/**
 *Submitted for verification at taikoscan.io on 2025-02-17
*/

// Sources flattened with hardhat v2.22.17 https://hardhat.org

// SPDX-License-Identifier: GPL-3.0 AND MIT

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.1) (utils/Context.sol)

pragma solidity ^0.8.20;

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

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

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }
}

// File @openzeppelin/contracts/access/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)

pragma solidity ^0.8.20;

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

    /**
     * @dev The caller account is not authorized to perform an operation.
     */
    error OwnableUnauthorizedAccount(address account);

    /**
     * @dev The owner is not a valid owner account. (eg. `address(0)`)
     */
    error OwnableInvalidOwner(address owner);

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

    /**
     * @dev Initializes the contract setting the address provided by the deployer as the initial owner.
     */
    constructor(address initialOwner) {
        if (initialOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(initialOwner);
    }

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

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

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        if (owner() != _msgSender()) {
            revert OwnableUnauthorizedAccount(_msgSender());
        }
    }

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

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        if (newOwner == address(0)) {
            revert OwnableInvalidOwner(address(0));
        }
        _transferOwnership(newOwner);
    }

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

// File @openzeppelin/contracts/utils/introspection/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/introspection/IERC165.sol)

pragma solidity ^0.8.20;

/**
 * @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);
}

// File @openzeppelin/contracts/interfaces/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/IERC2981.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface for the NFT Royalty Standard.
 *
 * A standardized way to retrieve royalty payment information for non-fungible tokens (NFTs) to enable universal
 * support for royalty payments across all NFT marketplaces and ecosystem participants.
 */
interface IERC2981 is IERC165 {
    /**
     * @dev Returns how much royalty is owed and to whom, based on a sale price that may be denominated in any unit of
     * exchange. The royalty amount is denominated and should be paid in that same unit of exchange.
     *
     * NOTE: ERC-2981 allows setting the royalty to 100% of the price. In that case all the price would be sent to the
     * royalty receiver and 0 tokens to the seller. Contracts dealing with royalty should consider empty transfers.
     */
    function royaltyInfo(
        uint256 tokenId,
        uint256 salePrice
    ) external view returns (address receiver, uint256 royaltyAmount);
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Errors.sol)

pragma solidity ^0.8.20;

/**
 * @dev Collection of common custom errors used in multiple contracts
 *
 * IMPORTANT: Backwards compatibility is not guaranteed in future versions of the library.
 * It is recommended to avoid relying on the error API for critical functionality.
 *
 * _Available since v5.1._
 */
library Errors {
    /**
     * @dev The ETH balance of the account is not enough to perform the operation.
     */
    error InsufficientBalance(uint256 balance, uint256 needed);

    /**
     * @dev A call to an address target failed. The target may have reverted.
     */
    error FailedCall();

    /**
     * @dev The deployment failed.
     */
    error FailedDeployment();

    /**
     * @dev A necessary precompile is missing.
     */
    error MissingPrecompile(address);
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Create2.sol)

pragma solidity ^0.8.20;

/**
 * @dev Helper to make usage of the `CREATE2` EVM opcode easier and safer.
 * `CREATE2` can be used to compute in advance the address where a smart
 * contract will be deployed, which allows for interesting new mechanisms known
 * as 'counterfactual interactions'.
 *
 * See the https://eips.ethereum.org/EIPS/eip-1014#motivation[EIP] for more
 * information.
 */
library Create2 {
    /**
     * @dev There's no code to deploy.
     */
    error Create2EmptyBytecode();

    /**
     * @dev Deploys a contract using `CREATE2`. The address where the contract
     * will be deployed can be known in advance via {computeAddress}.
     *
     * The bytecode for a contract can be obtained from Solidity with
     * `type(contractName).creationCode`.
     *
     * Requirements:
     *
     * - `bytecode` must not be empty.
     * - `salt` must have not been used for `bytecode` already.
     * - the factory must have a balance of at least `amount`.
     * - if `amount` is non-zero, `bytecode` must have a `payable` constructor.
     */
    function deploy(
        uint256 amount,
        bytes32 salt,
        bytes memory bytecode
    ) internal returns (address addr) {
        if (address(this).balance < amount) {
            revert Errors.InsufficientBalance(address(this).balance, amount);
        }
        if (bytecode.length == 0) {
            revert Create2EmptyBytecode();
        }
        assembly ("memory-safe") {
            addr := create2(amount, add(bytecode, 0x20), mload(bytecode), salt)
            // if no address was created, and returndata is not empty, bubble revert
            if and(iszero(addr), not(iszero(returndatasize()))) {
                let p := mload(0x40)
                returndatacopy(p, 0, returndatasize())
                revert(p, returndatasize())
            }
        }
        if (addr == address(0)) {
            revert Errors.FailedDeployment();
        }
    }

    /**
     * @dev Returns the address where a contract will be stored if deployed via {deploy}. Any change in the
     * `bytecodeHash` or `salt` will result in a new destination address.
     */
    function computeAddress(
        bytes32 salt,
        bytes32 bytecodeHash
    ) internal view returns (address) {
        return computeAddress(salt, bytecodeHash, address(this));
    }

    /**
     * @dev Returns the address where a contract will be stored if deployed via {deploy} from a contract located at
     * `deployer`. If `deployer` is this contract's address, returns the same value as {computeAddress}.
     */
    function computeAddress(
        bytes32 salt,
        bytes32 bytecodeHash,
        address deployer
    ) internal pure returns (address addr) {
        assembly ("memory-safe") {
            let ptr := mload(0x40) // Get free memory pointer

            // |                   | ↓ ptr ...  ↓ ptr + 0x0B (start) ...  ↓ ptr + 0x20 ...  ↓ ptr + 0x40 ...   |
            // |-------------------|---------------------------------------------------------------------------|
            // | bytecodeHash      |                                                        CCCCCCCCCCCCC...CC |
            // | salt              |                                      BBBBBBBBBBBBB...BB                   |
            // | deployer          | 000000...0000AAAAAAAAAAAAAAAAAAA...AA                                     |
            // | 0xFF              |            FF                                                             |
            // |-------------------|---------------------------------------------------------------------------|
            // | memory            | 000000...00FFAAAAAAAAAAAAAAAAAAA...AABBBBBBBBBBBBB...BBCCCCCCCCCCCCC...CC |
            // | keccak(start, 85) |            ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑ |

            mstore(add(ptr, 0x40), bytecodeHash)
            mstore(add(ptr, 0x20), salt)
            mstore(ptr, deployer) // Right-aligned with 12 preceding garbage bytes
            let start := add(ptr, 0x0b) // The hashed data starts at the final garbage byte which we will set to 0xff
            mstore8(start, 0xff)
            addr := and(
                keccak256(start, 85),
                0xffffffffffffffffffffffffffffffffffffffff
            )
        }
    }
}

// File @openzeppelin/contracts/proxy/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.2.0) (proxy/Clones.sol)

pragma solidity ^0.8.20;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[ERC-1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * The library includes functions to deploy a proxy using either `create` (traditional deployment) or `create2`
 * (salted deterministic deployment). It also includes functions to predict the addresses of clones deployed using the
 * deterministic method.
 */
library Clones {
    error CloneArgumentsTooLong();

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create opcode, which should never revert.
     */
    function clone(address implementation) internal returns (address instance) {
        return clone(implementation, 0);
    }

    /**
     * @dev Same as {xref-Clones-clone-address-}[clone], but with a `value` parameter to send native currency
     * to the new contract.
     *
     * NOTE: Using a non-zero value at creation will require the contract using this function (e.g. a factory)
     * to always have enough balance for new deployments. Consider exposing this function under a payable method.
     */
    function clone(
        address implementation,
        uint256 value
    ) internal returns (address instance) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        assembly ("memory-safe") {
            // Cleans the upper 96 bits of the `implementation` word, then packs the first 3 bytes
            // of the `implementation` address with the bytecode before the address.
            mstore(
                0x00,
                or(
                    shr(0xe8, shl(0x60, implementation)),
                    0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000
                )
            )
            // Packs the remaining 17 bytes of `implementation` with the bytecode after the address.
            mstore(
                0x20,
                or(shl(0x78, implementation), 0x5af43d82803e903d91602b57fd5bf3)
            )
            instance := create(value, 0x09, 0x37)
        }
        if (instance == address(0)) {
            revert Errors.FailedDeployment();
        }
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `implementation` and `salt` multiple times will revert, since
     * the clones cannot be deployed twice at the same address.
     */
    function cloneDeterministic(
        address implementation,
        bytes32 salt
    ) internal returns (address instance) {
        return cloneDeterministic(implementation, salt, 0);
    }

    /**
     * @dev Same as {xref-Clones-cloneDeterministic-address-bytes32-}[cloneDeterministic], but with
     * a `value` parameter to send native currency to the new contract.
     *
     * NOTE: Using a non-zero value at creation will require the contract using this function (e.g. a factory)
     * to always have enough balance for new deployments. Consider exposing this function under a payable method.
     */
    function cloneDeterministic(
        address implementation,
        bytes32 salt,
        uint256 value
    ) internal returns (address instance) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        assembly ("memory-safe") {
            // Cleans the upper 96 bits of the `implementation` word, then packs the first 3 bytes
            // of the `implementation` address with the bytecode before the address.
            mstore(
                0x00,
                or(
                    shr(0xe8, shl(0x60, implementation)),
                    0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000
                )
            )
            // Packs the remaining 17 bytes of `implementation` with the bytecode after the address.
            mstore(
                0x20,
                or(shl(0x78, implementation), 0x5af43d82803e903d91602b57fd5bf3)
            )
            instance := create2(value, 0x09, 0x37, salt)
        }
        if (instance == address(0)) {
            revert Errors.FailedDeployment();
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        assembly ("memory-safe") {
            let ptr := mload(0x40)
            mstore(add(ptr, 0x38), deployer)
            mstore(add(ptr, 0x24), 0x5af43d82803e903d91602b57fd5bf3ff)
            mstore(add(ptr, 0x14), implementation)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73)
            mstore(add(ptr, 0x58), salt)
            mstore(add(ptr, 0x78), keccak256(add(ptr, 0x0c), 0x37))
            predicted := and(
                keccak256(add(ptr, 0x43), 0x55),
                0xffffffffffffffffffffffffffffffffffffffff
            )
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt
    ) internal view returns (address predicted) {
        return predictDeterministicAddress(implementation, salt, address(this));
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behavior of `implementation` with custom
     * immutable arguments. These are provided through `args` and cannot be changed after deployment. To
     * access the arguments within the implementation, use {fetchCloneArgs}.
     *
     * This function uses the create opcode, which should never revert.
     */
    function cloneWithImmutableArgs(
        address implementation,
        bytes memory args
    ) internal returns (address instance) {
        return cloneWithImmutableArgs(implementation, args, 0);
    }

    /**
     * @dev Same as {xref-Clones-cloneWithImmutableArgs-address-bytes-}[cloneWithImmutableArgs], but with a `value`
     * parameter to send native currency to the new contract.
     *
     * NOTE: Using a non-zero value at creation will require the contract using this function (e.g. a factory)
     * to always have enough balance for new deployments. Consider exposing this function under a payable method.
     */
    function cloneWithImmutableArgs(
        address implementation,
        bytes memory args,
        uint256 value
    ) internal returns (address instance) {
        if (address(this).balance < value) {
            revert Errors.InsufficientBalance(address(this).balance, value);
        }
        bytes memory bytecode = _cloneCodeWithImmutableArgs(
            implementation,
            args
        );
        assembly ("memory-safe") {
            instance := create(value, add(bytecode, 0x20), mload(bytecode))
        }
        if (instance == address(0)) {
            revert Errors.FailedDeployment();
        }
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation` with custom
     * immutable arguments. These are provided through `args` and cannot be changed after deployment. To
     * access the arguments within the implementation, use {fetchCloneArgs}.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy the clone. Using the same
     * `implementation`, `args` and `salt` multiple times will revert, since the clones cannot be deployed twice
     * at the same address.
     */
    function cloneDeterministicWithImmutableArgs(
        address implementation,
        bytes memory args,
        bytes32 salt
    ) internal returns (address instance) {
        return
            cloneDeterministicWithImmutableArgs(implementation, args, salt, 0);
    }

    /**
     * @dev Same as {xref-Clones-cloneDeterministicWithImmutableArgs-address-bytes-bytes32-}[cloneDeterministicWithImmutableArgs],
     * but with a `value` parameter to send native currency to the new contract.
     *
     * NOTE: Using a non-zero value at creation will require the contract using this function (e.g. a factory)
     * to always have enough balance for new deployments. Consider exposing this function under a payable method.
     */
    function cloneDeterministicWithImmutableArgs(
        address implementation,
        bytes memory args,
        bytes32 salt,
        uint256 value
    ) internal returns (address instance) {
        bytes memory bytecode = _cloneCodeWithImmutableArgs(
            implementation,
            args
        );
        return Create2.deploy(value, salt, bytecode);
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministicWithImmutableArgs}.
     */
    function predictDeterministicAddressWithImmutableArgs(
        address implementation,
        bytes memory args,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes memory bytecode = _cloneCodeWithImmutableArgs(
            implementation,
            args
        );
        return Create2.computeAddress(salt, keccak256(bytecode), deployer);
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministicWithImmutableArgs}.
     */
    function predictDeterministicAddressWithImmutableArgs(
        address implementation,
        bytes memory args,
        bytes32 salt
    ) internal view returns (address predicted) {
        return
            predictDeterministicAddressWithImmutableArgs(
                implementation,
                args,
                salt,
                address(this)
            );
    }

    /**
     * @dev Get the immutable args attached to a clone.
     *
     * - If `instance` is a clone that was deployed using `clone` or `cloneDeterministic`, this
     *   function will return an empty array.
     * - If `instance` is a clone that was deployed using `cloneWithImmutableArgs` or
     *   `cloneDeterministicWithImmutableArgs`, this function will return the args array used at
     *   creation.
     * - If `instance` is NOT a clone deployed using this library, the behavior is undefined. This
     *   function should only be used to check addresses that are known to be clones.
     */
    function fetchCloneArgs(
        address instance
    ) internal view returns (bytes memory) {
        bytes memory result = new bytes(instance.code.length - 45); // revert if length is too short
        assembly ("memory-safe") {
            extcodecopy(instance, add(result, 32), 45, mload(result))
        }
        return result;
    }

    /**
     * @dev Helper that prepares the initcode of the proxy with immutable args.
     *
     * An assembly variant of this function requires copying the `args` array, which can be efficiently done using
     * `mcopy`. Unfortunately, that opcode is not available before cancun. A pure solidity implementation using
     * abi.encodePacked is more expensive but also more portable and easier to review.
     *
     * NOTE: https://eips.ethereum.org/EIPS/eip-170[EIP-170] limits the length of the contract code to 24576 bytes.
     * With the proxy code taking 45 bytes, that limits the length of the immutable args to 24531 bytes.
     */
    function _cloneCodeWithImmutableArgs(
        address implementation,
        bytes memory args
    ) private pure returns (bytes memory) {
        if (args.length > 24531) revert CloneArgumentsTooLong();
        return
            abi.encodePacked(
                hex"61",
                uint16(args.length + 45),
                hex"3d81600a3d39f3363d3d373d3d3d363d73",
                implementation,
                hex"5af43d82803e903d91602b57fd5bf3",
                args
            );
    }
}

// File @openzeppelin/contracts/utils/introspection/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/introspection/ERC165.sol)

pragma solidity ^0.8.20;

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC-165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(
        bytes4 interfaceId
    ) public view virtual returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// File @openzeppelin/contracts/token/common/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/common/ERC2981.sol)

pragma solidity ^0.8.20;

/**
 * @dev Implementation of the NFT Royalty Standard, a standardized way to retrieve royalty payment information.
 *
 * Royalty information can be specified globally for all token ids via {_setDefaultRoyalty}, and/or individually for
 * specific token ids via {_setTokenRoyalty}. The latter takes precedence over the first.
 *
 * Royalty is specified as a fraction of sale price. {_feeDenominator} is overridable but defaults to 10000, meaning the
 * fee is specified in basis points by default.
 *
 * IMPORTANT: ERC-2981 only specifies a way to signal royalty information and does not enforce its payment. See
 * https://eips.ethereum.org/EIPS/eip-2981#optional-royalty-payments[Rationale] in the ERC. Marketplaces are expected to
 * voluntarily pay royalties together with sales, but note that this standard is not yet widely supported.
 */
abstract contract ERC2981 is IERC2981, ERC165 {
    struct RoyaltyInfo {
        address receiver;
        uint96 royaltyFraction;
    }

    RoyaltyInfo private _defaultRoyaltyInfo;
    mapping(uint256 tokenId => RoyaltyInfo) private _tokenRoyaltyInfo;

    /**
     * @dev The default royalty set is invalid (eg. (numerator / denominator) >= 1).
     */
    error ERC2981InvalidDefaultRoyalty(uint256 numerator, uint256 denominator);

    /**
     * @dev The default royalty receiver is invalid.
     */
    error ERC2981InvalidDefaultRoyaltyReceiver(address receiver);

    /**
     * @dev The royalty set for an specific `tokenId` is invalid (eg. (numerator / denominator) >= 1).
     */
    error ERC2981InvalidTokenRoyalty(
        uint256 tokenId,
        uint256 numerator,
        uint256 denominator
    );

    /**
     * @dev The royalty receiver for `tokenId` is invalid.
     */
    error ERC2981InvalidTokenRoyaltyReceiver(uint256 tokenId, address receiver);

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(
        bytes4 interfaceId
    ) public view virtual override(IERC165, ERC165) returns (bool) {
        return
            interfaceId == type(IERC2981).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @inheritdoc IERC2981
     */
    function royaltyInfo(
        uint256 tokenId,
        uint256 salePrice
    ) public view virtual returns (address receiver, uint256 amount) {
        RoyaltyInfo storage _royaltyInfo = _tokenRoyaltyInfo[tokenId];
        address royaltyReceiver = _royaltyInfo.receiver;
        uint96 royaltyFraction = _royaltyInfo.royaltyFraction;

        if (royaltyReceiver == address(0)) {
            royaltyReceiver = _defaultRoyaltyInfo.receiver;
            royaltyFraction = _defaultRoyaltyInfo.royaltyFraction;
        }

        uint256 royaltyAmount = (salePrice * royaltyFraction) /
            _feeDenominator();

        return (royaltyReceiver, royaltyAmount);
    }

    /**
     * @dev The denominator with which to interpret the fee set in {_setTokenRoyalty} and {_setDefaultRoyalty} as a
     * fraction of the sale price. Defaults to 10000 so fees are expressed in basis points, but may be customized by an
     * override.
     */
    function _feeDenominator() internal pure virtual returns (uint96) {
        return 10000;
    }

    /**
     * @dev Sets the royalty information that all ids in this contract will default to.
     *
     * Requirements:
     *
     * - `receiver` cannot be the zero address.
     * - `feeNumerator` cannot be greater than the fee denominator.
     */
    function _setDefaultRoyalty(
        address receiver,
        uint96 feeNumerator
    ) internal virtual {
        uint256 denominator = _feeDenominator();
        if (feeNumerator > denominator) {
            // Royalty fee will exceed the sale price
            revert ERC2981InvalidDefaultRoyalty(feeNumerator, denominator);
        }
        if (receiver == address(0)) {
            revert ERC2981InvalidDefaultRoyaltyReceiver(address(0));
        }

        _defaultRoyaltyInfo = RoyaltyInfo(receiver, feeNumerator);
    }

    /**
     * @dev Removes default royalty information.
     */
    function _deleteDefaultRoyalty() internal virtual {
        delete _defaultRoyaltyInfo;
    }

    /**
     * @dev Sets the royalty information for a specific token id, overriding the global default.
     *
     * Requirements:
     *
     * - `receiver` cannot be the zero address.
     * - `feeNumerator` cannot be greater than the fee denominator.
     */
    function _setTokenRoyalty(
        uint256 tokenId,
        address receiver,
        uint96 feeNumerator
    ) internal virtual {
        uint256 denominator = _feeDenominator();
        if (feeNumerator > denominator) {
            // Royalty fee will exceed the sale price
            revert ERC2981InvalidTokenRoyalty(
                tokenId,
                feeNumerator,
                denominator
            );
        }
        if (receiver == address(0)) {
            revert ERC2981InvalidTokenRoyaltyReceiver(tokenId, address(0));
        }

        _tokenRoyaltyInfo[tokenId] = RoyaltyInfo(receiver, feeNumerator);
    }

    /**
     * @dev Resets royalty information for the token id back to the global default.
     */
    function _resetTokenRoyalty(uint256 tokenId) internal virtual {
        delete _tokenRoyaltyInfo[tokenId];
    }
}

// File @openzeppelin/contracts/interfaces/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (interfaces/draft-IERC6093.sol)
pragma solidity ^0.8.20;

/**
 * @dev Standard ERC-20 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-20 tokens.
 */
interface IERC20Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientBalance(
        address sender,
        uint256 balance,
        uint256 needed
    );

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC20InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC20InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `spender`’s `allowance`. Used in transfers.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     * @param allowance Amount of tokens a `spender` is allowed to operate with.
     * @param needed Minimum amount required to perform a transfer.
     */
    error ERC20InsufficientAllowance(
        address spender,
        uint256 allowance,
        uint256 needed
    );

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC20InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `spender` to be approved. Used in approvals.
     * @param spender Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC20InvalidSpender(address spender);
}

/**
 * @dev Standard ERC-721 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-721 tokens.
 */
interface IERC721Errors {
    /**
     * @dev Indicates that an address can't be an owner. For example, `address(0)` is a forbidden owner in ERC-20.
     * Used in balance queries.
     * @param owner Address of the current owner of a token.
     */
    error ERC721InvalidOwner(address owner);

    /**
     * @dev Indicates a `tokenId` whose `owner` is the zero address.
     * @param tokenId Identifier number of a token.
     */
    error ERC721NonexistentToken(uint256 tokenId);

    /**
     * @dev Indicates an error related to the ownership over a particular token. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param tokenId Identifier number of a token.
     * @param owner Address of the current owner of a token.
     */
    error ERC721IncorrectOwner(address sender, uint256 tokenId, address owner);

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC721InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC721InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param tokenId Identifier number of a token.
     */
    error ERC721InsufficientApproval(address operator, uint256 tokenId);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC721InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC721InvalidOperator(address operator);
}

/**
 * @dev Standard ERC-1155 Errors
 * Interface of the https://eips.ethereum.org/EIPS/eip-6093[ERC-6093] custom errors for ERC-1155 tokens.
 */
interface IERC1155Errors {
    /**
     * @dev Indicates an error related to the current `balance` of a `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     * @param balance Current balance for the interacting account.
     * @param needed Minimum amount required to perform a transfer.
     * @param tokenId Identifier number of a token.
     */
    error ERC1155InsufficientBalance(
        address sender,
        uint256 balance,
        uint256 needed,
        uint256 tokenId
    );

    /**
     * @dev Indicates a failure with the token `sender`. Used in transfers.
     * @param sender Address whose tokens are being transferred.
     */
    error ERC1155InvalidSender(address sender);

    /**
     * @dev Indicates a failure with the token `receiver`. Used in transfers.
     * @param receiver Address to which tokens are being transferred.
     */
    error ERC1155InvalidReceiver(address receiver);

    /**
     * @dev Indicates a failure with the `operator`’s approval. Used in transfers.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     * @param owner Address of the current owner of a token.
     */
    error ERC1155MissingApprovalForAll(address operator, address owner);

    /**
     * @dev Indicates a failure with the `approver` of a token to be approved. Used in approvals.
     * @param approver Address initiating an approval operation.
     */
    error ERC1155InvalidApprover(address approver);

    /**
     * @dev Indicates a failure with the `operator` to be approved. Used in approvals.
     * @param operator Address that may be allowed to operate on tokens without being their owner.
     */
    error ERC1155InvalidOperator(address operator);

    /**
     * @dev Indicates an array length mismatch between ids and values in a safeBatchTransferFrom operation.
     * Used in batch transfers.
     * @param idsLength Length of the array of token identifiers
     * @param valuesLength Length of the array of token amounts
     */
    error ERC1155InvalidArrayLength(uint256 idsLength, uint256 valuesLength);
}

// File @openzeppelin/contracts/token/ERC1155/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/IERC1155.sol)

pragma solidity ^0.8.20;

/**
 * @dev Required interface of an ERC-1155 compliant contract, as defined in the
 * https://eips.ethereum.org/EIPS/eip-1155[ERC].
 */
interface IERC1155 is IERC165 {
    /**
     * @dev Emitted when `value` amount of tokens of type `id` are transferred from `from` to `to` by `operator`.
     */
    event TransferSingle(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256 id,
        uint256 value
    );

    /**
     * @dev Equivalent to multiple {TransferSingle} events, where `operator`, `from` and `to` are the same for all
     * transfers.
     */
    event TransferBatch(
        address indexed operator,
        address indexed from,
        address indexed to,
        uint256[] ids,
        uint256[] values
    );

    /**
     * @dev Emitted when `account` grants or revokes permission to `operator` to transfer their tokens, according to
     * `approved`.
     */
    event ApprovalForAll(
        address indexed account,
        address indexed operator,
        bool approved
    );

    /**
     * @dev Emitted when the URI for token type `id` changes to `value`, if it is a non-programmatic URI.
     *
     * If an {URI} event was emitted for `id`, the standard
     * https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[guarantees] that `value` will equal the value
     * returned by {IERC1155MetadataURI-uri}.
     */
    event URI(string value, uint256 indexed id);

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

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {balanceOf}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(
        address[] calldata accounts,
        uint256[] calldata ids
    ) external view returns (uint256[] memory);

    /**
     * @dev Grants or revokes permission to `operator` to transfer the caller's tokens, according to `approved`,
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the zero address.
     */
    function setApprovalForAll(address operator, bool approved) external;

    /**
     * @dev Returns true if `operator` is approved to transfer ``account``'s tokens.
     *
     * See {setApprovalForAll}.
     */
    function isApprovedForAll(
        address account,
        address operator
    ) external view returns (bool);

    /**
     * @dev Transfers a `value` amount of tokens of type `id` from `from` to `to`.
     *
     * WARNING: This function can potentially allow a reentrancy attack when transferring tokens
     * to an untrusted contract, when invoking {onERC1155Received} on the receiver.
     * Ensure to follow the checks-effects-interactions pattern and consider employing
     * reentrancy guards when interacting with untrusted contracts.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If the caller is not `from`, it must have been approved to spend ``from``'s tokens via {setApprovalForAll}.
     * - `from` must have a balance of tokens of type `id` of at least `value` amount.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external;

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {safeTransferFrom}.
     *
     * WARNING: This function can potentially allow a reentrancy attack when transferring tokens
     * to an untrusted contract, when invoking {onERC1155BatchReceived} on the receiver.
     * Ensure to follow the checks-effects-interactions pattern and consider employing
     * reentrancy guards when interacting with untrusted contracts.
     *
     * Emits either a {TransferSingle} or a {TransferBatch} event, depending on the length of the array arguments.
     *
     * Requirements:
     *
     * - `ids` and `values` must have the same length.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external;
}

// File @openzeppelin/contracts/token/ERC1155/extensions/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/extensions/IERC1155MetadataURI.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface of the optional ERC1155MetadataExtension interface, as defined
 * in the https://eips.ethereum.org/EIPS/eip-1155#metadata-extensions[ERC].
 */
interface IERC1155MetadataURI is IERC1155 {
    /**
     * @dev Returns the URI for token type `id`.
     *
     * If the `\{id\}` substring is present in the URI, it must be replaced by
     * clients with the actual token type ID.
     */
    function uri(uint256 id) external view returns (string memory);
}

// File @openzeppelin/contracts/token/ERC1155/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/IERC1155Receiver.sol)

pragma solidity ^0.8.20;

/**
 * @dev Interface that must be implemented by smart contracts in order to receive
 * ERC-1155 token transfers.
 */
interface IERC1155Receiver is IERC165 {
    /**
     * @dev Handles the receipt of a single ERC-1155 token type. This function is
     * called at the end of a `safeTransferFrom` after the balance has been updated.
     *
     * NOTE: To accept the transfer, this must return
     * `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))`
     * (i.e. 0xf23a6e61, or its own function selector).
     *
     * @param operator The address which initiated the transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param id The ID of the token being transferred
     * @param value The amount of tokens being transferred
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155Received(address,address,uint256,uint256,bytes)"))` if transfer is allowed
     */
    function onERC1155Received(
        address operator,
        address from,
        uint256 id,
        uint256 value,
        bytes calldata data
    ) external returns (bytes4);

    /**
     * @dev Handles the receipt of a multiple ERC-1155 token types. This function
     * is called at the end of a `safeBatchTransferFrom` after the balances have
     * been updated.
     *
     * NOTE: To accept the transfer(s), this must return
     * `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))`
     * (i.e. 0xbc197c81, or its own function selector).
     *
     * @param operator The address which initiated the batch transfer (i.e. msg.sender)
     * @param from The address which previously owned the token
     * @param ids An array containing ids of each token being transferred (order and length must match values array)
     * @param values An array containing amounts of each token being transferred (order and length must match ids array)
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC1155BatchReceived(address,address,uint256[],uint256[],bytes)"))` if transfer is allowed
     */
    function onERC1155BatchReceived(
        address operator,
        address from,
        uint256[] calldata ids,
        uint256[] calldata values,
        bytes calldata data
    ) external returns (bytes4);
}

// File @openzeppelin/contracts/token/ERC1155/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/utils/ERC1155Utils.sol)

pragma solidity ^0.8.20;

/**
 * @dev Library that provide common ERC-1155 utility functions.
 *
 * See https://eips.ethereum.org/EIPS/eip-1155[ERC-1155].
 *
 * _Available since v5.1._
 */
library ERC1155Utils {
    /**
     * @dev Performs an acceptance check for the provided `operator` by calling {IERC1155-onERC1155Received}
     * on the `to` address. The `operator` is generally the address that initiated the token transfer (i.e. `msg.sender`).
     *
     * The acceptance call is not executed and treated as a no-op if the target address doesn't contain code (i.e. an EOA).
     * Otherwise, the recipient must implement {IERC1155Receiver-onERC1155Received} and return the acceptance magic value to accept
     * the transfer.
     */
    function checkOnERC1155Received(
        address operator,
        address from,
        address to,
        uint256 id,
        uint256 value,
        bytes memory data
    ) internal {
        if (to.code.length > 0) {
            try
                IERC1155Receiver(to).onERC1155Received(
                    operator,
                    from,
                    id,
                    value,
                    data
                )
            returns (bytes4 response) {
                if (response != IERC1155Receiver.onERC1155Received.selector) {
                    // Tokens rejected
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    // non-IERC1155Receiver implementer
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                } else {
                    assembly ("memory-safe") {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }

    /**
     * @dev Performs a batch acceptance check for the provided `operator` by calling {IERC1155-onERC1155BatchReceived}
     * on the `to` address. The `operator` is generally the address that initiated the token transfer (i.e. `msg.sender`).
     *
     * The acceptance call is not executed and treated as a no-op if the target address doesn't contain code (i.e. an EOA).
     * Otherwise, the recipient must implement {IERC1155Receiver-onERC1155Received} and return the acceptance magic value to accept
     * the transfer.
     */
    function checkOnERC1155BatchReceived(
        address operator,
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal {
        if (to.code.length > 0) {
            try
                IERC1155Receiver(to).onERC1155BatchReceived(
                    operator,
                    from,
                    ids,
                    values,
                    data
                )
            returns (bytes4 response) {
                if (
                    response != IERC1155Receiver.onERC1155BatchReceived.selector
                ) {
                    // Tokens rejected
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                }
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    // non-IERC1155Receiver implementer
                    revert IERC1155Errors.ERC1155InvalidReceiver(to);
                } else {
                    assembly ("memory-safe") {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        }
    }
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Comparators.sol)

pragma solidity ^0.8.20;

/**
 * @dev Provides a set of functions to compare values.
 *
 * _Available since v5.1._
 */
library Comparators {
    function lt(uint256 a, uint256 b) internal pure returns (bool) {
        return a < b;
    }

    function gt(uint256 a, uint256 b) internal pure returns (bool) {
        return a > b;
    }
}

// File @openzeppelin/contracts/utils/math/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (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 an uint of `bits` size.
     */
    error SafeCastOverflowedUintDowncast(uint8 bits, uint256 value);

    /**
     * @dev An int value doesn't fit in an 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 An 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))
        }
    }
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: 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)
        }
    }
}

// File @openzeppelin/contracts/utils/math/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/Math.sol)

pragma solidity ^0.8.20;

/**
 * @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 Returns the addition of two unsigned integers, with an success flag (no overflow).
     */
    function tryAdd(
        uint256 a,
        uint256 b
    ) internal pure returns (bool success, uint256 result) {
        unchecked {
            uint256 c = a + b;
            if (c < a) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, with an success flag (no overflow).
     */
    function trySub(
        uint256 a,
        uint256 b
    ) internal pure returns (bool success, uint256 result) {
        unchecked {
            if (b > a) return (false, 0);
            return (true, a - b);
        }
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, with an success flag (no overflow).
     */
    function tryMul(
        uint256 a,
        uint256 b
    ) internal pure returns (bool success, uint256 result) {
        unchecked {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) return (true, 0);
            uint256 c = a * b;
            if (c / a != b) return (false, 0);
            return (true, c);
        }
    }

    /**
     * @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 {
            if (b == 0) return (false, 0);
            return (true, 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 {
            if (b == 0) return (false, 0);
            return (true, a % b);
        }
    }

    /**
     * @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,
        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) {
        // (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 {
            // 512-bit multiply [prod1 prod0] = 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 = prod1 * 2²⁵⁶ + prod0.
            uint256 prod0 = x * y; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

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

            // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
            if (denominator <= prod1) {
                Panic.panic(
                    ternary(
                        denominator == 0,
                        Panic.DIVISION_BY_ZERO,
                        Panic.UNDER_OVERFLOW
                    )
                );
            }

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

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

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

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

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

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, 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 prod1 into prod0.
            prod0 |= prod1 * 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 prod1
            // is no longer required.
            result = prod0 * 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 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 byteArray) private pure returns (bool) {
        for (uint256 i = 0; i < byteArray.length; ++i) {
            if (byteArray[i] != 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 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 exp;
        unchecked {
            exp = 128 * SafeCast.toUint(value > (1 << 128) - 1);
            value >>= exp;
            result += exp;

            exp = 64 * SafeCast.toUint(value > (1 << 64) - 1);
            value >>= exp;
            result += exp;

            exp = 32 * SafeCast.toUint(value > (1 << 32) - 1);
            value >>= exp;
            result += exp;

            exp = 16 * SafeCast.toUint(value > (1 << 16) - 1);
            value >>= exp;
            result += exp;

            exp = 8 * SafeCast.toUint(value > (1 << 8) - 1);
            value >>= exp;
            result += exp;

            exp = 4 * SafeCast.toUint(value > (1 << 4) - 1);
            value >>= exp;
            result += exp;

            exp = 2 * SafeCast.toUint(value > (1 << 2) - 1);
            value >>= exp;
            result += exp;

            result += SafeCast.toUint(value > 1);
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(
        uint256 value,
        Rounding rounding
    ) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return
                result +
                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 value) internal pure returns (uint256) {
        uint256 result = 0;
        uint256 isGt;
        unchecked {
            isGt = SafeCast.toUint(value > (1 << 128) - 1);
            value >>= isGt * 128;
            result += isGt * 16;

            isGt = SafeCast.toUint(value > (1 << 64) - 1);
            value >>= isGt * 64;
            result += isGt * 8;

            isGt = SafeCast.toUint(value > (1 << 32) - 1);
            value >>= isGt * 32;
            result += isGt * 4;

            isGt = SafeCast.toUint(value > (1 << 16) - 1);
            value >>= isGt * 16;
            result += isGt * 2;

            result += SafeCast.toUint(value > (1 << 8) - 1);
        }
        return result;
    }

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

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/SlotDerivation.sol)
// This file was procedurally generated from scripts/generate/templates/SlotDerivation.js.

pragma solidity ^0.8.20;

/**
 * @dev Library for computing storage (and transient storage) locations from namespaces and deriving slots
 * corresponding to standard patterns. The derivation method for array and mapping matches the storage layout used by
 * the solidity language / compiler.
 *
 * See https://docs.soliditylang.org/en/v0.8.20/internals/layout_in_storage.html#mappings-and-dynamic-arrays[Solidity docs for mappings and dynamic arrays.].
 *
 * Example usage:
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using StorageSlot for bytes32;
 *     using SlotDerivation for bytes32;
 *
 *     // Declare a namespace
 *     string private constant _NAMESPACE = "<namespace>" // eg. OpenZeppelin.Slot
 *
 *     function setValueInNamespace(uint256 key, address newValue) internal {
 *         _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value = newValue;
 *     }
 *
 *     function getValueInNamespace(uint256 key) internal view returns (address) {
 *         return _NAMESPACE.erc7201Slot().deriveMapping(key).getAddressSlot().value;
 *     }
 * }
 * ```
 *
 * TIP: Consider using this library along with {StorageSlot}.
 *
 * NOTE: This library provides a way to manipulate storage locations in a non-standard way. Tooling for checking
 * upgrade safety will ignore the slots accessed through this library.
 *
 * _Available since v5.1._
 */
library SlotDerivation {
    /**
     * @dev Derive an ERC-7201 slot from a string (namespace).
     */
    function erc7201Slot(
        string memory namespace
    ) internal pure returns (bytes32 slot) {
        assembly ("memory-safe") {
            mstore(
                0x00,
                sub(keccak256(add(namespace, 0x20), mload(namespace)), 1)
            )
            slot := and(keccak256(0x00, 0x20), not(0xff))
        }
    }

    /**
     * @dev Add an offset to a slot to get the n-th element of a structure or an array.
     */
    function offset(
        bytes32 slot,
        uint256 pos
    ) internal pure returns (bytes32 result) {
        unchecked {
            return bytes32(uint256(slot) + pos);
        }
    }

    /**
     * @dev Derive the location of the first element in an array from the slot where the length is stored.
     */
    function deriveArray(bytes32 slot) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, slot)
            result := keccak256(0x00, 0x20)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        address key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, and(key, shr(96, not(0))))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        bool key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, iszero(iszero(key)))
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        bytes32 key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        uint256 key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        int256 key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            mstore(0x00, key)
            mstore(0x20, slot)
            result := keccak256(0x00, 0x40)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        string memory key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }

    /**
     * @dev Derive the location of a mapping element from the key.
     */
    function deriveMapping(
        bytes32 slot,
        bytes memory key
    ) internal pure returns (bytes32 result) {
        assembly ("memory-safe") {
            let length := mload(key)
            let begin := add(key, 0x20)
            let end := add(begin, length)
            let cache := mload(end)
            mstore(end, slot)
            result := keccak256(begin, add(length, 0x20))
            mstore(end, cache)
        }
    }
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: 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
        }
    }
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/Arrays.sol)
// This file was procedurally generated from scripts/generate/templates/Arrays.js.

pragma solidity ^0.8.20;

/**
 * @dev Collection of functions related to array types.
 */
library Arrays {
    using SlotDerivation for bytes32;
    using StorageSlot for bytes32;

    /**
     * @dev Sort an array of uint256 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        uint256[] memory array,
        function(uint256, uint256) pure returns (bool) comp
    ) internal pure returns (uint256[] memory) {
        _quickSort(_begin(array), _end(array), comp);
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of uint256 in increasing order.
     */
    function sort(
        uint256[] memory array
    ) internal pure returns (uint256[] memory) {
        sort(array, Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of address (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        address[] memory array,
        function(address, address) pure returns (bool) comp
    ) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of address in increasing order.
     */
    function sort(
        address[] memory array
    ) internal pure returns (address[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Sort an array of bytes32 (in memory) following the provided comparator function.
     *
     * This function does the sorting "in place", meaning that it overrides the input. The object is returned for
     * convenience, but that returned value can be discarded safely if the caller has a memory pointer to the array.
     *
     * NOTE: this function's cost is `O(n · log(n))` in average and `O(n²)` in the worst case, with n the length of the
     * array. Using it in view functions that are executed through `eth_call` is safe, but one should be very careful
     * when executing this as part of a transaction. If the array being sorted is too large, the sort operation may
     * consume more gas than is available in a block, leading to potential DoS.
     *
     * IMPORTANT: Consider memory side-effects when using custom comparator functions that access memory in an unsafe way.
     */
    function sort(
        bytes32[] memory array,
        function(bytes32, bytes32) pure returns (bool) comp
    ) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), _castToUint256Comp(comp));
        return array;
    }

    /**
     * @dev Variant of {sort} that sorts an array of bytes32 in increasing order.
     */
    function sort(
        bytes32[] memory array
    ) internal pure returns (bytes32[] memory) {
        sort(_castToUint256Array(array), Comparators.lt);
        return array;
    }

    /**
     * @dev Performs a quick sort of a segment of memory. The segment sorted starts at `begin` (inclusive), and stops
     * at end (exclusive). Sorting follows the `comp` comparator.
     *
     * Invariant: `begin <= end`. This is the case when initially called by {sort} and is preserved in subcalls.
     *
     * IMPORTANT: Memory locations between `begin` and `end` are not validated/zeroed. This function should
     * be used only if the limits are within a memory array.
     */
    function _quickSort(
        uint256 begin,
        uint256 end,
        function(uint256, uint256) pure returns (bool) comp
    ) private pure {
        unchecked {
            if (end - begin < 0x40) return;

            // Use first element as pivot
            uint256 pivot = _mload(begin);
            // Position where the pivot should be at the end of the loop
            uint256 pos = begin;

            for (uint256 it = begin + 0x20; it < end; it += 0x20) {
                if (comp(_mload(it), pivot)) {
                    // If the value stored at the iterator's position comes before the pivot, we increment the
                    // position of the pivot and move the value there.
                    pos += 0x20;
                    _swap(pos, it);
                }
            }

            _swap(begin, pos); // Swap pivot into place
            _quickSort(begin, pos, comp); // Sort the left side of the pivot
            _quickSort(pos + 0x20, end, comp); // Sort the right side of the pivot
        }
    }

    /**
     * @dev Pointer to the memory location of the first element of `array`.
     */
    function _begin(uint256[] memory array) private pure returns (uint256 ptr) {
        assembly ("memory-safe") {
            ptr := add(array, 0x20)
        }
    }

    /**
     * @dev Pointer to the memory location of the first memory word (32bytes) after `array`. This is the memory word
     * that comes just after the last element of the array.
     */
    function _end(uint256[] memory array) private pure returns (uint256 ptr) {
        unchecked {
            return _begin(array) + array.length * 0x20;
        }
    }

    /**
     * @dev Load memory word (as a uint256) at location `ptr`.
     */
    function _mload(uint256 ptr) private pure returns (uint256 value) {
        assembly {
            value := mload(ptr)
        }
    }

    /**
     * @dev Swaps the elements memory location `ptr1` and `ptr2`.
     */
    function _swap(uint256 ptr1, uint256 ptr2) private pure {
        assembly {
            let value1 := mload(ptr1)
            let value2 := mload(ptr2)
            mstore(ptr1, value2)
            mstore(ptr2, value1)
        }
    }

    /// @dev Helper: low level cast address memory array to uint256 memory array
    function _castToUint256Array(
        address[] memory input
    ) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 memory array to uint256 memory array
    function _castToUint256Array(
        bytes32[] memory input
    ) private pure returns (uint256[] memory output) {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast address comp function to uint256 comp function
    function _castToUint256Comp(
        function(address, address) pure returns (bool) input
    )
        private
        pure
        returns (function(uint256, uint256) pure returns (bool) output)
    {
        assembly {
            output := input
        }
    }

    /// @dev Helper: low level cast bytes32 comp function to uint256 comp function
    function _castToUint256Comp(
        function(bytes32, bytes32) pure returns (bool) input
    )
        private
        pure
        returns (function(uint256, uint256) pure returns (bool) output)
    {
        assembly {
            output := input
        }
    }

    /**
     * @dev Searches a sorted `array` and returns the first index that contains
     * a value greater or equal to `element`. If no such index exists (i.e. all
     * values in the array are strictly less than `element`), the array length is
     * returned. Time complexity O(log n).
     *
     * NOTE: The `array` is expected to be sorted in ascending order, and to
     * contain no repeated elements.
     *
     * IMPORTANT: Deprecated. This implementation behaves as {lowerBound} but lacks
     * support for repeated elements in the array. The {lowerBound} function should
     * be used instead.
     */
    function findUpperBound(
        uint256[] storage array,
        uint256 element
    ) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }

        // At this point `low` is the exclusive upper bound. We will return the inclusive upper bound.
        if (low > 0 && unsafeAccess(array, low - 1).value == element) {
            return low - 1;
        } else {
            return low;
        }
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value greater or equal than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/lower_bound[lower_bound].
     */
    function lowerBound(
        uint256[] storage array,
        uint256 element
    ) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Searches an `array` sorted in ascending order and returns the first
     * index that contains a value strictly greater than `element`. If no such index
     * exists (i.e. all values in the array are strictly less than `element`), the array
     * length is returned. Time complexity O(log n).
     *
     * See C++'s https://en.cppreference.com/w/cpp/algorithm/upper_bound[upper_bound].
     */
    function upperBound(
        uint256[] storage array,
        uint256 element
    ) internal view returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeAccess(array, mid).value > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Same as {lowerBound}, but with an array in memory.
     */
    function lowerBoundMemory(
        uint256[] memory array,
        uint256 element
    ) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) < element) {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            } else {
                high = mid;
            }
        }

        return low;
    }

    /**
     * @dev Same as {upperBound}, but with an array in memory.
     */
    function upperBoundMemory(
        uint256[] memory array,
        uint256 element
    ) internal pure returns (uint256) {
        uint256 low = 0;
        uint256 high = array.length;

        if (high == 0) {
            return 0;
        }

        while (low < high) {
            uint256 mid = Math.average(low, high);

            // Note that mid will always be strictly less than high (i.e. it will be a valid array index)
            // because Math.average rounds towards zero (it does integer division with truncation).
            if (unsafeMemoryAccess(array, mid) > element) {
                high = mid;
            } else {
                // this cannot overflow because mid < high
                unchecked {
                    low = mid + 1;
                }
            }
        }

        return low;
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(
        address[] storage arr,
        uint256 pos
    ) internal pure returns (StorageSlot.AddressSlot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getAddressSlot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(
        bytes32[] storage arr,
        uint256 pos
    ) internal pure returns (StorageSlot.Bytes32Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getBytes32Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeAccess(
        uint256[] storage arr,
        uint256 pos
    ) internal pure returns (StorageSlot.Uint256Slot storage) {
        bytes32 slot;
        assembly ("memory-safe") {
            slot := arr.slot
        }
        return slot.deriveArray().offset(pos).getUint256Slot();
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(
        address[] memory arr,
        uint256 pos
    ) internal pure returns (address res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(
        bytes32[] memory arr,
        uint256 pos
    ) internal pure returns (bytes32 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.
     *
     * WARNING: Only use if you are certain `pos` is lower than the array length.
     */
    function unsafeMemoryAccess(
        uint256[] memory arr,
        uint256 pos
    ) internal pure returns (uint256 res) {
        assembly {
            res := mload(add(add(arr, 0x20), mul(pos, 0x20)))
        }
    }

    /**
     * @dev Helper to set the length of an dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(address[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of an dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(bytes32[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }

    /**
     * @dev Helper to set the length of an dynamic array. Directly writing to `.length` is forbidden.
     *
     * WARNING: this does not clear elements if length is reduced, of initialize elements if length is increased.
     */
    function unsafeSetLength(uint256[] storage array, uint256 len) internal {
        assembly ("memory-safe") {
            sstore(array.slot, len)
        }
    }
}

// File @openzeppelin/contracts/token/ERC1155/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/ERC1155.sol)

pragma solidity ^0.8.20;

/**
 * @dev Implementation of the basic standard multi-token.
 * See https://eips.ethereum.org/EIPS/eip-1155
 * Originally based on code by Enjin: https://github.com/enjin/erc-1155
 */
abstract contract ERC1155 is
    Context,
    ERC165,
    IERC1155,
    IERC1155MetadataURI,
    IERC1155Errors
{
    using Arrays for uint256[];
    using Arrays for address[];

    mapping(uint256 id => mapping(address account => uint256))
        private _balances;

    mapping(address account => mapping(address operator => bool))
        private _operatorApprovals;

    // Used as the URI for all token types by relying on ID substitution, e.g. https://token-cdn-domain/{id}.json
    string private _uri;

    /**
     * @dev See {_setURI}.
     */
    constructor(string memory uri_) {
        _setURI(uri_);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(
        bytes4 interfaceId
    ) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC1155).interfaceId ||
            interfaceId == type(IERC1155MetadataURI).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC1155MetadataURI-uri}.
     *
     * This implementation returns the same URI for *all* token types. It relies
     * on the token type ID substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the ERC].
     *
     * Clients calling this function must replace the `\{id\}` substring with the
     * actual token type ID.
     */
    function uri(uint256 /* id */) public view virtual returns (string memory) {
        return _uri;
    }

    /**
     * @dev See {IERC1155-balanceOf}.
     */
    function balanceOf(
        address account,
        uint256 id
    ) public view virtual returns (uint256) {
        return _balances[id][account];
    }

    /**
     * @dev See {IERC1155-balanceOfBatch}.
     *
     * Requirements:
     *
     * - `accounts` and `ids` must have the same length.
     */
    function balanceOfBatch(
        address[] memory accounts,
        uint256[] memory ids
    ) public view virtual returns (uint256[] memory) {
        if (accounts.length != ids.length) {
            revert ERC1155InvalidArrayLength(ids.length, accounts.length);
        }

        uint256[] memory batchBalances = new uint256[](accounts.length);

        for (uint256 i = 0; i < accounts.length; ++i) {
            batchBalances[i] = balanceOf(
                accounts.unsafeMemoryAccess(i),
                ids.unsafeMemoryAccess(i)
            );
        }

        return batchBalances;
    }

    /**
     * @dev See {IERC1155-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC1155-isApprovedForAll}.
     */
    function isApprovedForAll(
        address account,
        address operator
    ) public view virtual returns (bool) {
        return _operatorApprovals[account][operator];
    }

    /**
     * @dev See {IERC1155-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 value,
        bytes memory data
    ) public virtual {
        address sender = _msgSender();
        if (from != sender && !isApprovedForAll(from, sender)) {
            revert ERC1155MissingApprovalForAll(sender, from);
        }
        _safeTransferFrom(from, to, id, value, data);
    }

    /**
     * @dev See {IERC1155-safeBatchTransferFrom}.
     */
    function safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) public virtual {
        address sender = _msgSender();
        if (from != sender && !isApprovedForAll(from, sender)) {
            revert ERC1155MissingApprovalForAll(sender, from);
        }
        _safeBatchTransferFrom(from, to, ids, values, data);
    }

    /**
     * @dev Transfers a `value` amount of tokens of type `id` from `from` to `to`. Will mint (or burn) if `from`
     * (or `to`) is the zero address.
     *
     * Emits a {TransferSingle} event if the arrays contain one element, and {TransferBatch} otherwise.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement either {IERC1155Receiver-onERC1155Received}
     *   or {IERC1155Receiver-onERC1155BatchReceived} and return the acceptance magic value.
     * - `ids` and `values` must have the same length.
     *
     * NOTE: The ERC-1155 acceptance check is not performed in this function. See {_updateWithAcceptanceCheck} instead.
     */
    function _update(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values
    ) internal virtual {
        if (ids.length != values.length) {
            revert ERC1155InvalidArrayLength(ids.length, values.length);
        }

        address operator = _msgSender();

        for (uint256 i = 0; i < ids.length; ++i) {
            uint256 id = ids.unsafeMemoryAccess(i);
            uint256 value = values.unsafeMemoryAccess(i);

            if (from != address(0)) {
                uint256 fromBalance = _balances[id][from];
                if (fromBalance < value) {
                    revert ERC1155InsufficientBalance(
                        from,
                        fromBalance,
                        value,
                        id
                    );
                }
                unchecked {
                    // Overflow not possible: value <= fromBalance
                    _balances[id][from] = fromBalance - value;
                }
            }

            if (to != address(0)) {
                _balances[id][to] += value;
            }
        }

        if (ids.length == 1) {
            uint256 id = ids.unsafeMemoryAccess(0);
            uint256 value = values.unsafeMemoryAccess(0);
            emit TransferSingle(operator, from, to, id, value);
        } else {
            emit TransferBatch(operator, from, to, ids, values);
        }
    }

    /**
     * @dev Version of {_update} that performs the token acceptance check by calling
     * {IERC1155Receiver-onERC1155Received} or {IERC1155Receiver-onERC1155BatchReceived} on the receiver address if it
     * contains code (eg. is a smart contract at the moment of execution).
     *
     * IMPORTANT: Overriding this function is discouraged because it poses a reentrancy risk from the receiver. So any
     * update to the contract state after this function would break the check-effect-interaction pattern. Consider
     * overriding {_update} instead.
     */
    function _updateWithAcceptanceCheck(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal virtual {
        _update(from, to, ids, values);
        if (to != address(0)) {
            address operator = _msgSender();
            if (ids.length == 1) {
                uint256 id = ids.unsafeMemoryAccess(0);
                uint256 value = values.unsafeMemoryAccess(0);
                ERC1155Utils.checkOnERC1155Received(
                    operator,
                    from,
                    to,
                    id,
                    value,
                    data
                );
            } else {
                ERC1155Utils.checkOnERC1155BatchReceived(
                    operator,
                    from,
                    to,
                    ids,
                    values,
                    data
                );
            }
        }
    }

    /**
     * @dev Transfers a `value` tokens of token type `id` from `from` to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `from` must have a balance of tokens of type `id` of at least `value` amount.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _safeTransferFrom(
        address from,
        address to,
        uint256 id,
        uint256 value,
        bytes memory data
    ) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(
            id,
            value
        );
        _updateWithAcceptanceCheck(from, to, ids, values, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_safeTransferFrom}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     * - `ids` and `values` must have the same length.
     */
    function _safeBatchTransferFrom(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        _updateWithAcceptanceCheck(from, to, ids, values, data);
    }

    /**
     * @dev Sets a new URI for all token types, by relying on the token type ID
     * substitution mechanism
     * https://eips.ethereum.org/EIPS/eip-1155#metadata[defined in the ERC].
     *
     * By this mechanism, any occurrence of the `\{id\}` substring in either the
     * URI or any of the values in the JSON file at said URI will be replaced by
     * clients with the token type ID.
     *
     * For example, the `https://token-cdn-domain/\{id\}.json` URI would be
     * interpreted by clients as
     * `https://token-cdn-domain/000000000000000000000000000000000000000000000000000000000004cce0.json`
     * for token type ID 0x4cce0.
     *
     * See {uri}.
     *
     * Because these URIs cannot be meaningfully represented by the {URI} event,
     * this function emits no events.
     */
    function _setURI(string memory newuri) internal virtual {
        _uri = newuri;
    }

    /**
     * @dev Creates a `value` amount of tokens of type `id`, and assigns them to `to`.
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155Received} and return the
     * acceptance magic value.
     */
    function _mint(
        address to,
        uint256 id,
        uint256 value,
        bytes memory data
    ) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(
            id,
            value
        );
        _updateWithAcceptanceCheck(address(0), to, ids, values, data);
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_mint}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `ids` and `values` must have the same length.
     * - `to` cannot be the zero address.
     * - If `to` refers to a smart contract, it must implement {IERC1155Receiver-onERC1155BatchReceived} and return the
     * acceptance magic value.
     */
    function _mintBatch(
        address to,
        uint256[] memory ids,
        uint256[] memory values,
        bytes memory data
    ) internal {
        if (to == address(0)) {
            revert ERC1155InvalidReceiver(address(0));
        }
        _updateWithAcceptanceCheck(address(0), to, ids, values, data);
    }

    /**
     * @dev Destroys a `value` amount of tokens of type `id` from `from`
     *
     * Emits a {TransferSingle} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `from` must have at least `value` amount of tokens of type `id`.
     */
    function _burn(address from, uint256 id, uint256 value) internal {
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        (uint256[] memory ids, uint256[] memory values) = _asSingletonArrays(
            id,
            value
        );
        _updateWithAcceptanceCheck(from, address(0), ids, values, "");
    }

    /**
     * @dev xref:ROOT:erc1155.adoc#batch-operations[Batched] version of {_burn}.
     *
     * Emits a {TransferBatch} event.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `from` must have at least `value` amount of tokens of type `id`.
     * - `ids` and `values` must have the same length.
     */
    function _burnBatch(
        address from,
        uint256[] memory ids,
        uint256[] memory values
    ) internal {
        if (from == address(0)) {
            revert ERC1155InvalidSender(address(0));
        }
        _updateWithAcceptanceCheck(from, address(0), ids, values, "");
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Emits an {ApprovalForAll} event.
     *
     * Requirements:
     *
     * - `operator` cannot be the zero address.
     */
    function _setApprovalForAll(
        address owner,
        address operator,
        bool approved
    ) internal virtual {
        if (operator == address(0)) {
            revert ERC1155InvalidOperator(address(0));
        }
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Creates an array in memory with only one value for each of the elements provided.
     */
    function _asSingletonArrays(
        uint256 element1,
        uint256 element2
    ) private pure returns (uint256[] memory array1, uint256[] memory array2) {
        assembly ("memory-safe") {
            // Load the free memory pointer
            array1 := mload(0x40)
            // Set array length to 1
            mstore(array1, 1)
            // Store the single element at the next word after the length (where content starts)
            mstore(add(array1, 0x20), element1)

            // Repeat for next array locating it right after the first array
            array2 := add(array1, 0x40)
            mstore(array2, 1)
            mstore(add(array2, 0x20), element2)

            // Update the free memory pointer by pointing after the second array
            mstore(0x40, add(array2, 0x40))
        }
    }
}

// File @openzeppelin/contracts/token/ERC1155/extensions/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (token/ERC1155/extensions/ERC1155Supply.sol)

pragma solidity ^0.8.20;

/**
 * @dev Extension of ERC-1155 that adds tracking of total supply per id.
 *
 * Useful for scenarios where Fungible and Non-fungible tokens have to be
 * clearly identified. Note: While a totalSupply of 1 might mean the
 * corresponding is an NFT, there is no guarantees that no other token with the
 * same id are not going to be minted.
 *
 * NOTE: This contract implies a global limit of 2**256 - 1 to the number of tokens
 * that can be minted.
 *
 * CAUTION: This extension should not be added in an upgrade to an already deployed contract.
 */
abstract contract ERC1155Supply is ERC1155 {
    using Arrays for uint256[];

    mapping(uint256 id => uint256) private _totalSupply;
    uint256 private _totalSupplyAll;

    /**
     * @dev Total value of tokens in with a given id.
     */
    function totalSupply(uint256 id) public view virtual returns (uint256) {
        return _totalSupply[id];
    }

    /**
     * @dev Total value of tokens.
     */
    function totalSupply() public view virtual returns (uint256) {
        return _totalSupplyAll;
    }

    /**
     * @dev Indicates whether any token exist with a given id, or not.
     */
    function exists(uint256 id) public view virtual returns (bool) {
        return totalSupply(id) > 0;
    }

    /**
     * @dev See {ERC1155-_update}.
     */
    function _update(
        address from,
        address to,
        uint256[] memory ids,
        uint256[] memory values
    ) internal virtual override {
        super._update(from, to, ids, values);

        if (from == address(0)) {
            uint256 totalMintValue = 0;
            for (uint256 i = 0; i < ids.length; ++i) {
                uint256 value = values.unsafeMemoryAccess(i);
                // Overflow check required: The rest of the code assumes that totalSupply never overflows
                _totalSupply[ids.unsafeMemoryAccess(i)] += value;
                totalMintValue += value;
            }
            // Overflow check required: The rest of the code assumes that totalSupplyAll never overflows
            _totalSupplyAll += totalMintValue;
        }

        if (to == address(0)) {
            uint256 totalBurnValue = 0;
            for (uint256 i = 0; i < ids.length; ++i) {
                uint256 value = values.unsafeMemoryAccess(i);

                unchecked {
                    // Overflow not possible: values[i] <= balanceOf(from, ids[i]) <= totalSupply(ids[i])
                    _totalSupply[ids.unsafeMemoryAccess(i)] -= value;
                    // Overflow not possible: sum_i(values[i]) <= sum_i(totalSupply(ids[i])) <= totalSupplyAll
                    totalBurnValue += value;
                }
            }
            unchecked {
                // Overflow not possible: totalBurnValue = sum_i(values[i]) <= sum_i(totalSupply(ids[i])) <= totalSupplyAll
                _totalSupplyAll -= totalBurnValue;
            }
        }
    }
}

// File @openzeppelin/contracts/utils/math/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.20;

/**
 * @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);
        }
    }
}

// File @openzeppelin/contracts/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.2.0) (utils/Strings.sol)

pragma solidity ^0.8.20;

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

    bytes16 private constant HEX_DIGITS = "0123456789abcdef";
    uint8 private constant ADDRESS_LENGTH = 20;

    /**
     * @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(buffer, add(32, 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 Returns true if the two strings are equal.
     */
    function equal(
        string memory a,
        string memory b
    ) internal pure returns (bool) {
        return
            bytes(a).length == bytes(b).length &&
            keccak256(bytes(a)) == keccak256(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} 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} 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} 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} 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} 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 guaratees 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} 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} 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} 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 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(buffer, add(0x20, offset)))
        }
    }
}

// File @openzeppelin/contracts/utils/cryptography/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (utils/cryptography/MessageHashUtils.sol)

pragma solidity ^0.8.20;

/**
 * @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 {
    /**
     * @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://eth.wiki/json-rpc/API#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://eth.wiki/json-rpc/API#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 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)
        }
    }
}

// File @openzeppelin/contracts/proxy/utils/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.0.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.20;

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Storage of the initializable contract.
     *
     * It's implemented on a custom ERC-7201 namespace to reduce the risk of storage collisions
     * when using with upgradeable contracts.
     *
     * @custom:storage-location erc7201:openzeppelin.storage.Initializable
     */
    struct InitializableStorage {
        /**
         * @dev Indicates that the contract has been initialized.
         */
        uint64 _initialized;
        /**
         * @dev Indicates that the contract is in the process of being initialized.
         */
        bool _initializing;
    }

    // keccak256(abi.encode(uint256(keccak256("openzeppelin.storage.Initializable")) - 1)) & ~bytes32(uint256(0xff))
    bytes32 private constant INITIALIZABLE_STORAGE =
        0xf0c57e16840df040f15088dc2f81fe391c3923bec73e23a9662efc9c229c6a00;

    /**
     * @dev The contract is already initialized.
     */
    error InvalidInitialization();

    /**
     * @dev The contract is not initializing.
     */
    error NotInitializing();

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint64 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that in the context of a constructor an `initializer` may be invoked any
     * number of times. This behavior in the constructor can be useful during testing and is not expected to be used in
     * production.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        // Cache values to avoid duplicated sloads
        bool isTopLevelCall = !$._initializing;
        uint64 initialized = $._initialized;

        // Allowed calls:
        // - initialSetup: the contract is not in the initializing state and no previous version was
        //                 initialized
        // - construction: the contract is initialized at version 1 (no reininitialization) and the
        //                 current contract is just being deployed
        bool initialSetup = initialized == 0 && isTopLevelCall;
        bool construction = initialized == 1 && address(this).code.length == 0;

        if (!initialSetup && !construction) {
            revert InvalidInitialization();
        }
        $._initialized = 1;
        if (isTopLevelCall) {
            $._initializing = true;
        }
        _;
        if (isTopLevelCall) {
            $._initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: Setting the version to 2**64 - 1 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint64 version) {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing || $._initialized >= version) {
            revert InvalidInitialization();
        }
        $._initialized = version;
        $._initializing = true;
        _;
        $._initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        _checkInitializing();
        _;
    }

    /**
     * @dev Reverts if the contract is not in an initializing state. See {onlyInitializing}.
     */
    function _checkInitializing() internal view virtual {
        if (!_isInitializing()) {
            revert NotInitializing();
        }
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        // solhint-disable-next-line var-name-mixedcase
        InitializableStorage storage $ = _getInitializableStorage();

        if ($._initializing) {
            revert InvalidInitialization();
        }
        if ($._initialized != type(uint64).max) {
            $._initialized = type(uint64).max;
            emit Initialized(type(uint64).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint64) {
        return _getInitializableStorage()._initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _getInitializableStorage()._initializing;
    }

    /**
     * @dev Returns a pointer to the storage namespace.
     */
    // solhint-disable-next-line var-name-mixedcase
    function _getInitializableStorage()
        private
        pure
        returns (InitializableStorage storage $)
    {
        assembly {
            $.slot := INITIALIZABLE_STORAGE
        }
    }
}

// File @openzeppelin/contracts/utils/cryptography/[email protected]

// Original license: SPDX_License_Identifier: MIT
// OpenZeppelin Contracts (last updated v5.1.0) (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 derives the `address(0)`.
     */
    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.
     *
     * 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 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.
     *
     * 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 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 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);
        }
    }
}

// File hardhat/[email protected]

// Original license: SPDX_License_Identifier: MIT
pragma solidity >=0.4.22 <0.9.0;

library console {
    address constant CONSOLE_ADDRESS =
        0x000000000000000000636F6e736F6c652e6c6f67;

    function _sendLogPayloadImplementation(bytes memory payload) internal view {
        address consoleAddress = CONSOLE_ADDRESS;
        /// @solidity memory-safe-assembly
        assembly {
            pop(
                staticcall(
                    gas(),
                    consoleAddress,
                    add(payload, 32),
                    mload(payload),
                    0,
                    0
                )
            )
        }
    }

    function _castToPure(
        function(bytes memory) internal view fnIn
    ) internal pure returns (function(bytes memory) pure fnOut) {
        assembly {
            fnOut := fnIn
        }
    }

    function _sendLogPayload(bytes memory payload) internal pure {
        _castToPure(_sendLogPayloadImplementation)(payload);
    }

    function log() internal pure {
        _sendLogPayload(abi.encodeWithSignature("log()"));
    }

    function logInt(int256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(int256)", p0));
    }

    function logUint(uint256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256)", p0));
    }

    function logString(string memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function logBool(bool p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function logAddress(address p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function logBytes(bytes memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes)", p0));
    }

    function logBytes1(bytes1 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes1)", p0));
    }

    function logBytes2(bytes2 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes2)", p0));
    }

    function logBytes3(bytes3 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes3)", p0));
    }

    function logBytes4(bytes4 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes4)", p0));
    }

    function logBytes5(bytes5 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes5)", p0));
    }

    function logBytes6(bytes6 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes6)", p0));
    }

    function logBytes7(bytes7 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes7)", p0));
    }

    function logBytes8(bytes8 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes8)", p0));
    }

    function logBytes9(bytes9 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes9)", p0));
    }

    function logBytes10(bytes10 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes10)", p0));
    }

    function logBytes11(bytes11 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes11)", p0));
    }

    function logBytes12(bytes12 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes12)", p0));
    }

    function logBytes13(bytes13 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes13)", p0));
    }

    function logBytes14(bytes14 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes14)", p0));
    }

    function logBytes15(bytes15 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes15)", p0));
    }

    function logBytes16(bytes16 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes16)", p0));
    }

    function logBytes17(bytes17 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes17)", p0));
    }

    function logBytes18(bytes18 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes18)", p0));
    }

    function logBytes19(bytes19 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes19)", p0));
    }

    function logBytes20(bytes20 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes20)", p0));
    }

    function logBytes21(bytes21 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes21)", p0));
    }

    function logBytes22(bytes22 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes22)", p0));
    }

    function logBytes23(bytes23 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes23)", p0));
    }

    function logBytes24(bytes24 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes24)", p0));
    }

    function logBytes25(bytes25 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes25)", p0));
    }

    function logBytes26(bytes26 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes26)", p0));
    }

    function logBytes27(bytes27 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes27)", p0));
    }

    function logBytes28(bytes28 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes28)", p0));
    }

    function logBytes29(bytes29 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes29)", p0));
    }

    function logBytes30(bytes30 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes30)", p0));
    }

    function logBytes31(bytes31 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes31)", p0));
    }

    function logBytes32(bytes32 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bytes32)", p0));
    }

    function log(uint256 p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256)", p0));
    }

    function log(string memory p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string)", p0));
    }

    function log(bool p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool)", p0));
    }

    function log(address p0) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address)", p0));
    }

    function log(uint256 p0, uint256 p1) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,uint256)", p0, p1)
        );
    }

    function log(uint256 p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,string)", p0, p1));
    }

    function log(uint256 p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(uint256,bool)", p0, p1));
    }

    function log(uint256 p0, address p1) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,address)", p0, p1)
        );
    }

    function log(string memory p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,uint256)", p0, p1));
    }

    function log(string memory p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,string)", p0, p1));
    }

    function log(string memory p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,bool)", p0, p1));
    }

    function log(string memory p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(string,address)", p0, p1));
    }

    function log(bool p0, uint256 p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,uint256)", p0, p1));
    }

    function log(bool p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,string)", p0, p1));
    }

    function log(bool p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,bool)", p0, p1));
    }

    function log(bool p0, address p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(bool,address)", p0, p1));
    }

    function log(address p0, uint256 p1) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,uint256)", p0, p1)
        );
    }

    function log(address p0, string memory p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,string)", p0, p1));
    }

    function log(address p0, bool p1) internal pure {
        _sendLogPayload(abi.encodeWithSignature("log(address,bool)", p0, p1));
    }

    function log(address p0, address p1) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,address)", p0, p1)
        );
    }

    function log(uint256 p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,uint256,uint256)", p0, p1, p2)
        );
    }

    function log(uint256 p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,uint256,string)", p0, p1, p2)
        );
    }

    function log(uint256 p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,uint256,bool)", p0, p1, p2)
        );
    }

    function log(uint256 p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,uint256,address)", p0, p1, p2)
        );
    }

    function log(uint256 p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,string,uint256)", p0, p1, p2)
        );
    }

    function log(uint256 p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,string,string)", p0, p1, p2)
        );
    }

    function log(uint256 p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,string,bool)", p0, p1, p2)
        );
    }

    function log(uint256 p0, string memory p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,string,address)", p0, p1, p2)
        );
    }

    function log(uint256 p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,bool,uint256)", p0, p1, p2)
        );
    }

    function log(uint256 p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,bool,string)", p0, p1, p2)
        );
    }

    function log(uint256 p0, bool p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,bool,bool)", p0, p1, p2)
        );
    }

    function log(uint256 p0, bool p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,bool,address)", p0, p1, p2)
        );
    }

    function log(uint256 p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,address,uint256)", p0, p1, p2)
        );
    }

    function log(uint256 p0, address p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,address,string)", p0, p1, p2)
        );
    }

    function log(uint256 p0, address p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,address,bool)", p0, p1, p2)
        );
    }

    function log(uint256 p0, address p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(uint256,address,address)", p0, p1, p2)
        );
    }

    function log(string memory p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,uint256,uint256)", p0, p1, p2)
        );
    }

    function log(string memory p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,uint256,string)", p0, p1, p2)
        );
    }

    function log(string memory p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,uint256,bool)", p0, p1, p2)
        );
    }

    function log(string memory p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,uint256,address)", p0, p1, p2)
        );
    }

    function log(string memory p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,string,uint256)", p0, p1, p2)
        );
    }

    function log(
        string memory p0,
        string memory p1,
        string memory p2
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,string,string)", p0, p1, p2)
        );
    }

    function log(string memory p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,string,bool)", p0, p1, p2)
        );
    }

    function log(string memory p0, string memory p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,string,address)", p0, p1, p2)
        );
    }

    function log(string memory p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,bool,uint256)", p0, p1, p2)
        );
    }

    function log(string memory p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,bool,string)", p0, p1, p2)
        );
    }

    function log(string memory p0, bool p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,bool,bool)", p0, p1, p2)
        );
    }

    function log(string memory p0, bool p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,bool,address)", p0, p1, p2)
        );
    }

    function log(string memory p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,address,uint256)", p0, p1, p2)
        );
    }

    function log(string memory p0, address p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,address,string)", p0, p1, p2)
        );
    }

    function log(string memory p0, address p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,address,bool)", p0, p1, p2)
        );
    }

    function log(string memory p0, address p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(string,address,address)", p0, p1, p2)
        );
    }

    function log(bool p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,uint256,uint256)", p0, p1, p2)
        );
    }

    function log(bool p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,uint256,string)", p0, p1, p2)
        );
    }

    function log(bool p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,uint256,bool)", p0, p1, p2)
        );
    }

    function log(bool p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,uint256,address)", p0, p1, p2)
        );
    }

    function log(bool p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,string,uint256)", p0, p1, p2)
        );
    }

    function log(bool p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,string,string)", p0, p1, p2)
        );
    }

    function log(bool p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,string,bool)", p0, p1, p2)
        );
    }

    function log(bool p0, string memory p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,string,address)", p0, p1, p2)
        );
    }

    function log(bool p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,bool,uint256)", p0, p1, p2)
        );
    }

    function log(bool p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,bool,string)", p0, p1, p2)
        );
    }

    function log(bool p0, bool p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,bool,bool)", p0, p1, p2)
        );
    }

    function log(bool p0, bool p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,bool,address)", p0, p1, p2)
        );
    }

    function log(bool p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,address,uint256)", p0, p1, p2)
        );
    }

    function log(bool p0, address p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,address,string)", p0, p1, p2)
        );
    }

    function log(bool p0, address p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,address,bool)", p0, p1, p2)
        );
    }

    function log(bool p0, address p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,address,address)", p0, p1, p2)
        );
    }

    function log(address p0, uint256 p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,uint256,uint256)", p0, p1, p2)
        );
    }

    function log(address p0, uint256 p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,uint256,string)", p0, p1, p2)
        );
    }

    function log(address p0, uint256 p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,uint256,bool)", p0, p1, p2)
        );
    }

    function log(address p0, uint256 p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,uint256,address)", p0, p1, p2)
        );
    }

    function log(address p0, string memory p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,string,uint256)", p0, p1, p2)
        );
    }

    function log(address p0, string memory p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,string,string)", p0, p1, p2)
        );
    }

    function log(address p0, string memory p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,string,bool)", p0, p1, p2)
        );
    }

    function log(address p0, string memory p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,string,address)", p0, p1, p2)
        );
    }

    function log(address p0, bool p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,bool,uint256)", p0, p1, p2)
        );
    }

    function log(address p0, bool p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,bool,string)", p0, p1, p2)
        );
    }

    function log(address p0, bool p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,bool,bool)", p0, p1, p2)
        );
    }

    function log(address p0, bool p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,bool,address)", p0, p1, p2)
        );
    }

    function log(address p0, address p1, uint256 p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,address,uint256)", p0, p1, p2)
        );
    }

    function log(address p0, address p1, string memory p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,address,string)", p0, p1, p2)
        );
    }

    function log(address p0, address p1, bool p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,address,bool)", p0, p1, p2)
        );
    }

    function log(address p0, address p1, address p2) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(address,address,address)", p0, p1, p2)
        );
    }

    function log(uint256 p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        uint256 p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,uint256,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        uint256 p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        bool p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        bool p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        address p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        string memory p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,string,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        bool p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        bool p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        bool p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        bool p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        bool p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,bool,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        uint256 p0,
        address p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(uint256 p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(uint256,address,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        uint256 p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        bool p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        bool p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        address p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        uint256 p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,uint256,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        uint256 p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        bool p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        bool p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        bool p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        address p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        string memory p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,string,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        bool p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,bool,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        uint256 p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        bool p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(string memory p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        bool p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        address p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        string memory p0,
        address p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(string,address,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        uint256 p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        uint256 p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        uint256 p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        uint256 p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        uint256 p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,uint256,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, string memory p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, string memory p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, string memory p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, string memory p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        string memory p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,string,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, uint256 p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, string memory p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        bool p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, string memory p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature("log(bool,bool,bool,bool)", p0, p1, p2, p3)
        );
    }

    function log(bool p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, address p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,bool,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        address p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        address p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        address p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        address p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        bool p0,
        address p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(bool p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(bool,address,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        uint256 p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, uint256 p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,uint256,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        uint256 p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        uint256 p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        uint256 p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        bool p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, string memory p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        bool p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        address p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        address p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        string memory p1,
        address p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,string,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        bool p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        bool p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        bool p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, string memory p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        bool p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, bool p2, string memory p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        bool p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, bool p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,bool,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, uint256 p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,uint256,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        uint256 p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,uint256,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, uint256 p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,uint256,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, uint256 p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,uint256,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        string memory p2,
        uint256 p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,string,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        string memory p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,string,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        string memory p2,
        bool p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,string,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        string memory p2,
        address p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,string,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, bool p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,bool,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        bool p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,bool,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, bool p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,bool,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, bool p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,bool,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, address p2, uint256 p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,address,uint256)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(
        address p0,
        address p1,
        address p2,
        string memory p3
    ) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,address,string)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, address p2, bool p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,address,bool)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }

    function log(address p0, address p1, address p2, address p3) internal pure {
        _sendLogPayload(
            abi.encodeWithSignature(
                "log(address,address,address,address)",
                p0,
                p1,
                p2,
                p3
            )
        );
    }
}

// File contracts/IntraverseProtocol.sol

// Original license: SPDX_License_Identifier: GPL-3.0
pragma solidity ^0.8.24;

contract IntraverseProtocol is
    Initializable,
    Context,
    ERC1155Supply,
    ERC2981,
    Ownable
{
    using ECDSA for bytes32;
    using MessageHashUtils for bytes32;

    uint256 private constant MIN_RARITIES = 2;
    uint256 private constant MAX_RARITIES = 20;

    error InvalidPhase();
    error InvalidRarity();
    error InvalidBurningConfig(uint256 expected, uint256 actual);
    error InvalidUnlockConfig(uint256 expected, uint256 actual);
    error InvalidLimitsConfig();
    error UserNotWhitelisted();
    error InvalidTokenId();
    error MaxMintCountReached();
    error NoMoreMintsAvailableForUser(address user);
    error TotalMintLimitReachedForUser(address user);
    error GlobalMintLimitReached();
    error InvalidRecipient(address expected, address actual);
    error NotEnoughTimePassed();
    error RarityNotYetUnlocked();
    error AlreadyCheckedInToday();
    error MaxRarityAlreadyUnlocked();

    enum Phase {
        SETUP,
        WHITELIST,
        PUBLIC
    }

    struct Roles {
        address initialOwner;
        address royaltiesReceiver;
        address whitelistSigner;
    }

    struct Config {
        uint256 maxRarity;
        uint256 baseUnlockTime;
        uint256 restoreMintFactor;
        uint256 initialUnlockedRarity;
        uint16 checkInInterval;
        uint256 maxMintPerWallet;
        uint256 maxMintCount;
        uint256 mintLimit;
        uint256[] burnConfig;
    }

    Phase public currentPhase = Phase.SETUP;

    Roles public roles;
    Config public config;

    uint256 public mintGlobalCount;

    /// @notice counter for each user's mint
    mapping(address => uint256) public mintCount;

    /// @notice counter for each user's burn
    mapping(address => uint256) public burnCount;

    /// @notice store the last check in time for each user
    mapping(address => uint256) public lastCheckIn;

    /// @notice store the last check in time for each user
    mapping(address => uint256) public checkInCount;

    /// @notice User's unlocked rarity level
    mapping(address => uint256) public rarityUnlocked;

    string private contractUri;

    event Mint(address indexed recipient, uint256 tokenId);
    event TokenUpgraded(
        address indexed owner,
        uint256 fromTokenId,
        uint256 toTokenId
    );
    event CheckIn(address indexed user, uint256 newRarity);

    modifier onlyPhase(Phase _phase) {
        if (currentPhase != _phase) revert InvalidPhase();
        _;
    }

    modifier notInPhase(Phase _phase) {
        if (currentPhase == _phase) revert InvalidPhase();
        _;
    }

    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor() ERC1155("") Ownable(msg.sender) {
        _disableInitializers();
    }

    function initialize(
        Roles memory _roles,
        Config memory _config,
        uint96 _defaultRoyalties,
        string memory _baseUri,
        string memory _contractUri
    ) public initializer {
        _setURI(_baseUri);
        _transferOwnership(_roles.initialOwner);

        roles = _roles;
        _updateContractConfig(_config);
        contractUri = _contractUri;
        _setDefaultRoyalty(roles.royaltiesReceiver, _defaultRoyalties);
    }

    function checkIn() public {
        // Calculate the current day number since the base timestamp
        uint256 currentDay = (block.timestamp - config.baseUnlockTime) / 1 days;

        // Use if statement with custom error instead of require
        if (
            lastCheckIn[_msgSender()] >=
            config.baseUnlockTime + currentDay * 1 days
        ) {
            revert AlreadyCheckedInToday();
        }

        if (rarityUnlocked[_msgSender()] >= config.maxRarity) {
            revert MaxRarityAlreadyUnlocked();
        }

        // Update the user's last check-in timestamp
        lastCheckIn[_msgSender()] = block.timestamp;

        checkInCount[_msgSender()] += 1;

        if (checkInCount[_msgSender()] % config.checkInInterval == 0) {
            rarityUnlocked[_msgSender()] = getUnlockedRarity(_msgSender()) + 1;
        }

        emit CheckIn(_msgSender(), rarityUnlocked[_msgSender()]);
    }

    /**
     * @notice Get the rarity that can be unlocked today for a user
     * @param user The user's address
     * @return The rarity available for unlocking today
     */
    function getNextRarity(address user) public view returns (uint256) {
        return rarityUnlocked[user] + 1;
    }

    /**
     * @notice Calculate the current day since the base timestamp
     * @return The current day number
     */
    function getCurrentDay() public view returns (uint256) {
        return (block.timestamp - config.baseUnlockTime) / 1 days;
    }

    /// @notice Admin can update the phase
    function updatePhase(Phase _phase) public onlyOwner {
        currentPhase = _phase;
    }

    /// @notice Returns the contract-level metadata URI
    function contractURI() public view returns (string memory) {
        return contractUri;
    }

    /// @notice Owner can update the contract URI
    function updateContractURI(
        string memory _contractUri
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        contractUri = _contractUri;
    }

    /// @notice Owner can update the base URI
    function updateMetadata(
        string memory _baseUri
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        _setURI(_baseUri);
    }

    /// @notice Owner can update the whitelist signer
    function updateWhitelistSigner(
        address _whitelistSigner
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        roles.whitelistSigner = _whitelistSigner;
    }

    /// @notice Owner can update the royalties receiver
    function updateRoyaltiesReceiver(
        address _royaltiesReceiver
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        roles.royaltiesReceiver = _royaltiesReceiver;
    }

    /// @notice Owner can update the contract config
    function _updateContractConfig(Config memory _config) internal {
        if (
            _config.maxRarity < MIN_RARITIES || _config.maxRarity > MAX_RARITIES
        ) {
            revert InvalidRarity();
        }

        if (_config.burnConfig.length != _config.maxRarity - 1) {
            revert InvalidBurningConfig(
                _config.maxRarity - 1,
                _config.burnConfig.length
            );
        }

        config = _config;
    }

    function updateContractConfig(
        Config memory _config
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        _updateContractConfig(_config);
    }

    function getBurnConfig() public view returns (uint256[] memory) {
        return config.burnConfig;
    }

    function getConfig() public view returns (Config memory) {
        return config;
    }

    function getRoles() public view returns (Roles memory) {
        return roles;
    }

    /// @param recipient the address that will receive the minted tokens
    /// @param amount the amount of tokens to mint for the given type of mint
    function mintInitialSupply(
        address recipient,
        uint256 tokenId,
        uint256 amount
    ) public onlyOwner onlyPhase(Phase.SETUP) {
        _mint(recipient, tokenId, amount, new bytes(0));
    }

    function canMint(
        uint256 _mintCount,
        uint256 _burnCount
    ) public view returns (bool) {
        if (config.restoreMintFactor == 0) {
            return _mintCount < config.mintLimit;
        }

        uint256 mintQuota = config.mintLimit +
            (_burnCount / config.restoreMintFactor) *
            config.mintLimit;
        return _mintCount < mintQuota;
    }

    /**
     * @notice Generate a hash for the given message
     * @param message The message to hash
     * @return bytes32 hash of the message
     */
    function getMessageHash(
        string memory message
    ) public pure returns (bytes32) {
        return keccak256(abi.encodePacked(message));
    }

    /**
     * @notice Verify the signature of a message
     * @param message The original message
     * @param signature The signature to verify
     * @return bool indicating whether the signature is valid
     */
    function verifySignature(
        string memory message,
        bytes memory signature
    ) public view returns (bool) {
        bytes32 messageHash = getMessageHash(message);
        address recoveredSigner = messageHash.toEthSignedMessageHash().recover(
            signature
        );
        return recoveredSigner == roles.whitelistSigner;
    }

    function messageFromAddress(
        address _address
    ) public pure returns (string memory) {
        return string.concat("address:", Strings.toHexString(_address));
    }

    /// @notice Free mint a token
    /// @param recipient the address that will receive the minted token
    function mint(address recipient, bytes memory signature) public {
        if (currentPhase == Phase.SETUP) {
            revert InvalidPhase();
        } else if (currentPhase == Phase.WHITELIST) {
            string memory message = messageFromAddress(recipient);

            if (!verifySignature(message, signature)) {
                revert UserNotWhitelisted();
            }
        }

        if (mintGlobalCount >= config.maxMintCount) {
            revert MaxMintCountReached();
        }

        if (mintCount[recipient] >= config.maxMintPerWallet) {
            revert TotalMintLimitReachedForUser(recipient);
        }

        if (canMint(mintCount[recipient], burnCount[recipient]) == false) {
            revert NoMoreMintsAvailableForUser(recipient);
        }

        mintCount[recipient] += 1;
        mintGlobalCount += 1;

        _mint(recipient, 1, 1, new bytes(0));
    }

    function getUnlockedRarity(address user) public view returns (uint256) {
        if (rarityUnlocked[user] == 0) {
            return config.initialUnlockedRarity;
        } else {
            return rarityUnlocked[user];
        }
    }

    /// @notice Upgrade a token to the next rarity according to the burn config
    /// @param _tokenId the token ID to upgrade to the next rarity
    function upgradeTokenTo(uint256 _tokenId) public {
        if (_tokenId <= 0 || _tokenId > config.maxRarity) {
            revert InvalidRarity();
        }

        if (_tokenId > getUnlockedRarity(_msgSender()) + 1) {
            revert RarityNotYetUnlocked();
        }

        // Token IDs starts from 1 while rarities start from 0
        uint256 rarityIndex = _tokenId - 1;

        // Rarities are shifted by 1 since there is no config
        // for the first rarity
        uint256 configIndex = rarityIndex - 1;

        uint256 amountToBurn = config.burnConfig[configIndex];

        _burn(_msgSender(), rarityIndex, amountToBurn);
        _mint(_msgSender(), _tokenId, 1, new bytes(0));

        // Counts the burn transactions, not the amount of tokens burned
        burnCount[_msgSender()] += 1;

        emit TokenUpgraded(msg.sender, rarityIndex, _tokenId);
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(
        bytes4 _interfaceId
    ) public view virtual override(ERC1155, ERC2981) returns (bool) {
        return
            _interfaceId == type(IERC1155).interfaceId ||
            _interfaceId == type(ERC2981).interfaceId ||
            super.supportsInterface(_interfaceId);
    }
}

// File contracts/IntraverseProtocolCloneFactory.sol

// Original license: SPDX_License_Identifier: GPL-3.0
pragma solidity ^0.8.24;

contract IntraverseProtocolCloneFactory is Ownable {
    using Clones for address;

    address public immutable implementation;
    address[] public clones;

    event CloneDeployed(address clone);

    constructor() Ownable(msg.sender) {
        implementation = address(new IntraverseProtocol());
    }

    function _deployClone(
        IntraverseProtocol.Roles memory _roles,
        IntraverseProtocol.Config memory _config,
        uint96 _defaultRoyalties,
        string memory _baseUri,
        string memory _contractUri
    ) internal returns (address) {
        address clone = implementation.clone();

        IntraverseProtocol(clone).initialize(
            _roles,
            _config,
            _defaultRoyalties,
            _baseUri,
            _contractUri
        );

        clones.push(clone);
        emit CloneDeployed(clone);

        return clone;
    }

    function deployClone(
        IntraverseProtocol.Roles memory _roles,
        IntraverseProtocol.Config memory _config,
        uint96 _defaultRoyalties,
        string memory _baseUri,
        string memory _contractUri,
        uint256 _numberOfClones
    ) external onlyOwner returns (address[] memory) {
        for (uint256 i = 0; i < _numberOfClones; i++) {
            _deployClone(
                _roles,
                _config,
                _defaultRoyalties,
                _baseUri,
                _contractUri
            );
        }

        return clones;
    }

    function getClones() external view returns (address[] memory) {
        return clones;
    }
}

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