24, value)
            success := call(gas(), token, 0, 0x00, 0x44, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
        }
    }

    /**
     * @dev Imitates a Solidity `token.transferFrom(from, to, value)` call, relaxing the requirement on the return
     * value: the return value is optional (but if data is returned, it must not be false).
     *
     * @param token The token targeted by the call.
     * @param from The sender of the tokens
     * @param to The recipient of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeTransferFrom(
        IERC20 token,
        address from,
        address to,
        uint256 value,
        bool bubble
    ) private returns (bool success) {
        bytes4 selector = IERC20.transferFrom.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(from, shr(96, not(0))))
            mstore(0x24, and(to, shr(96, not(0))))
            mstore(0x44, value)
            success := call(gas(), token, 0, 0x00, 0x64, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
            mstore(0x60, 0)
        }
    }

    /**
     * @dev Imitates a Solidity `token.approve(spender, value)` call, relaxing the requirement on the return value:
     * the return value is optional (but if data is returned, it must not be false).
     *
     * @param token The token targeted by the call.
     * @param spender The spender of the tokens
     * @param value The amount of token to transfer
     * @param bubble Behavior switch if the transfer call reverts: bubble the revert reason or return a false boolean.
     */
    function _safeApprove(IERC20 token, address spender, uint256 value, bool bubble) private returns (bool success) {
        bytes4 selector = IERC20.approve.selector;

        assembly ("memory-safe") {
            let fmp := mload(0x40)
            mstore(0x00, selector)
            mstore(0x04, and(spender, shr(96, not(0))))
            mstore(0x24, value)
            success := call(gas(), token, 0, 0x00, 0x44, 0x00, 0x20)
            // if call success and return is true, all is good.
            // otherwise (not success or return is not true), we need to perform further checks
            if iszero(and(success, eq(mload(0x00), 1))) {
                // if the call was a failure and bubble is enabled, bubble the error
                if and(iszero(success), bubble) {
                    returndatacopy(fmp, 0x00, returndatasize())
                    revert(fmp, returndatasize())
                }
                // if the return value is not true, then the call is only successful if:
                // - the token address has code
                // - the returndata is empty
                success := and(success, and(iszero(returndatasize()), gt(extcodesize(token), 0)))
            }
            mstore(0x40, fmp)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC1363.sol)

pragma solidity >=0.6.2;

import {IERC20} from "./IERC20.sol";
import {IERC165} from "./IERC165.sol";

/**
 * @title IERC1363
 * @dev Interface of the ERC-1363 standard as defined in the https://eips.ethereum.org/EIPS/eip-1363[ERC-1363].
 *
 * Defines an extension interface for ERC-20 tokens that supports executing code on a recipient contract
 * after `transfer` or `transferFrom`, or code on a spender contract after `approve`, in a single transaction.
 */
interface IERC1363 is IERC20, IERC165 {
    /*
     * Note: the ERC-165 identifier for this interface is 0xb0202a11.
     * 0xb0202a11 ===
     *   bytes4(keccak256('transferAndCall(address,uint256)')) ^
     *   bytes4(keccak256('transferAndCall(address,uint256,bytes)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256)')) ^
     *   bytes4(keccak256('transferFromAndCall(address,address,uint256,bytes)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256)')) ^
     *   bytes4(keccak256('approveAndCall(address,uint256,bytes)'))
     */

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferAndCall(address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the allowance mechanism
     * and then calls {IERC1363Receiver-onTransferReceived} on `to`.
     * @param from The address which you want to send tokens from.
     * @param to The address which you want to transfer to.
     * @param value The amount of tokens to be transferred.
     * @param data Additional data with no specified format, sent in call to `to`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function transferFromAndCall(address from, address to, uint256 value, bytes calldata data) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value) external returns (bool);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens and then calls {IERC1363Spender-onApprovalReceived} on `spender`.
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     * @param data Additional data with no specified format, sent in call to `spender`.
     * @return A boolean value indicating whether the operation succeeded unless throwing.
     */
    function approveAndCall(address spender, uint256 value, bytes calldata data) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC165.sol)

pragma solidity >=0.4.16;

import {IERC165} from "../utils/introspection/IERC165.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/IERC20.sol)

pragma solidity >=0.4.16;

import {IERC20} from "../token/ERC20/IERC20.sol";

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (interfaces/draft-IERC7821.sol)

pragma solidity >=0.5.0;

/**
 * @dev Interface for minimal batch executor.
 */
interface IERC7821 {
    /**
     * @dev Executes the calls in `executionData`.
     * Reverts and bubbles up error if any call fails.
     *
     * `executionData` encoding:
     * - If `opData` is empty, `executionData` is simply `abi.encode(calls)`.
     * - Else, `executionData` is `abi.encode(calls, opData)`.
     *   See: https://eips.ethereum.org/EIPS/eip-7579
     *
     * Supported modes:
     * - `bytes32(0x01000000000000000000...)`: does not support optional `opData`.
     * - `bytes32(0x01000000000078210001...)`: supports optional `opData`.
     *
     * Authorization checks:
     * - If `opData` is empty, the implementation SHOULD require that
     *   `msg.sender == address(this)`.
     * - If `opData` is not empty, the implementation SHOULD use the signature
     *   encoded in `opData` to determine if the caller can perform the execution.
     *
     * `opData` may be used to store additional data for authentication,
     * paymaster data, gas limits, etc.
     *
     * For calldata compression efficiency, if a Call.to is `address(0)`,
     * it will be replaced with `address(this)`.
     */
    function execute(bytes32 mode, bytes calldata executionData) external payable;

    /**
     * @dev This function is provided for frontends to detect support.
     * Only returns true for:
     * - `bytes32(0x01000000000000000000...)`: does not support optional `opData`.
     * - `bytes32(0x01000000000078210001...)`: supports optional `opData`.
     */
    function supportsExecutionMode(bytes32 mode) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (token/ERC20/IERC20.sol)

pragma solidity >=0.4.16;

/**
 * @dev Interface of the ERC-20 standard as defined in the ERC.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the value of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the value of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves a `value` amount of tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 value) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets a `value` amount of tokens as the allowance of `spender` over the
     * caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 value) external returns (bool);

    /**
     * @dev Moves a `value` amount of tokens from `from` to `to` using the
     * allowance mechanism. `value` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 value) external returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Panic.sol)

pragma solidity ^0.8.20;

/**
 * @dev Helper library for emitting standardized panic codes.
 *
 * ```solidity
 * contract Example {
 *      using Panic for uint256;
 *
 *      // Use any of the declared internal constants
 *      function foo() { Panic.GENERIC.panic(); }
 *
 *      // Alternatively
 *      function foo() { Panic.panic(Panic.GENERIC); }
 * }
 * ```
 *
 * Follows the list from https://github.com/ethereum/solidity/blob/v0.8.24/libsolutil/ErrorCodes.h[libsolutil].
 *
 * _Available since v5.1._
 */
// slither-disable-next-line unused-state
library Panic {
    /// @dev generic / unspecified error
    uint256 internal constant GENERIC = 0x00;
    /// @dev used by the assert() builtin
    uint256 internal constant ASSERT = 0x01;
    /// @dev arithmetic underflow or overflow
    uint256 internal constant UNDER_OVERFLOW = 0x11;
    /// @dev division or modulo by zero
    uint256 internal constant DIVISION_BY_ZERO = 0x12;
    /// @dev enum conversion error
    uint256 internal constant ENUM_CONVERSION_ERROR = 0x21;
    /// @dev invalid encoding in storage
    uint256 internal constant STORAGE_ENCODING_ERROR = 0x22;
    /// @dev empty array pop
    uint256 internal constant EMPTY_ARRAY_POP = 0x31;
    /// @dev array out of bounds access
    uint256 internal constant ARRAY_OUT_OF_BOUNDS = 0x32;
    /// @dev resource error (too large allocation or too large array)
    uint256 internal constant RESOURCE_ERROR = 0x41;
    /// @dev calling invalid internal function
    uint256 internal constant INVALID_INTERNAL_FUNCTION = 0x51;

    /// @dev Reverts with a panic code. Recommended to use with
    /// the internal constants with predefined codes.
    function panic(uint256 code) internal pure {
        assembly ("memory-safe") {
            mstore(0x00, 0x4e487b71)
            mstore(0x20, code)
            revert(0x1c, 0x24)
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.5.0) (utils/ReentrancyGuard.sol)

pragma solidity ^0.8.20;

import {StorageSlot} from "./StorageSlot.sol";

/**
 * @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 EIP-1153 (transient storage) is available on the chain you're deploying at,
 * consider using {ReentrancyGuardTransient} instead.
 *
 * 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].
 *
 * IMPORTANT: Deprecated. This storage-based reentrancy guard will be removed and replaced
 * by the {ReentrancyGuardTransient} variant in v6.0.
 *
 * @custom:stateless
 */
abstract contract ReentrancyGuard {
    using StorageSlot for bytes32;

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.ReentrancyGuard")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant REENTRANCY_GUARD_STORAGE =
        0x9b779b17422d0df92223018b32b4d1fa46e071723d6817e2486d003becc55f00;

    // 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;

    /**
     * @dev Unauthorized reentrant call.
     */
    error ReentrancyGuardReentrantCall();

    constructor() {
        _reentrancyGuardStorageSlot().getUint256Slot().value = 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();
    }

    /**
     * @dev A `view` only version of {nonReentrant}. Use to block view functions
     * from being called, preventing reading from inconsistent contract state.
     *
     * CAUTION: This is a "view" modifier and does not change the reentrancy
     * status. Use it only on view functions. For payable or non-payable functions,
     * use the standard {nonReentrant} modifier instead.
     */
    modifier nonReentrantView() {
        _nonReentrantBeforeView();
        _;
    }

    function _nonReentrantBeforeView() private view {
        if (_reentrancyGuardEntered()) {
            revert ReentrancyGuardReentrantCall();
        }
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be NOT_ENTERED
        _nonReentrantBeforeView();

        // Any calls to nonReentrant after this point will fail
        _reentrancyGuardStorageSlot().getUint256Slot().value = ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _reentrancyGuardStorageSlot().getUint256Slot().value = 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 _reentrancyGuardStorageSlot().getUint256Slot().value == ENTERED;
    }

    function _reentrancyGuardStorageSlot() internal pure virtual returns (bytes32) {
        return REENTRANCY_GUARD_STORAGE;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC-1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     // Define the slot. Alternatively, use the SlotDerivation library to derive the slot.
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(newImplementation.code.length > 0);
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {SlotDerivation}.
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct Int256Slot {
        int256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `Int256Slot` with member `value` located at `slot`.
     */
    function getInt256Slot(bytes32 slot) internal pure returns (Int256Slot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns a `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns a `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        assembly ("memory-safe") {
            r.slot := store.slot
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/Strings.sol)

pragma solidity ^0.8.24;

import {Math} from "./math/Math.sol";
import {SafeCast} from "./math/SafeCast.sol";
import {SignedMath} from "./math/SignedMath.sol";
import {Bytes} from "./Bytes.sol";

/**
 * @dev String operations.
 */
library Strings {
    using SafeCast for *;

    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;
    uint256 private constant SPECIAL_CHARS_LOOKUP =
        0xffffffff | // first 32 bits corresponding to the control characters (U+0000 to U+001F)
            (1 << 0x22) | // double quote
            (1 << 0x5c); // backslash

    /**
     * @dev The `value` string doesn't fit in the specified `length`.
     */
    error StringsInsufficientHexLength(uint256 value, uint256 length);

    /**
     * @dev The string being parsed contains characters that are not in scope of the given base.
     */
    error StringsInvalidChar();

    /**
     * @dev The string being parsed is not a properly formatted address.
     */
    error StringsInvalidAddressFormat();

    /**
     * @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;
            assembly ("memory-safe") {
                ptr := add(add(buffer, 0x20), length)
            }
            while (true) {
                ptr--;
                assembly ("memory-safe") {
                    mstore8(ptr, byte(mod(value, 10), HEX_DIGITS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toStringSigned(int256 value) internal pure returns (string memory) {
        return string.concat(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) {
        uint256 localValue = value;
        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] = HEX_DIGITS[localValue & 0xf];
            localValue >>= 4;
        }
        if (localValue != 0) {
            revert StringsInsufficientHexLength(value, length);
        }
        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 Converts an `address` with fixed length of 20 bytes to its checksummed ASCII `string` hexadecimal
     * representation, according to EIP-55.
     */
    function toChecksumHexString(address addr) internal pure returns (string memory) {
        bytes memory buffer = bytes(toHexString(addr));

        // hash the hex part of buffer (skip length + 2 bytes, length 40)
        uint256 hashValue;
        assembly ("memory-safe") {
            hashValue := shr(96, keccak256(add(buffer, 0x22), 40))
        }

        for (uint256 i = 41; i > 1; --i) {
            // possible values for buffer[i] are 48 (0) to 57 (9) and 97 (a) to 102 (f)
            if (hashValue & 0xf > 7 && uint8(buffer[i]) > 96) {
                // case shift by xoring with 0x20
                buffer[i] ^= 0x20;
            }
            hashValue >>= 4;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `bytes` buffer to its ASCII `string` hexadecimal representation.
     */
    function toHexString(bytes memory input) internal pure returns (string memory) {
        unchecked {
            bytes memory buffer = new bytes(2 * input.length + 2);
            buffer[0] = "0";
            buffer[1] = "x";
            for (uint256 i = 0; i < input.length; ++i) {
                uint8 v = uint8(input[i]);
                buffer[2 * i + 2] = HEX_DIGITS[v >> 4];
                buffer[2 * i + 3] = HEX_DIGITS[v & 0xf];
            }
            return string(buffer);
        }
    }

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

    /**
     * @dev Parse a decimal string and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input) internal pure returns (uint256) {
        return parseUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[0-9]*`
     * - The result must fit into an `uint256` type
     */
    function parseUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseUint-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        uint256 result = 0;
        for (uint256 i = begin; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 9) return (false, 0);
            result *= 10;
            result += chr;
        }
        return (true, result);
    }

    /**
     * @dev Parse a decimal string and returns the value as a `int256`.
     *
     * Requirements:
     * - The string must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input) internal pure returns (int256) {
        return parseInt(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseInt-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `[-+]?[0-9]*`
     * - The result must fit in an `int256` type.
     */
    function parseInt(string memory input, uint256 begin, uint256 end) internal pure returns (int256) {
        (bool success, int256 value) = tryParseInt(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseInt-string} that returns false if the parsing fails because of an invalid character or if
     * the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(string memory input) internal pure returns (bool success, int256 value) {
        return _tryParseIntUncheckedBounds(input, 0, bytes(input).length);
    }

    uint256 private constant ABS_MIN_INT256 = 2 ** 255;

    /**
     * @dev Variant of {parseInt-string-uint256-uint256} that returns false if the parsing fails because of an invalid
     * character or if the result does not fit in a `int256`.
     *
     * NOTE: This function will revert if the absolute value of the result does not fit in a `uint256`.
     */
    function tryParseInt(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, int256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseIntUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseInt-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseIntUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, int256 value) {
        bytes memory buffer = bytes(input);

        // Check presence of a negative sign.
        bytes1 sign = begin == end ? bytes1(0) : bytes1(_unsafeReadBytesOffset(buffer, begin)); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        bool positiveSign = sign == bytes1("+");
        bool negativeSign = sign == bytes1("-");
        uint256 offset = (positiveSign || negativeSign).toUint();

        (bool absSuccess, uint256 absValue) = tryParseUint(input, begin + offset, end);

        if (absSuccess && absValue < ABS_MIN_INT256) {
            return (true, negativeSign ? -int256(absValue) : int256(absValue));
        } else if (absSuccess && negativeSign && absValue == ABS_MIN_INT256) {
            return (true, type(int256).min);
        } else return (false, 0);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as a `uint256`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input) internal pure returns (uint256) {
        return parseHexUint(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]*`
     * - The result must fit in an `uint256` type.
     */
    function parseHexUint(string memory input, uint256 begin, uint256 end) internal pure returns (uint256) {
        (bool success, uint256 value) = tryParseHexUint(input, begin, end);
        if (!success) revert StringsInvalidChar();
        return value;
    }

    /**
     * @dev Variant of {parseHexUint-string} that returns false if the parsing fails because of an invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(string memory input) internal pure returns (bool success, uint256 value) {
        return _tryParseHexUintUncheckedBounds(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseHexUint-string-uint256-uint256} that returns false if the parsing fails because of an
     * invalid character.
     *
     * NOTE: This function will revert if the result does not fit in a `uint256`.
     */
    function tryParseHexUint(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, uint256 value) {
        if (end > bytes(input).length || begin > end) return (false, 0);
        return _tryParseHexUintUncheckedBounds(input, begin, end);
    }

    /**
     * @dev Implementation of {tryParseHexUint-string-uint256-uint256} that does not check bounds. Caller should make sure that
     * `begin <= end <= input.length`. Other inputs would result in undefined behavior.
     */
    function _tryParseHexUintUncheckedBounds(
        string memory input,
        uint256 begin,
        uint256 end
    ) private pure returns (bool success, uint256 value) {
        bytes memory buffer = bytes(input);

        // skip 0x prefix if present
        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(buffer, begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 offset = hasPrefix.toUint() * 2;

        uint256 result = 0;
        for (uint256 i = begin + offset; i < end; ++i) {
            uint8 chr = _tryParseChr(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (chr > 15) return (false, 0);
            result *= 16;
            unchecked {
                // Multiplying by 16 is equivalent to a shift of 4 bits (with additional overflow check).
                // This guarantees that adding a value < 16 will not cause an overflow, hence the unchecked.
                result += chr;
            }
        }
        return (true, result);
    }

    /**
     * @dev Parse a hexadecimal string (with or without "0x" prefix), and returns the value as an `address`.
     *
     * Requirements:
     * - The string must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input) internal pure returns (address) {
        return parseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string} that parses a substring of `input` located between position `begin` (included) and
     * `end` (excluded).
     *
     * Requirements:
     * - The substring must be formatted as `(0x)?[0-9a-fA-F]{40}`
     */
    function parseAddress(string memory input, uint256 begin, uint256 end) internal pure returns (address) {
        (bool success, address value) = tryParseAddress(input, begin, end);
        if (!success) revert StringsInvalidAddressFormat();
        return value;
    }

    /**
     * @dev Variant of {parseAddress-string} that returns false if the parsing fails because the input is not a properly
     * formatted address. See {parseAddress-string} requirements.
     */
    function tryParseAddress(string memory input) internal pure returns (bool success, address value) {
        return tryParseAddress(input, 0, bytes(input).length);
    }

    /**
     * @dev Variant of {parseAddress-string-uint256-uint256} that returns false if the parsing fails because input is not a properly
     * formatted address. See {parseAddress-string-uint256-uint256} requirements.
     */
    function tryParseAddress(
        string memory input,
        uint256 begin,
        uint256 end
    ) internal pure returns (bool success, address value) {
        if (end > bytes(input).length || begin > end) return (false, address(0));

        bool hasPrefix = (end > begin + 1) && bytes2(_unsafeReadBytesOffset(bytes(input), begin)) == bytes2("0x"); // don't do out-of-bound (possibly unsafe) read if sub-string is empty
        uint256 expectedLength = 40 + hasPrefix.toUint() * 2;

        // check that input is the correct length
        if (end - begin == expectedLength) {
            // length guarantees that this does not overflow, and value is at most type(uint160).max
            (bool s, uint256 v) = _tryParseHexUintUncheckedBounds(input, begin, end);
            return (s, address(uint160(v)));
        } else {
            return (false, address(0));
        }
    }

    function _tryParseChr(bytes1 chr) private pure returns (uint8) {
        uint8 value = uint8(chr);

        // Try to parse `chr`:
        // - Case 1: [0-9]
        // - Case 2: [a-f]
        // - Case 3: [A-F]
        // - otherwise not supported
        unchecked {
            if (value > 47 && value < 58) value -= 48;
            else if (value > 96 && value < 103) value -= 87;
            else if (value > 64 && value < 71) value -= 55;
            else return type(uint8).max;
        }

        return value;
    }

    /**
     * @dev Escape special characters in JSON strings. This can be useful to prevent JSON injection in NFT metadata.
     *
     * WARNING: This function should only be used in double quoted JSON strings. Single quotes are not escaped.
     *
     * NOTE: This function escapes backslashes (including those in \uXXXX sequences) and the characters in ranges
     * defined in section 2.5 of RFC-4627 (U+0000 to U+001F, U+0022 and U+005C). All control characters in U+0000
     * to U+001F are escaped (\b, \t, \n, \f, \r use short form; others use \u00XX). ECMAScript's `JSON.parse` does
     * recover escaped unicode characters that are not in this range, but other tooling may provide different results.
     */
    function escapeJSON(string memory input) internal pure returns (string memory) {
        bytes memory buffer = bytes(input);

        // Put output at the FMP. Memory will be reserved later when we figure out the actual length of the escaped
        // string. All write are done using _unsafeWriteBytesOffset, which avoid the (expensive) length checks for
        // each character written.
        bytes memory output;
        assembly ("memory-safe") {
            output := mload(0x40)
        }
        uint256 outputLength = 0;

        for (uint256 i = 0; i < buffer.length; ++i) {
            uint8 char = uint8(bytes1(_unsafeReadBytesOffset(buffer, i)));
            if (((SPECIAL_CHARS_LOOKUP & (1 << char)) != 0)) {
                _unsafeWriteBytesOffset(output, outputLength++, "\\");
                if (char == 0x08) _unsafeWriteBytesOffset(output, outputLength++, "b");
                else if (char == 0x09) _unsafeWriteBytesOffset(output, outputLength++, "t");
                else if (char == 0x0a) _unsafeWriteBytesOffset(output, outputLength++, "n");
                else if (char == 0x0c) _unsafeWriteBytesOffset(output, outputLength++, "f");
                else if (char == 0x0d) _unsafeWriteBytesOffset(output, outputLength++, "r");
                else if (char == 0x5c) _unsafeWriteBytesOffset(output, outputLength++, "\\");
                else if (char == 0x22) {
                    // solhint-disable-next-line quotes
                    _unsafeWriteBytesOffset(output, outputLength++, '"');
                } else {
                    // U+0000 to U+001F without short form: output \u00XX
                    _unsafeWriteBytesOffset(output, outputLength++, "u");
                    _unsafeWriteBytesOffset(output, outputLength++, "0");
                    _unsafeWriteBytesOffset(output, outputLength++, "0");
                    _unsafeWriteBytesOffset(output, outputLength++, HEX_DIGITS[char >> 4]);
                    _unsafeWriteBytesOffset(output, outputLength++, HEX_DIGITS[char & 0x0f]);
                }
            } else {
                _unsafeWriteBytesOffset(output, outputLength++, bytes1(char));
            }
        }
        // write the actual length and reserve memory
        assembly ("memory-safe") {
            mstore(output, outputLength)
            mstore(0x40, add(output, add(outputLength, 0x20)))
        }

        return string(output);
    }

    /**
     * @dev Reads a bytes32 from a bytes array without bounds checking.
     *
     * NOTE: making this function internal would mean it could be used with memory unsafe offset, and marking the
     * assembly block as such would prevent some optimizations.
     */
    function _unsafeReadBytesOffset(bytes memory buffer, uint256 offset) private pure returns (bytes32 value) {
        // This is not memory safe in the general case, but all calls to this private function are within bounds.
        assembly ("memory-safe") {
            value := mload(add(add(buffer, 0x20), offset))
        }
    }

    /**
     * @dev Write a bytes1 to a bytes array without bounds checking.
     *
     * NOTE: making this function internal would mean it could be used with memory unsafe offset, and marking the
     * assembly block as such would prevent some optimizations.
     */
    function _unsafeWriteBytesOffset(bytes memory buffer, uint256 offset, bytes1 value) private pure {
        // This is not memory safe in the general case, but all calls to this private function are within bounds.
        assembly ("memory-safe") {
            mstore8(add(add(buffer, 0x20), offset), shr(248, value))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.20;

/**
 * @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
    }

    /**
     * @dev The signature is invalid.
     */
    error ECDSAInvalidSignature();

    /**
     * @dev The signature has an invalid length.
     */
    error ECDSAInvalidSignatureLength(uint256 length);

    /**
     * @dev The signature has an S value that is in the upper half order.
     */
    error ECDSAInvalidSignatureS(bytes32 s);

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with `signature` or an error. This will not
     * return address(0) without also returning an error description. Errors are documented using an enum (error type)
     * and a bytes32 providing additional information about the error.
     *
     * If no error is returned, then the address can be used for verification purposes.
     *
     * The `ecrecover` EVM precompile 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.
     *
     * NOTE: This function only supports 65-byte signatures. ERC-2098 short signatures are rejected. This restriction
     * is DEPRECATED and will be removed in v6.0. Developers SHOULD NOT use signatures as unique identifiers; use hash
     * invalidation or nonces for replay protection.
     *
     * 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 {MessageHashUtils-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]
     */
    function tryRecover(
        bytes32 hash,
        bytes memory signature
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        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.
            assembly ("memory-safe") {
                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, bytes32(signature.length));
        }
    }

    /**
     * @dev Variant of {tryRecover} that takes a signature in calldata
     */
    function tryRecoverCalldata(
        bytes32 hash,
        bytes calldata signature
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, calldata slices would work here, but are
            // significantly more expensive (length check) than using calldataload in assembly.
            assembly ("memory-safe") {
                r := calldataload(signature.offset)
                s := calldataload(add(signature.offset, 0x20))
                v := byte(0, calldataload(add(signature.offset, 0x40)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength, bytes32(signature.length));
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM precompile 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.
     *
     * NOTE: This function only supports 65-byte signatures. ERC-2098 short signatures are rejected. This restriction
     * is DEPRECATED and will be removed in v6.0. Developers SHOULD NOT use signatures as unique identifiers; use hash
     * invalidation or nonces for replay protection.
     *
     * 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 {MessageHashUtils-toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, signature);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Variant of {recover} that takes a signature in calldata
     */
    function recoverCalldata(bytes32 hash, bytes calldata signature) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecoverCalldata(hash, signature);
        _throwError(error, errorArg);
        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[ERC-2098 short signatures]
     */
    function tryRecover(
        bytes32 hash,
        bytes32 r,
        bytes32 vs
    ) internal pure returns (address recovered, RecoverError err, bytes32 errArg) {
        unchecked {
            bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
            // We do not check for an overflow here since the shift operation results in 0 or 1.
            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.
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error, bytes32 errorArg) = tryRecover(hash, r, vs);
        _throwError(error, errorArg);
        return recovered;
    }

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

        // 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, bytes32(0));
        }

        return (signer, RecoverError.NoError, bytes32(0));
    }

    /**
     * @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, bytes32 errorArg) = tryRecover(hash, v, r, s);
        _throwError(error, errorArg);
        return recovered;
    }

    /**
     * @dev Parse a signature into its `v`, `r` and `s` components. Supports 65-byte and 64-byte (ERC-2098)
     * formats. Returns (0,0,0) for invalid signatures.
     *
     * For 64-byte signatures, `v` is automatically normalized to 27 or 28.
     * For 65-byte signatures, `v` is returned as-is and MUST already be 27 or 28 for use with ecrecover.
     *
     * Consider validating the result before use, or use {tryRecover}/{recover} which perform full validation.
     */
    function parse(bytes memory signature) internal pure returns (uint8 v, bytes32 r, bytes32 s) {
        assembly ("memory-safe") {
            // Check the signature length
            switch mload(signature)
            // - case 65: r,s,v signature (standard)
            case 65 {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098)
            case 64 {
                let vs := mload(add(signature, 0x40))
                r := mload(add(signature, 0x20))
                s := and(vs, shr(1, not(0)))
                v := add(shr(255, vs), 27)
            }
            default {
                r := 0
                s := 0
                v := 0
            }
        }
    }

    /**
     * @dev Variant of {parse} that takes a signature in calldata
     */
    function parseCalldata(bytes calldata signature) internal pure returns (uint8 v, bytes32 r, bytes32 s) {
        assembly ("memory-safe") {
            // Check the signature length
            switch signature.length
            // - case 65: r,s,v signature (standard)
            case 65 {
                r := calldataload(signature.offset)
                s := calldataload(add(signature.offset, 0x20))
                v := byte(0, calldataload(add(signature.offset, 0x40)))
            }
            // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098)
            case 64 {
                let vs := calldataload(add(signature.offset, 0x20))
                r := calldataload(signature.offset)
                s := and(vs, shr(1, not(0)))
                v := add(shr(255, vs), 27)
            }
            default {
                r := 0
                s := 0
                v := 0
            }
        }
    }

    /**
     * @dev Optionally reverts with the corresponding custom error according to the `error` argument provided.
     */
    function _throwError(RecoverError error, bytes32 errorArg) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert ECDSAInvalidSignature();
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert ECDSAInvalidSignatureLength(uint256(errorArg));
        } else if (error == RecoverError.InvalidSignatureS) {
            revert ECDSAInvalidSignatureS(errorArg);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/cryptography/MessageHashUtils.sol)

pragma solidity ^0.8.24;

import {Strings} from "../Strings.sol";

/**
 * @dev Signature message hash utilities for producing digests to be consumed by {ECDSA} recovery or signing.
 *
 * The library provides methods for generating a hash of a message that conforms to the
 * https://eips.ethereum.org/EIPS/eip-191[ERC-191] and https://eips.ethereum.org/EIPS/eip-712[EIP 712]
 * specifications.
 */
library MessageHashUtils {
    error ERC5267ExtensionsNotSupported();

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing a bytes32 `messageHash` with
     * `"\x19Ethereum Signed Message:\n32"` and hashing the result. It corresponds with the
     * hash signed when using the https://ethereum.org/en/developers/docs/apis/json-rpc/#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * NOTE: The `messageHash` parameter is intended to be the result of hashing a raw message with
     * keccak256, although any bytes32 value can be safely used because the final digest will
     * be re-hashed.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes32 messageHash) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            mstore(0x00, "\x19Ethereum Signed Message:\n32") // 32 is the bytes-length of messageHash
            mstore(0x1c, messageHash) // 0x1c (28) is the length of the prefix
            digest := keccak256(0x00, 0x3c) // 0x3c is the length of the prefix (0x1c) + messageHash (0x20)
        }
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x45` (`personal_sign` messages).
     *
     * The digest is calculated by prefixing an arbitrary `message` with
     * `"\x19Ethereum Signed Message:\n" + len(message)` and hashing the result. It corresponds with the
     * hash signed when using the https://ethereum.org/en/developers/docs/apis/json-rpc/#eth_sign[`eth_sign`] JSON-RPC method.
     *
     * See {ECDSA-recover}.
     */
    function toEthSignedMessageHash(bytes memory message) internal pure returns (bytes32) {
        return
            keccak256(bytes.concat("\x19Ethereum Signed Message:\n", bytes(Strings.toString(message.length)), message));
    }

    /**
     * @dev Returns the keccak256 digest of an ERC-191 signed data with version
     * `0x00` (data with intended validator).
     *
     * The digest is calculated by prefixing an arbitrary `data` with `"\x19\x00"` and the intended
     * `validator` address. Then hashing the result.
     *
     * See {ECDSA-recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(hex"19_00", validator, data));
    }

    /**
     * @dev Variant of {toDataWithIntendedValidatorHash-address-bytes} optimized for cases where `data` is a bytes32.
     */
    function toDataWithIntendedValidatorHash(
        address validator,
        bytes32 messageHash
    ) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            mstore(0x00, hex"19_00")
            mstore(0x02, shl(96, validator))
            mstore(0x16, messageHash)
            digest := keccak256(0x00, 0x36)
        }
    }

    /**
     * @dev Returns the keccak256 digest of an EIP-712 typed data (ERC-191 version `0x01`).
     *
     * The digest is calculated from a `domainSeparator` and a `structHash`, by prefixing them with
     * `\x19\x01` and hashing the result. It corresponds to the hash signed by the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`] JSON-RPC method as part of EIP-712.
     *
     * See {ECDSA-recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 digest) {
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            mstore(ptr, hex"19_01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            digest := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns the EIP-712 domain separator constructed from an `eip712Domain`. See {IERC5267-eip712Domain}
     *
     * This function dynamically constructs the domain separator based on which fields are present in the
     * `fields` parameter. It contains flags that indicate which domain fields are present:
     *
     * * Bit 0 (0x01): name
     * * Bit 1 (0x02): version
     * * Bit 2 (0x04): chainId
     * * Bit 3 (0x08): verifyingContract
     * * Bit 4 (0x10): salt
     *
     * Arguments that correspond to fields which are not present in `fields` are ignored. For example, if `fields` is
     * `0x0f` (`0b01111`), then the `salt` parameter is ignored.
     */
    function toDomainSeparator(
        bytes1 fields,
        string memory name,
        string memory version,
        uint256 chainId,
        address verifyingContract,
        bytes32 salt
    ) internal pure returns (bytes32 hash) {
        return
            toDomainSeparator(
                fields,
                keccak256(bytes(name)),
                keccak256(bytes(version)),
                chainId,
                verifyingContract,
                salt
            );
    }

    /// @dev Variant of {toDomainSeparator-bytes1-string-string-uint256-address-bytes32} that uses hashed name and version.
    function toDomainSeparator(
        bytes1 fields,
        bytes32 nameHash,
        bytes32 versionHash,
        uint256 chainId,
        address verifyingContract,
        bytes32 salt
    ) internal pure returns (bytes32 hash) {
        bytes32 domainTypeHash = toDomainTypeHash(fields);

        assembly ("memory-safe") {
            // align fields to the right for easy processing
            fields := shr(248, fields)

            // FMP used as scratch space
            let fmp := mload(0x40)
            mstore(fmp, domainTypeHash)

            let ptr := add(fmp, 0x20)
            if and(fields, 0x01) {
                mstore(ptr, nameHash)
                ptr := add(ptr, 0x20)
            }
            if and(fields, 0x02) {
                mstore(ptr, versionHash)
                ptr := add(ptr, 0x20)
            }
            if and(fields, 0x04) {
                mstore(ptr, chainId)
                ptr := add(ptr, 0x20)
            }
            if and(fields, 0x08) {
                mstore(ptr, verifyingContract)
                ptr := add(ptr, 0x20)
            }
            if and(fields, 0x10) {
                mstore(ptr, salt)
                ptr := add(ptr, 0x20)
            }

            hash := keccak256(fmp, sub(ptr, fmp))
        }
    }

    /// @dev Builds an EIP-712 domain type hash depending on the `fields` provided, following https://eips.ethereum.org/EIPS/eip-5267[ERC-5267]
    function toDomainTypeHash(bytes1 fields) internal pure returns (bytes32 hash) {
        if (fields & 0x20 == 0x20) revert ERC5267ExtensionsNotSupported();

        assembly ("memory-safe") {
            // align fields to the right for easy processing
            fields := shr(248, fields)

            // FMP used as scratch space
            let fmp := mload(0x40)
            mstore(fmp, "EIP712Domain(")

            let ptr := add(fmp, 0x0d)
            // name field
            if and(fields, 0x01) {
                mstore(ptr, "string name,")
                ptr := add(ptr, 0x0c)
            }
            // version field
            if and(fields, 0x02) {
                mstore(ptr, "string version,")
                ptr := add(ptr, 0x0f)
            }
            // chainId field
            if and(fields, 0x04) {
                mstore(ptr, "uint256 chainId,")
                ptr := add(ptr, 0x10)
            }
            // verifyingContract field
            if and(fields, 0x08) {
                mstore(ptr, "address verifyingContract,")
                ptr := add(ptr, 0x1a)
            }
            // salt field
            if and(fields, 0x10) {
                mstore(ptr, "bytes32 salt,")
                ptr := add(ptr, 0x0d)
            }
            // if any field is enabled, remove the trailing comma
            ptr := sub(ptr, iszero(iszero(and(fields, 0x1f))))
            // add the closing brace
            mstore8(ptr, 0x29) // add closing brace
            ptr := add(ptr, 1)

            hash := keccak256(fmp, sub(ptr, fmp))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.4.0) (utils/introspection/IERC165.sol)

pragma solidity >=0.4.16;

/**
 * @dev Interface of the ERC-165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[ERC].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[ERC section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

import {Panic} from "../Panic.sol";
import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Floor, // Toward negative infinity
        Ceil, // Toward positive infinity
        Trunc, // Toward zero
        Expand // Away from zero
    }

    /**
     * @dev Return the 512-bit addition of two uint256.
     *
     * The result is stored in two 256 variables such that sum = high * 2²⁵⁶ + low.
     */
    function add512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        assembly ("memory-safe") {
            low := add(a, b)
            high := lt(low, a)
        }
    }

    /**
     * @dev Return the 512-bit multiplication of two uint256.
     *
     * The result is stored in two 256 variables such that product = high * 2²⁵⁶ + low.
     */
    function mul512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
        // 512-bit multiply [high low] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
        // the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
        // variables such that product = high * 2²⁵⁶ + low.
        assembly ("memory-safe") {
            let mm := mulmod(a, b, not(0))
            low := mul(a, b)
            high := sub(sub(mm, low), lt(mm, low))
        }
    }

    /**
     * @dev Returns the addition of two unsigned integers, with a success flag (no overflow).
     */
    function tryAdd(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            success = c >= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with a success flag (no overflow).
     */
    function trySub(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a - b;
            success = c <= a;
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with a success flag (no overflow).
     */
    function tryMul(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a * b;
            assembly ("memory-safe") {
                // Only true when the multiplication doesn't overflow
                // (c / a == b) || (a == 0)
                success := or(eq(div(c, a), b), iszero(a))
            }
            // equivalent to: success ? c : 0
            result = c * SafeCast.toUint(success);
        }
    }

    /**
     * @dev Returns the division of two unsigned integers, with a success flag (no division by zero).
     */
    function tryDiv(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `DIV` opcode returns zero when the denominator is 0.
                result := div(a, b)
            }
        }
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers, with a success flag (no division by zero).
     */
    function tryMod(uint256 a, uint256 b) internal pure returns (bool success, uint256 result) {
        unchecked {
            success = b > 0;
            assembly ("memory-safe") {
                // The `MOD` opcode returns zero when the denominator is 0.
                result := mod(a, b)
            }
        }
    }

    /**
     * @dev Unsigned saturating addition, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingAdd(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryAdd(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Unsigned saturating subtraction, bounds to zero instead of overflowing.
     */
    function saturatingSub(uint256 a, uint256 b) internal pure returns (uint256) {
        (, uint256 result) = trySub(a, b);
        return result;
    }

    /**
     * @dev Unsigned saturating multiplication, bounds to `2²⁵⁶ - 1` instead of overflowing.
     */
    function saturatingMul(uint256 a, uint256 b) internal pure returns (uint256) {
        (bool success, uint256 result) = tryMul(a, b);
        return ternary(success, result, type(uint256).max);
    }

    /**
     * @dev Branchless ternary evaluation for `condition ? a : b`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `condition ? a : b`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, uint256 a, uint256 b) internal pure returns (uint256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * SafeCast.toUint(condition));
        }
    }

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

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return ternary(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) {
        unchecked {
            // (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 towards infinity instead
     * of rounding towards zero.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        if (b == 0) {
            // Guarantee the same behavior as in a regular Solidity division.
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }

        // The following calculation ensures accurate ceiling division without overflow.
        // Since a is non-zero, (a - 1) / b will not overflow.
        // The largest possible result occurs when (a - 1) / b is type(uint256).max,
        // but the largest value we can obtain is type(uint256).max - 1, which happens
        // when a = type(uint256).max and b = 1.
        unchecked {
            return SafeCast.toUint(a > 0) * ((a - 1) / b + 1);
        }
    }

    /**
     * @dev Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or
     * denominator == 0.
     *
     * 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 {
            (uint256 high, uint256 low) = mul512(x, y);

            // Handle non-overflow cases, 256 by 256 division.
            if (high == 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 low / denominator;
            }

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= high) {
                Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
            }

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

            // Make division exact by subtracting the remainder from [high low].
            uint256 remainder;
            assembly ("memory-safe") {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                high := sub(high, gt(remainder, low))
                low := sub(low, 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.

            uint256 twos = denominator & (0 - denominator);
            assembly ("memory-safe") {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [high low] by twos.
                low := div(low, twos)

                // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from high into low.
            low |= high * twos;

            // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
            // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv ≡ 1 mod 2⁴.
            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 2⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2¹⁶
            inverse *= 2 - denominator * inverse; // inverse mod 2³²
            inverse *= 2 - denominator * inverse; // inverse mod 2⁶⁴
            inverse *= 2 - denominator * inverse; // inverse mod 2¹²⁸
            inverse *= 2 - denominator * inverse; // inverse mod 2²⁵⁶

            // 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 2²⁵⁶. Since the preconditions guarantee that the outcome is
            // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and high
            // is no longer required.
            result = low * inverse;
            return result;
        }
    }

    /**
     * @dev 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) {
        return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
    }

    /**
     * @dev Calculates floor(x * y >> n) with full precision. Throws if result overflows a uint256.
     */
    function mulShr(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 result) {
        unchecked {
            (uint256 high, uint256 low) = mul512(x, y);
            if (high >= 1 << n) {
                Panic.panic(Panic.UNDER_OVERFLOW);
            }
            return (high << (256 - n)) | (low >> n);
        }
    }

    /**
     * @dev Calculates x * y >> n with full precision, following the selected rounding direction.
     */
    function mulShr(uint256 x, uint256 y, uint8 n, Rounding rounding) internal pure returns (uint256) {
        return mulShr(x, y, n) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, 1 << n) > 0);
    }

    /**
     * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
     *
     * If n is a prime, then Z/nZ is a field. In that case all elements are inversible, except 0.
     * If n is not a prime, then Z/nZ is not a field, and some elements might not be inversible.
     *
     * If the input value is not inversible, 0 is returned.
     *
     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Fermat's little theorem and get the
     * inverse using `Math.modExp(a, n - 2, n)`. See {invModPrime}.
     */
    function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
        unchecked {
            if (n == 0) return 0;

            // The inverse modulo is calculated using the Extended Euclidean Algorithm (iterative version)
            // Used to compute integers x and y such that: ax + ny = gcd(a, n).
            // When the gcd is 1, then the inverse of a modulo n exists and it's x.
            // ax + ny = 1
            // ax = 1 + (-y)n
            // ax ≡ 1 (mod n) # x is the inverse of a modulo n

            // If the remainder is 0 the gcd is n right away.
            uint256 remainder = a % n;
            uint256 gcd = n;

            // Therefore the initial coefficients are:
            // ax + ny = gcd(a, n) = n
            // 0a + 1n = n
            int256 x = 0;
            int256 y = 1;

            while (remainder != 0) {
                uint256 quotient = gcd / remainder;

                (gcd, remainder) = (
                    // The old remainder is the next gcd to try.
                    remainder,
                    // Compute the next remainder.
                    // Can't overflow given that (a % gcd) * (gcd // (a % gcd)) <= gcd
                    // where gcd is at most n (capped to type(uint256).max)
                    gcd - remainder * quotient
                );

                (x, y) = (
                    // Increment the coefficient of a.
                    y,
                    // Decrement the coefficient of n.
                    // Can overflow, but the result is casted to uint256 so that the
                    // next value of y is "wrapped around" to a value between 0 and n - 1.
                    x - y * int256(quotient)
                );
            }

            if (gcd != 1) return 0; // No inverse exists.
            return ternary(x < 0, n - uint256(-x), uint256(x)); // Wrap the result if it's negative.
        }
    }

    /**
     * @dev Variant of {invMod}. More efficient, but only works if `p` is known to be a prime greater than `2`.
     *
     * From https://en.wikipedia.org/wiki/Fermat%27s_little_theorem[Fermat's little theorem], we know that if p is
     * prime, then `a**(p-1) ≡ 1 mod p`. As a consequence, we have `a * a**(p-2) ≡ 1 mod p`, which means that
     * `a**(p-2)` is the modular multiplicative inverse of a in Fp.
     *
     * NOTE: this function does NOT check that `p` is a prime greater than `2`.
     */
    function invModPrime(uint256 a, uint256 p) internal view returns (uint256) {
        unchecked {
            return Math.modExp(a, p - 2, p);
        }
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m)
     *
     * Requirements:
     * - modulus can't be zero
     * - underlying staticcall to precompile must succeed
     *
     * IMPORTANT: The result is only valid if the underlying call succeeds. When using this function, make
     * sure the chain you're using it on supports the precompiled contract for modular exponentiation
     * at address 0x05 as specified in https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise,
     * the underlying function will succeed given the lack of a revert, but the result may be incorrectly
     * interpreted as 0.
     */
    function modExp(uint256 b, uint256 e, uint256 m) internal view returns (uint256) {
        (bool success, uint256 result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m).
     * It includes a success flag indicating if the operation succeeded. Operation will be marked as failed if trying
     * to operate modulo 0 or if the underlying precompile reverted.
     *
     * IMPORTANT: The result is only valid if the success flag is true. When using this function, make sure the chain
     * you're using it on supports the precompiled contract for modular exponentiation at address 0x05 as specified in
     * https://eips.ethereum.org/EIPS/eip-198[EIP-198]. Otherwise, the underlying function will succeed given the lack
     * of a revert, but the result may be incorrectly interpreted as 0.
     */
    function tryModExp(uint256 b, uint256 e, uint256 m) internal view returns (bool success, uint256 result) {
        if (m == 0) return (false, 0);
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            // | Offset    | Content    | Content (Hex)                                                      |
            // |-----------|------------|--------------------------------------------------------------------|
            // | 0x00:0x1f | size of b  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x20:0x3f | size of e  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x40:0x5f | size of m  | 0x0000000000000000000000000000000000000000000000000000000000000020 |
            // | 0x60:0x7f | value of b | 0x<.............................................................b> |
            // | 0x80:0x9f | value of e | 0x<.............................................................e> |
            // | 0xa0:0xbf | value of m | 0x<.............................................................m> |
            mstore(ptr, 0x20)
            mstore(add(ptr, 0x20), 0x20)
            mstore(add(ptr, 0x40), 0x20)
            mstore(add(ptr, 0x60), b)
            mstore(add(ptr, 0x80), e)
            mstore(add(ptr, 0xa0), m)

            // Given the result < m, it's guaranteed to fit in 32 bytes,
            // so we can use the memory scratch space located at offset 0.
            success := staticcall(gas(), 0x05, ptr, 0xc0, 0x00, 0x20)
            result := mload(0x00)
        }
    }

    /**
     * @dev Variant of {modExp} that supports inputs of arbitrary length.
     */
    function modExp(bytes memory b, bytes memory e, bytes memory m) internal view returns (bytes memory) {
        (bool success, bytes memory result) = tryModExp(b, e, m);
        if (!success) {
            Panic.panic(Panic.DIVISION_BY_ZERO);
        }
        return result;
    }

    /**
     * @dev Variant of {tryModExp} that supports inputs of arbitrary length.
     */
    function tryModExp(
        bytes memory b,
        bytes memory e,
        bytes memory m
    ) internal view returns (bool success, bytes memory result) {
        if (_zeroBytes(m)) return (false, new bytes(0));

        uint256 mLen = m.length;

        // Encode call args in result and move the free memory pointer
        result = abi.encodePacked(b.length, e.length, mLen, b, e, m);

        assembly ("memory-safe") {
            let dataPtr := add(result, 0x20)
            // Write result on top of args to avoid allocating extra memory.
            success := staticcall(gas(), 0x05, dataPtr, mload(result), dataPtr, mLen)
            // Overwrite the length.
            // result.length > returndatasize() is guaranteed because returndatasize() == m.length
            mstore(result, mLen)
            // Set the memory pointer after the returned data.
            mstore(0x40, add(dataPtr, mLen))
        }
    }

    /**
     * @dev Returns whether the provided byte array is zero.
     */
    function _zeroBytes(bytes memory buffer) private pure returns (bool) {
        uint256 chunk;
        for (uint256 i = 0; i < buffer.length; i += 0x20) {
            // See _unsafeReadBytesOffset from utils/Bytes.sol
            assembly ("memory-safe") {
                chunk := mload(add(add(buffer, 0x20), i))
            }
            if (chunk >> (8 * saturatingSub(i + 0x20, buffer.length)) != 0) {
                return false;
            }
        }
        return true;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded
     * towards zero.
     *
     * This method is based on Newton's method for computing square roots; the algorithm is restricted to only
     * using integer operations.
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        unchecked {
            // Take care of easy edge cases when a == 0 or a == 1
            if (a <= 1) {
                return a;
            }

            // In this function, we use Newton's method to get a root of `f(x) := x² - a`. It involves building a
            // sequence x_n that converges toward sqrt(a). For each iteration x_n, we also define the error between
            // the current value as `ε_n = | x_n - sqrt(a) |`.
            //
            // For our first estimation, we consider `e` the smallest power of 2 which is bigger than the square root
            // of the target. (i.e. `2**(e-1) ≤ sqrt(a) < 2**e`). We know that `e ≤ 128` because `(2¹²⁸)² = 2²⁵⁶` is
            // bigger than any uint256.
            //
            // By noticing that
            // `2**(e-1) ≤ sqrt(a) < 2**e → (2**(e-1))² ≤ a < (2**e)² → 2**(2*e-2) ≤ a < 2**(2*e)`
            // we can deduce that `e - 1` is `log2(a) / 2`. We can thus compute `x_n = 2**(e-1)` using a method similar
            // to the msb function.
            uint256 aa = a;
            uint256 xn = 1;

            if (aa >= (1 << 128)) {
                aa >>= 128;
                xn <<= 64;
            }
            if (aa >= (1 << 64)) {
                aa >>= 64;
                xn <<= 32;
            }
            if (aa >= (1 << 32)) {
                aa >>= 32;
                xn <<= 16;
            }
            if (aa >= (1 << 16)) {
                aa >>= 16;
                xn <<= 8;
            }
            if (aa >= (1 << 8)) {
                aa >>= 8;
                xn <<= 4;
            }
            if (aa >= (1 << 4)) {
                aa >>= 4;
                xn <<= 2;
            }
            if (aa >= (1 << 2)) {
                xn <<= 1;
            }

            // We now have x_n such that `x_n = 2**(e-1) ≤ sqrt(a) < 2**e = 2 * x_n`. This implies ε_n ≤ 2**(e-1).
            //
            // We can refine our estimation by noticing that the middle of that interval minimizes the error.
            // If we move x_n to equal 2**(e-1) + 2**(e-2), then we reduce the error to ε_n ≤ 2**(e-2).
            // This is going to be our x_0 (and ε_0)
            xn = (3 * xn) >> 1; // ε_0 := | x_0 - sqrt(a) | ≤ 2**(e-2)

            // From here, Newton's method give us:
            // x_{n+1} = (x_n + a / x_n) / 2
            //
            // One should note that:
            // x_{n+1}² - a = ((x_n + a / x_n) / 2)² - a
            //              = ((x_n² + a) / (2 * x_n))² - a
            //              = (x_n⁴ + 2 * a * x_n² + a²) / (4 * x_n²) - a
            //              = (x_n⁴ + 2 * a * x_n² + a² - 4 * a * x_n²) / (4 * x_n²)
            //              = (x_n⁴ - 2 * a * x_n² + a²) / (4 * x_n²)
            //              = (x_n² - a)² / (2 * x_n)²
            //              = ((x_n² - a) / (2 * x_n))²
            //              ≥ 0
            // Which proves that for all n ≥ 1, sqrt(a) ≤ x_n
            //
            // This gives us the proof of quadratic convergence of the sequence:
            // ε_{n+1} = | x_{n+1} - sqrt(a) |
            //         = | (x_n + a / x_n) / 2 - sqrt(a) |
            //         = | (x_n² + a - 2*x_n*sqrt(a)) / (2 * x_n) |
            //         = | (x_n - sqrt(a))² / (2 * x_n) |
            //         = | ε_n² / (2 * x_n) |
            //         = ε_n² / | (2 * x_n) |
            //
            // For the first iteration, we have a special case where x_0 is known:
            // ε_1 = ε_0² / | (2 * x_0) |
            //     ≤ (2**(e-2))² / (2 * (2**(e-1) + 2**(e-2)))
            //     ≤ 2**(2*e-4) / (3 * 2**(e-1))
            //     ≤ 2**(e-3) / 3
            //     ≤ 2**(e-3-log2(3))
            //     ≤ 2**(e-4.5)
            //
            // For the following iterations, we use the fact that, 2**(e-1) ≤ sqrt(a) ≤ x_n:
            // ε_{n+1} = ε_n² / | (2 * x_n) |
            //         ≤ (2**(e-k))² / (2 * 2**(e-1))
            //         ≤ 2**(2*e-2*k) / 2**e
            //         ≤ 2**(e-2*k)
            xn = (xn + a / xn) >> 1; // ε_1 := | x_1 - sqrt(a) | ≤ 2**(e-4.5)  -- special case, see above
            xn = (xn + a / xn) >> 1; // ε_2 := | x_2 - sqrt(a) | ≤ 2**(e-9)    -- general case with k = 4.5
            xn = (xn + a / xn) >> 1; // ε_3 := | x_3 - sqrt(a) | ≤ 2**(e-18)   -- general case with k = 9
            xn = (xn + a / xn) >> 1; // ε_4 := | x_4 - sqrt(a) | ≤ 2**(e-36)   -- general case with k = 18
            xn = (xn + a / xn) >> 1; // ε_5 := | x_5 - sqrt(a) | ≤ 2**(e-72)   -- general case with k = 36
            xn = (xn + a / xn) >> 1; // ε_6 := | x_6 - sqrt(a) | ≤ 2**(e-144)  -- general case with k = 72

            // Because e ≤ 128 (as discussed during the first estimation phase), we know have reached a precision
            // ε_6 ≤ 2**(e-144) < 1. Given we're operating on integers, then we can ensure that xn is now either
            // sqrt(a) or sqrt(a) + 1.
            return xn - SafeCast.toUint(xn > a / xn);
        }
    }

    /**
     * @dev 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 + SafeCast.toUint(unsignedRoundsUp(rounding) && result * result < a);
        }
    }

    /**
     * @dev Return the log in base 2 of a positive value rounded towards zero.
     * Returns 0 if given 0.
     */
    function log2(uint256 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // If upper 8 bits of 16-bit half set, add 8 to result
        r |= SafeCast.toUint((x >> r) > 0xff) << 3;
        // If upper 4 bits of 8-bit half set, add 4 to result
        r |= SafeCast.toUint((x >> r) > 0xf) << 2;

        // Shifts value right by the current result and use it as an index into this lookup table:
        //
        // | x (4 bits) |  index  | table[index] = MSB position |
        // |------------|---------|-----------------------------|
        // |    0000    |    0    |        table[0] = 0         |
        // |    0001    |    1    |        table[1] = 0         |
        // |    0010    |    2    |        table[2] = 1         |
        // |    0011    |    3    |        table[3] = 1         |
        // |    0100    |    4    |        table[4] = 2         |
        // |    0101    |    5    |        table[5] = 2         |
        // |    0110    |    6    |        table[6] = 2         |
        // |    0111    |    7    |        table[7] = 2         |
        // |    1000    |    8    |        table[8] = 3         |
        // |    1001    |    9    |        table[9] = 3         |
        // |    1010    |   10    |        table[10] = 3        |
        // |    1011    |   11    |        table[11] = 3        |
        // |    1100    |   12    |        table[12] = 3        |
        // |    1101    |   13    |        table[13] = 3        |
        // |    1110    |   14    |        table[14] = 3        |
        // |    1111    |   15    |        table[15] = 3        |
        //
        // The lookup table is represented as a 32-byte value with the MSB positions for 0-15 in the first 16 bytes (most significant half).
        assembly ("memory-safe") {
            r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030300000000000000000000000000000000))
        }
    }

    /**
     * @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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << result < value);
        }
    }

    /**
     * @dev Return the log in base 10 of a positive value rounded towards zero.
     * 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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 10 ** result < value);
        }
    }

    /**
     * @dev Return the log in base 256 of a positive value rounded towards zero.
     * 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 x) internal pure returns (uint256 r) {
        // If value has upper 128 bits set, log2 result is at least 128
        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
        // If upper 64 bits of 128-bit half set, add 64 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
        // If upper 32 bits of 64-bit half set, add 32 to result
        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
        // If upper 16 bits of 32-bit half set, add 16 to result
        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
        // Add 1 if upper 8 bits of 16-bit half set, and divide accumulated result by 8
        return (r >> 3) | SafeCast.toUint((x >> r) > 0xff);
    }

    /**
     * @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 + SafeCast.toUint(unsignedRoundsUp(rounding) && 1 << (result << 3) < value);
        }
    }

    /**
     * @dev Returns whether a provided rounding mode is considered rounding up for unsigned integers.
     */
    function unsignedRoundsUp(Rounding rounding) internal pure returns (bool) {
        return uint8(rounding) % 2 == 1;
    }

    /**
     * @dev Counts the number of leading zero bits in a uint256.
     */
    function clz(uint256 x) internal pure returns (uint256) {
        return ternary(x == 0, 256, 255 - log2(x));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.6.0) (utils/math/SafeCast.sol)
// This file was procedurally generated from scripts/generate/templates/SafeCast.js.

pragma solidity ^0.8.20;

/**
 * @dev Wrappers over Solidity's uintXX/intXX/bool casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeCast {
    /**
     * @dev Value doesn't fit in a uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in a uint of `bits` size.
     */
    error SafeCastOverflowedIntToUint(int256 value);

    /**
     * @dev Value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedIntDowncast(uint8 bits, int256 value);

    /**
     * @dev A uint value doesn't fit in an int of `bits` size.
     */
    error SafeCastOverflowedUintToInt(uint256 value);

    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        if (value > type(uint248).max) {
            revert SafeCastOverflowedUintDowncast(248, value);
        }
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        if (value > type(uint240).max) {
            revert SafeCastOverflowedUintDowncast(240, value);
        }
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        if (value > type(uint232).max) {
            revert SafeCastOverflowedUintDowncast(232, value);
        }
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        if (value > type(uint224).max) {
            revert SafeCastOverflowedUintDowncast(224, value);
        }
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        if (value > type(uint216).max) {
            revert SafeCastOverflowedUintDowncast(216, value);
        }
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        if (value > type(uint208).max) {
            revert SafeCastOverflowedUintDowncast(208, value);
        }
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        if (value > type(uint200).max) {
            revert SafeCastOverflowedUintDowncast(200, value);
        }
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        if (value > type(uint192).max) {
            revert SafeCastOverflowedUintDowncast(192, value);
        }
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        if (value > type(uint184).max) {
            revert SafeCastOverflowedUintDowncast(184, value);
        }
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        if (value > type(uint176).max) {
            revert SafeCastOverflowedUintDowncast(176, value);
        }
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        if (value > type(uint168).max) {
            revert SafeCastOverflowedUintDowncast(168, value);
        }
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        if (value > type(uint160).max) {
            revert SafeCastOverflowedUintDowncast(160, value);
        }
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        if (value > type(uint152).max) {
            revert SafeCastOverflowedUintDowncast(152, value);
        }
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        if (value > type(uint144).max) {
            revert SafeCastOverflowedUintDowncast(144, value);
        }
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        if (value > type(uint136).max) {
            revert SafeCastOverflowedUintDowncast(136, value);
        }
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        if (value > type(uint128).max) {
            revert SafeCastOverflowedUintDowncast(128, value);
        }
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        if (value > type(uint120).max) {
            revert SafeCastOverflowedUintDowncast(120, value);
        }
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        if (value > type(uint112).max) {
            revert SafeCastOverflowedUintDowncast(112, value);
        }
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        if (value > type(uint104).max) {
            revert SafeCastOverflowedUintDowncast(104, value);
        }
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        if (value > type(uint96).max) {
            revert SafeCastOverflowedUintDowncast(96, value);
        }
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        if (value > type(uint88).max) {
            revert SafeCastOverflowedUintDowncast(88, value);
        }
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        if (value > type(uint80).max) {
            revert SafeCastOverflowedUintDowncast(80, value);
        }
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        if (value > type(uint72).max) {
            revert SafeCastOverflowedUintDowncast(72, value);
        }
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        if (value > type(uint64).max) {
            revert SafeCastOverflowedUintDowncast(64, value);
        }
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        if (value > type(uint56).max) {
            revert SafeCastOverflowedUintDowncast(56, value);
        }
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        if (value > type(uint48).max) {
            revert SafeCastOverflowedUintDowncast(48, value);
        }
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        if (value > type(uint40).max) {
            revert SafeCastOverflowedUintDowncast(40, value);
        }
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        if (value > type(uint32).max) {
            revert SafeCastOverflowedUintDowncast(32, value);
        }
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        if (value > type(uint24).max) {
            revert SafeCastOverflowedUintDowncast(24, value);
        }
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        if (value > type(uint16).max) {
            revert SafeCastOverflowedUintDowncast(16, value);
        }
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        if (value > type(uint8).max) {
            revert SafeCastOverflowedUintDowncast(8, value);
        }
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        if (value < 0) {
            revert SafeCastOverflowedIntToUint(value);
        }
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     */
    function toInt248(int256 value) internal pure returns (int248 downcasted) {
        downcasted = int248(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(248, value);
        }
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     */
    function toInt240(int256 value) internal pure returns (int240 downcasted) {
        downcasted = int240(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(240, value);
        }
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     */
    function toInt232(int256 value) internal pure returns (int232 downcasted) {
        downcasted = int232(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(232, value);
        }
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     */
    function toInt224(int256 value) internal pure returns (int224 downcasted) {
        downcasted = int224(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(224, value);
        }
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     */
    function toInt216(int256 value) internal pure returns (int216 downcasted) {
        downcasted = int216(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(216, value);
        }
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     */
    function toInt208(int256 value) internal pure returns (int208 downcasted) {
        downcasted = int208(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(208, value);
        }
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     */
    function toInt200(int256 value) internal pure returns (int200 downcasted) {
        downcasted = int200(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(200, value);
        }
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     */
    function toInt192(int256 value) internal pure returns (int192 downcasted) {
        downcasted = int192(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(192, value);
        }
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     */
    function toInt184(int256 value) internal pure returns (int184 downcasted) {
        downcasted = int184(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(184, value);
        }
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     */
    function toInt176(int256 value) internal pure returns (int176 downcasted) {
        downcasted = int176(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(176, value);
        }
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     */
    function toInt168(int256 value) internal pure returns (int168 downcasted) {
        downcasted = int168(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(168, value);
        }
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     */
    function toInt160(int256 value) internal pure returns (int160 downcasted) {
        downcasted = int160(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(160, value);
        }
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     */
    function toInt152(int256 value) internal pure returns (int152 downcasted) {
        downcasted = int152(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(152, value);
        }
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     */
    function toInt144(int256 value) internal pure returns (int144 downcasted) {
        downcasted = int144(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(144, value);
        }
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     */
    function toInt136(int256 value) internal pure returns (int136 downcasted) {
        downcasted = int136(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(136, value);
        }
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     */
    function toInt128(int256 value) internal pure returns (int128 downcasted) {
        downcasted = int128(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(128, value);
        }
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     */
    function toInt120(int256 value) internal pure returns (int120 downcasted) {
        downcasted = int120(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(120, value);
        }
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     */
    function toInt112(int256 value) internal pure returns (int112 downcasted) {
        downcasted = int112(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(112, value);
        }
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     */
    function toInt104(int256 value) internal pure returns (int104 downcasted) {
        downcasted = int104(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(104, value);
        }
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     */
    function toInt96(int256 value) internal pure returns (int96 downcasted) {
        downcasted = int96(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(96, value);
        }
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     */
    function toInt88(int256 value) internal pure returns (int88 downcasted) {
        downcasted = int88(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(88, value);
        }
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     */
    function toInt80(int256 value) internal pure returns (int80 downcasted) {
        downcasted = int80(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(80, value);
        }
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     */
    function toInt72(int256 value) internal pure returns (int72 downcasted) {
        downcasted = int72(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(72, value);
        }
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     */
    function toInt64(int256 value) internal pure returns (int64 downcasted) {
        downcasted = int64(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(64, value);
        }
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     */
    function toInt56(int256 value) internal pure returns (int56 downcasted) {
        downcasted = int56(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(56, value);
        }
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     */
    function toInt48(int256 value) internal pure returns (int48 downcasted) {
        downcasted = int48(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(48, value);
        }
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     */
    function toInt40(int256 value) internal pure returns (int40 downcasted) {
        downcasted = int40(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(40, value);
        }
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     */
    function toInt32(int256 value) internal pure returns (int32 downcasted) {
        downcasted = int32(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(32, value);
        }
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     */
    function toInt24(int256 value) internal pure returns (int24 downcasted) {
        downcasted = int24(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(24, value);
        }
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     */
    function toInt16(int256 value) internal pure returns (int16 downcasted) {
        downcasted = int16(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(16, value);
        }
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     */
    function toInt8(int256 value) internal pure returns (int8 downcasted) {
        downcasted = int8(value);
        if (downcasted != value) {
            revert SafeCastOverflowedIntDowncast(8, value);
        }
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        if (value > uint256(type(int256).max)) {
            revert SafeCastOverflowedUintToInt(value);
        }
        return int256(value);
    }

    /**
     * @dev Cast a boolean (false or true) to a uint256 (0 or 1) with no jump.
     */
    function toUint(bool b) internal pure returns (uint256 u) {
        assembly ("memory-safe") {
            u := iszero(iszero(b))
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

import {SafeCast} from "./SafeCast.sol";

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Branchless ternary evaluation for `a ? b : c`. Gas costs are constant.
     *
     * IMPORTANT: This function may reduce bytecode size and consume less gas when used standalone.
     * However, the compiler may optimize Solidity ternary operations (i.e. `a ? b : c`) to only compute
     * one branch when needed, making this function more expensive.
     */
    function ternary(bool condition, int256 a, int256 b) internal pure returns (int256) {
        unchecked {
            // branchless ternary works because:
            // b ^ (a ^ b) == a
            // b ^ 0 == b
            return b ^ ((a ^ b) * int256(SafeCast.toUint(condition)));
        }
    }

    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return ternary(a > b, a, b);
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return ternary(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 {
            // Formula from the "Bit Twiddling Hacks" by Sean Eron Anderson.
            // Since `n` is a signed integer, the generated bytecode will use the SAR opcode to perform the right shift,
            // taking advantage of the most significant (or "sign" bit) in two's complement representation.
            // This opcode adds new most significant bits set to the value of the previous most significant bit. As a result,
            // the mask will either be `bytes32(0)` (if n is positive) or `~bytes32(0)` (if n is negative).
            int256 mask = n >> 255;

            // A `bytes32(0)` mask leaves the input unchanged, while a `~bytes32(0)` mask complements it.
            return uint256((n + mask) ^ mask);
        }
    }
}