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/**
 *Submitted for verification at lineascan.build/ on 2023-07-18
*/

// Sources flattened with hardhat v2.16.1 https://hardhat.org

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

// SPDX-License-Identifier: AGPL-3.0

// OpenZeppelin Contracts v4.4.1 (access/IAccessControl.sol)

pragma solidity ^0.8.0;

/**
 * @dev External interface of AccessControl declared to support ERC165 detection.
 */
interface IAccessControlUpgradeable {
    /**
     * @dev Emitted when `newAdminRole` is set as ``role``'s admin role, replacing `previousAdminRole`
     *
     * `DEFAULT_ADMIN_ROLE` is the starting admin for all roles, despite
     * {RoleAdminChanged} not being emitted signaling this.
     *
     * _Available since v3.1._
     */
    event RoleAdminChanged(bytes32 indexed role, bytes32 indexed previousAdminRole, bytes32 indexed newAdminRole);

    /**
     * @dev Emitted when `account` is granted `role`.
     *
     * `sender` is the account that originated the contract call, an admin role
     * bearer except when using {AccessControl-_setupRole}.
     */
    event RoleGranted(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Emitted when `account` is revoked `role`.
     *
     * `sender` is the account that originated the contract call:
     *   - if using `revokeRole`, it is the admin role bearer
     *   - if using `renounceRole`, it is the role bearer (i.e. `account`)
     */
    event RoleRevoked(bytes32 indexed role, address indexed account, address indexed sender);

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) external view returns (bool);

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {AccessControl-_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) external view returns (bytes32);

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function grantRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     */
    function revokeRole(bytes32 role, address account) external;

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been granted `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     */
    function renounceRole(bytes32 role, address account) external;
}


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


// OpenZeppelin Contracts (last updated v4.9.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}


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


// OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

/**
 * @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 Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 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 functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _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 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _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() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @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 {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized != type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

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


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


// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}


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


// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165Upgradeable {
    /**
     * @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[EIP 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-upgradeable/utils/introspection/[email protected]


// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;


/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 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);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165Upgradeable is Initializable, IERC165Upgradeable {
    function __ERC165_init() internal onlyInitializing {
    }

    function __ERC165_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165Upgradeable).interfaceId;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}


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


// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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


// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

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

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

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

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


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


// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;


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

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

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMathUpgradeable.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, MathUpgradeable.log256(value) + 1);
        }
    }

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

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

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


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


// OpenZeppelin Contracts (last updated v4.9.0) (access/AccessControl.sol)

pragma solidity ^0.8.0;





/**
 * @dev Contract module that allows children to implement role-based access
 * control mechanisms. This is a lightweight version that doesn't allow enumerating role
 * members except through off-chain means by accessing the contract event logs. Some
 * applications may benefit from on-chain enumerability, for those cases see
 * {AccessControlEnumerable}.
 *
 * Roles are referred to by their `bytes32` identifier. These should be exposed
 * in the external API and be unique. The best way to achieve this is by
 * using `public constant` hash digests:
 *
 * ```solidity
 * bytes32 public constant MY_ROLE = keccak256("MY_ROLE");
 * ```
 *
 * Roles can be used to represent a set of permissions. To restrict access to a
 * function call, use {hasRole}:
 *
 * ```solidity
 * function foo() public {
 *     require(hasRole(MY_ROLE, msg.sender));
 *     ...
 * }
 * ```
 *
 * Roles can be granted and revoked dynamically via the {grantRole} and
 * {revokeRole} functions. Each role has an associated admin role, and only
 * accounts that have a role's admin role can call {grantRole} and {revokeRole}.
 *
 * By default, the admin role for all roles is `DEFAULT_ADMIN_ROLE`, which means
 * that only accounts with this role will be able to grant or revoke other
 * roles. More complex role relationships can be created by using
 * {_setRoleAdmin}.
 *
 * WARNING: The `DEFAULT_ADMIN_ROLE` is also its own admin: it has permission to
 * grant and revoke this role. Extra precautions should be taken to secure
 * accounts that have been granted it. We recommend using {AccessControlDefaultAdminRules}
 * to enforce additional security measures for this role.
 */
abstract contract AccessControlUpgradeable is Initializable, ContextUpgradeable, IAccessControlUpgradeable, ERC165Upgradeable {
    function __AccessControl_init() internal onlyInitializing {
    }

    function __AccessControl_init_unchained() internal onlyInitializing {
    }
    struct RoleData {
        mapping(address => bool) members;
        bytes32 adminRole;
    }

    mapping(bytes32 => RoleData) private _roles;

    bytes32 public constant DEFAULT_ADMIN_ROLE = 0x00;

    /**
     * @dev Modifier that checks that an account has a specific role. Reverts
     * with a standardized message including the required role.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     *
     * _Available since v4.1._
     */
    modifier onlyRole(bytes32 role) {
        _checkRole(role);
        _;
    }

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

    /**
     * @dev Returns `true` if `account` has been granted `role`.
     */
    function hasRole(bytes32 role, address account) public view virtual override returns (bool) {
        return _roles[role].members[account];
    }

    /**
     * @dev Revert with a standard message if `_msgSender()` is missing `role`.
     * Overriding this function changes the behavior of the {onlyRole} modifier.
     *
     * Format of the revert message is described in {_checkRole}.
     *
     * _Available since v4.6._
     */
    function _checkRole(bytes32 role) internal view virtual {
        _checkRole(role, _msgSender());
    }

    /**
     * @dev Revert with a standard message if `account` is missing `role`.
     *
     * The format of the revert reason is given by the following regular expression:
     *
     *  /^AccessControl: account (0x[0-9a-f]{40}) is missing role (0x[0-9a-f]{64})$/
     */
    function _checkRole(bytes32 role, address account) internal view virtual {
        if (!hasRole(role, account)) {
            revert(
                string(
                    abi.encodePacked(
                        "AccessControl: account ",
                        StringsUpgradeable.toHexString(account),
                        " is missing role ",
                        StringsUpgradeable.toHexString(uint256(role), 32)
                    )
                )
            );
        }
    }

    /**
     * @dev Returns the admin role that controls `role`. See {grantRole} and
     * {revokeRole}.
     *
     * To change a role's admin, use {_setRoleAdmin}.
     */
    function getRoleAdmin(bytes32 role) public view virtual override returns (bytes32) {
        return _roles[role].adminRole;
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleGranted} event.
     */
    function grantRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _grantRole(role, account);
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * If `account` had been granted `role`, emits a {RoleRevoked} event.
     *
     * Requirements:
     *
     * - the caller must have ``role``'s admin role.
     *
     * May emit a {RoleRevoked} event.
     */
    function revokeRole(bytes32 role, address account) public virtual override onlyRole(getRoleAdmin(role)) {
        _revokeRole(role, account);
    }

    /**
     * @dev Revokes `role` from the calling account.
     *
     * Roles are often managed via {grantRole} and {revokeRole}: this function's
     * purpose is to provide a mechanism for accounts to lose their privileges
     * if they are compromised (such as when a trusted device is misplaced).
     *
     * If the calling account had been revoked `role`, emits a {RoleRevoked}
     * event.
     *
     * Requirements:
     *
     * - the caller must be `account`.
     *
     * May emit a {RoleRevoked} event.
     */
    function renounceRole(bytes32 role, address account) public virtual override {
        require(account == _msgSender(), "AccessControl: can only renounce roles for self");

        _revokeRole(role, account);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * If `account` had not been already granted `role`, emits a {RoleGranted}
     * event. Note that unlike {grantRole}, this function doesn't perform any
     * checks on the calling account.
     *
     * May emit a {RoleGranted} event.
     *
     * [WARNING]
     * ====
     * This function should only be called from the constructor when setting
     * up the initial roles for the system.
     *
     * Using this function in any other way is effectively circumventing the admin
     * system imposed by {AccessControl}.
     * ====
     *
     * NOTE: This function is deprecated in favor of {_grantRole}.
     */
    function _setupRole(bytes32 role, address account) internal virtual {
        _grantRole(role, account);
    }

    /**
     * @dev Sets `adminRole` as ``role``'s admin role.
     *
     * Emits a {RoleAdminChanged} event.
     */
    function _setRoleAdmin(bytes32 role, bytes32 adminRole) internal virtual {
        bytes32 previousAdminRole = getRoleAdmin(role);
        _roles[role].adminRole = adminRole;
        emit RoleAdminChanged(role, previousAdminRole, adminRole);
    }

    /**
     * @dev Grants `role` to `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleGranted} event.
     */
    function _grantRole(bytes32 role, address account) internal virtual {
        if (!hasRole(role, account)) {
            _roles[role].members[account] = true;
            emit RoleGranted(role, account, _msgSender());
        }
    }

    /**
     * @dev Revokes `role` from `account`.
     *
     * Internal function without access restriction.
     *
     * May emit a {RoleRevoked} event.
     */
    function _revokeRole(bytes32 role, address account) internal virtual {
        if (hasRole(role, account)) {
            _roles[role].members[account] = false;
            emit RoleRevoked(role, account, _msgSender());
        }
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}


// File @openzeppelin/contracts-upgradeable/security/[email protected]


// OpenZeppelin Contracts (last updated v4.9.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

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

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

    uint256 private _status;

    function __ReentrancyGuard_init() internal onlyInitializing {
        __ReentrancyGuard_init_unchained();
    }

    function __ReentrancyGuard_init_unchained() internal onlyInitializing {
        _status = _NOT_ENTERED;
    }

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

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

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

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

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

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}


// File contracts/interfaces/IL2MessageManager.sol


pragma solidity ^0.8.19;

interface IL2MessageManager {
  /**
   * @dev Emitted when L1->L2 message hashes have been added to L2 storage.
   */
  event L1L2MessageHashesAddedToInbox(bytes32[] messageHashes);

  /**
   * @dev Thrown when the message hashes list length is higher than one hundred.
   */
  error MessageHashesListLengthHigherThanOneHundred(uint256 length);

  /**
   * @dev Thrown when the message hashes array is empty.
   */
  error EmptyMessageHashesArray();

  /**
   * @dev Thrown when the message does not exist or has already been claimed.
   */
  error MessageDoesNotExistOrHasAlreadyBeenClaimed();

  /**
   * @notice Anchor L1-> L2 message hashes.
   * @param _messageHashes New message hashes to anchor on L2.
   */
  function addL1L2MessageHashes(bytes32[] calldata _messageHashes) external;
}


// File contracts/interfaces/IPauseManager.sol


pragma solidity ^0.8.19;

interface IPauseManager {
  /**
   * @dev Thrown when a specific pause type is paused.
   */
  error IsPaused(bytes32 pauseType);

  /**
   * @dev Thrown when a specific pause type is not paused and expected to be.
   */
  error IsNotPaused(bytes32 pauseType);

  /**
   * @dev Emitted when a pause type is paused.
   */
  event Paused(address messageSender, bytes32 pauseType);

  /**
   * @dev Emitted when a pause type is unpaused.
   */
  event UnPaused(address messageSender, bytes32 pauseType);
}


// File contracts/messageService/lib/PauseManager.sol



pragma solidity ^0.8.19;



/**
 * @title Contract to manage cross-chain function pausing.
 * @author ConsenSys Software Inc.
 */
abstract contract PauseManager is Initializable, IPauseManager, AccessControlUpgradeable {
  bytes32 public constant PAUSE_MANAGER_ROLE = keccak256("PAUSE_MANAGER_ROLE");

  bytes32 public constant GENERAL_PAUSE_TYPE = keccak256("GENERAL_PAUSE_TYPE");
  bytes32 public constant L1_L2_PAUSE_TYPE = keccak256("L1_L2_PAUSE_TYPE");
  bytes32 public constant L2_L1_PAUSE_TYPE = keccak256("L2_L1_PAUSE_TYPE");
  bytes32 public constant PROVING_SYSTEM_PAUSE_TYPE = keccak256("PROVING_SYSTEM_PAUSE_TYPE");

  mapping(bytes32 => bool) public pauseTypeStatuses;

  uint256[10] private _gap;

  /**
   * @dev Modifier to make a function callable only when the type is not paused.
   *
   * Requirements:
   *
   * - The type must not be paused.
   */
  modifier whenTypeNotPaused(bytes32 _pauseType) {
    _requireTypeNotPaused(_pauseType);
    _;
  }

  /**
   * @dev Modifier to make a function callable only when the type is paused.
   *
   * Requirements:
   *
   * - The type must not be paused.
   */
  modifier whenTypePaused(bytes32 _pauseType) {
    _requireTypePaused(_pauseType);
    _;
  }

  /**
   * @dev Throws if the type is not paused.
   * @param _pauseType The keccak256 pause type being checked,
   */
  function _requireTypePaused(bytes32 _pauseType) internal view virtual {
    if (!pauseTypeStatuses[_pauseType]) {
      revert IsNotPaused(_pauseType);
    }
  }

  /**
   * @dev Throws if the type is paused.
   * @param _pauseType The keccak256 pause type being checked,
   */
  function _requireTypeNotPaused(bytes32 _pauseType) internal view virtual {
    if (pauseTypeStatuses[_pauseType]) {
      revert IsPaused(_pauseType);
    }
  }

  /**
   * @notice Pauses functionality by specific type.
   * @dev Requires PAUSE_MANAGER_ROLE.
   * @param _pauseType keccak256 pause type.
   **/
  function pauseByType(bytes32 _pauseType) external whenTypeNotPaused(_pauseType) onlyRole(PAUSE_MANAGER_ROLE) {
    pauseTypeStatuses[_pauseType] = true;
    emit Paused(_msgSender(), _pauseType);
  }

  /**
   * @notice Unpauses functionality by specific type.
   * @dev Requires PAUSE_MANAGER_ROLE.
   * @param _pauseType keccak256 pause type.
   **/
  function unPauseByType(bytes32 _pauseType) external whenTypePaused(_pauseType) onlyRole(PAUSE_MANAGER_ROLE) {
    pauseTypeStatuses[_pauseType] = false;
    emit UnPaused(_msgSender(), _pauseType);
  }
}


// File contracts/messageService/l2/L2MessageManager.sol


pragma solidity ^0.8.19;



/**
 * @title Contract to manage cross-chain message hashes storage and statuses on L2.
 * @author ConsenSys Software Inc.
 */
abstract contract L2MessageManager is Initializable, PauseManager, IL2MessageManager {
  uint8 public constant INBOX_STATUS_UNKNOWN = 0;
  uint8 public constant INBOX_STATUS_RECEIVED = 1;
  uint8 public constant INBOX_STATUS_CLAIMED = 2;

  /// @dev There is a uint232 worth of storage layout here

  bytes32 public constant L1_L2_MESSAGE_SETTER_ROLE = keccak256("L1_L2_MESSAGE_SETTER_ROLE");

  /**
   * @dev Mapping to store L1->L2 message hashes status.
   * @dev messageHash => messageStatus (0: unknown, 1: received, 2: claimed).
   */
  mapping(bytes32 => uint256) public inboxL1L2MessageStatus;

  /// @dev Keep free storage slots for future implementation updates to avoid storage collision.
  // *******************************************************************************************
  // NB: THIS GAP HAS BEEN PUSHED OUT IN FAVOUR OF THE GAP INSIDE THE REENTRANCY CODE
  //uint256[50] private __gap;
  // NB: DO NOT USE THIS GAP
  // *******************************************************************************************

  /**
   * @notice Initialises L2 message manager contract.
   * @param _l1l2MessageSetter The address owning the L1_L2_MESSAGE_SETTER_ROLE role.
   **/
  function __L2MessageManager_init(address _l1l2MessageSetter) internal onlyInitializing {
    _grantRole(L1_L2_MESSAGE_SETTER_ROLE, _l1l2MessageSetter);
  }

  /**
   * @notice Add a cross-chain L1->L2 message hashes in storage.
   * @dev Only address that has the role 'L1_L2_MESSAGE_SETTER_ROLE' are allowed to call this function.
   * @param _messageHashes Message hashes array.
   */
  function addL1L2MessageHashes(bytes32[] calldata _messageHashes) external onlyRole(L1_L2_MESSAGE_SETTER_ROLE) {
    uint256 messageHashesLength = _messageHashes.length;

    if (messageHashesLength > 100) {
      revert MessageHashesListLengthHigherThanOneHundred(messageHashesLength);
    }

    for (uint256 i; i < messageHashesLength; ) {
      bytes32 messageHash = _messageHashes[i];
      if (inboxL1L2MessageStatus[messageHash] == INBOX_STATUS_UNKNOWN) {
        inboxL1L2MessageStatus[messageHash] = INBOX_STATUS_RECEIVED;
      }
      unchecked {
        i++;
      }
    }

    emit L1L2MessageHashesAddedToInbox(_messageHashes);
  }

  /**
   * @notice Update the status of L1->L2 message when a user claim a message on L2.
   * @param _messageHash Hash of the message.
   */
  function _updateL1L2MessageStatusToClaimed(bytes32 _messageHash) internal {
    if (inboxL1L2MessageStatus[_messageHash] != INBOX_STATUS_RECEIVED) {
      revert MessageDoesNotExistOrHasAlreadyBeenClaimed();
    }

    inboxL1L2MessageStatus[_messageHash] = INBOX_STATUS_CLAIMED;
  }
}


// File contracts/interfaces/IGenericErrors.sol


pragma solidity ^0.8.19;

interface IGenericErrors {
  /**
   * @dev Thrown when a parameter is the zero address.
   */
  error ZeroAddressNotAllowed();
}


// File contracts/interfaces/IMessageService.sol


pragma solidity ^0.8.19;

interface IMessageService {
  /**
   * @dev Emitted when a message is sent.
   * @dev We include the message hash to save hashing costs on the rollup.
   */
  event MessageSent(
    address indexed _from,
    address indexed _to,
    uint256 _fee,
    uint256 _value,
    uint256 _nonce,
    bytes _calldata,
    bytes32 indexed _messageHash
  );

  /**
   * @dev Emitted when a message is claimed.
   */
  event MessageClaimed(bytes32 indexed _messageHash);

  /**
   * @dev Thrown when fees are lower than the minimum fee.
   */
  error FeeTooLow();

  /**
   * @dev Thrown when fees are lower than value.
   */
  error ValueShouldBeGreaterThanFee();

  /**
   * @dev Thrown when the value sent is less than the fee.
   * @dev Value to forward on is msg.value - _fee.
   */
  error ValueSentTooLow();

  /**
   * @dev Thrown when the destination address reverts.
   */
  error MessageSendingFailed(address destination);

  /**
   * @dev Thrown when the destination address reverts.
   */
  error FeePaymentFailed(address recipient);

  /**
   * @notice Sends a message for transporting from the given chain.
   * @dev This function should be called with a msg.value = _value + _fee. The fee will be paid on the destination chain.
   * @param _to The destination address on the destination chain.
   * @param _fee The message service fee on the origin chain.
   * @param _calldata The calldata used by the destination message service to call the destination contract.
   */
  function sendMessage(address _to, uint256 _fee, bytes calldata _calldata) external payable;

  /**
   * @notice Deliver a message to the destination chain.
   * @notice Is called automatically by the Postman, dApp or end user.
   * @param _from The msg.sender calling the origin message service.
   * @param _to The destination address on the destination chain.
   * @param _value The value to be transferred to the destination address.
   * @param _fee The message service fee on the origin chain.
   * @param _feeRecipient Address that will receive the fees.
   * @param _calldata The calldata used by the destination message service to call/forward to the destination contract.
   * @param _nonce Unique message number.
   */
  function claimMessage(
    address _from,
    address _to,
    uint256 _fee,
    uint256 _value,
    address payable _feeRecipient,
    bytes calldata _calldata,
    uint256 _nonce
  ) external;

  /**
   * @notice Returns the original sender of the message on the origin layer.
   * @return The original sender of the message on the origin layer.
   */
  function sender() external view returns (address);
}


// File contracts/messageService/lib/Codec.sol


pragma solidity ^0.8.19;

/**
 * @title Decoding functions for message service anchoring and bytes slicing.
 * @author ConsenSys Software Inc.
 * @notice You can use this to slice bytes and extract anchoring hashes from calldata.
 **/
library CodecV2 {
  /**
   * @notice Decodes a collection of bytes32 (hashes) from the calldata of a transaction.
   * @dev Extracts and decodes skipping the function selector (selector is expected in the input).
   * @dev A check beforehand must be performed to confirm this is the correct type of transaction.
   * @param _calldataWithSelector The calldata for the transaction.
   * @return bytes32[] - array of message hashes.
   **/
  function _extractXDomainAddHashes(bytes memory _calldataWithSelector) internal pure returns (bytes32[] memory) {
    assembly {
      let len := sub(mload(_calldataWithSelector), 4)
      _calldataWithSelector := add(_calldataWithSelector, 0x4)
      mstore(_calldataWithSelector, len)
    }

    return abi.decode(_calldataWithSelector, (bytes32[]));
  }
}


// File contracts/interfaces/IRateLimiter.sol


pragma solidity ^0.8.19;

interface IRateLimiter {
  /**
   * @dev Thrown when an amount breaches the limit in the period.
   */
  error RateLimitExceeded();

  /**
   * @dev Thrown when the period is initialised to zero.
   */
  error PeriodIsZero();

  /**
   * @dev Thrown when the limit is initialised to zero.
   */
  error LimitIsZero();

  /**
   * @dev Emitted when the amount in the period is reset to zero.
   */
  event AmountUsedInPeriodReset(address indexed resettingAddress);

  /**
   * @dev Emitted when the limit is changed.
   * @dev If the current used amount is higher than the new limit, the used amount is lowered to the limit.
   */
  event LimitAmountChanged(
    address indexed amountChangeBy,
    uint256 amount,
    bool amountUsedLoweredToLimit,
    bool usedAmountResetToZero
  );

  /**
   * @notice Resets the rate limit amount to the amount specified.
   * @param _amount New message hashes.
   */
  function resetRateLimitAmount(uint256 _amount) external;

  /**
   * @notice Resets the amount used in the period to zero.
   */
  function resetAmountUsedInPeriod() external;
}


// File contracts/messageService/lib/RateLimiter.sol


pragma solidity ^0.8.19;



/**
 * @title Rate Limiter by period and amount using the block timestamp.
 * @author ConsenSys Software Inc.
 * @notice You can use this control numeric limits over a period using timestamp.
 **/
contract RateLimiter is Initializable, IRateLimiter, AccessControlUpgradeable {
  bytes32 public constant RATE_LIMIT_SETTER_ROLE = keccak256("RATE_LIMIT_SETTER_ROLE");

  uint256 public periodInSeconds; // how much time before limit resets.
  uint256 public limitInWei; // max ether to withdraw per period.

  // @dev Public for ease of consumption.
  // @notice The time at which the current period ends at.
  uint256 public currentPeriodEnd;

  // @dev Public for ease of consumption.
  // @notice Amounts already withdrawn this period.
  uint256 public currentPeriodAmountInWei;

  uint256[10] private _gap;

  /**
   * @notice Initialises the limits and period for the rate limiter.
   * @param _periodInSeconds The length of the period in seconds.
   * @param _limitInWei The limit allowed in the period in Wei.
   **/
  function __RateLimiter_init(uint256 _periodInSeconds, uint256 _limitInWei) internal onlyInitializing {
    if (_periodInSeconds == 0) {
      revert PeriodIsZero();
    }

    if (_limitInWei == 0) {
      revert LimitIsZero();
    }

    periodInSeconds = _periodInSeconds;
    limitInWei = _limitInWei;
    currentPeriodEnd = block.timestamp + _periodInSeconds;
  }

  /**
   * @notice Increments the amount used in the period.
   * @dev The amount determining logic is external to this (e.g. fees are included when calling here).
   * @dev Reverts if the limit is breached.
   * @param _usedAmount The amount used to be added.
   **/
  function _addUsedAmount(uint256 _usedAmount) internal {
    uint256 currentPeriodAmountTemp;

    if (currentPeriodEnd < block.timestamp) {
      currentPeriodEnd = block.timestamp + periodInSeconds;
      currentPeriodAmountTemp = _usedAmount;
    } else {
      currentPeriodAmountTemp = currentPeriodAmountInWei + _usedAmount;
    }

    if (currentPeriodAmountTemp > limitInWei) {
      revert RateLimitExceeded();
    }

    currentPeriodAmountInWei = currentPeriodAmountTemp;
  }

  /**
   * @notice Resets the rate limit amount.
   * @dev If the used amount is higher, it is set to the limit to avoid confusion/issues.
   * @dev Only the RATE_LIMIT_SETTER_ROLE is allowed to execute this function.
   * @dev Emits the LimitAmountChanged event.
   * @dev usedLimitAmountToSet will use the default value of zero if period has expired
   * @param _amount The amount to reset the limit to.
   **/
  function resetRateLimitAmount(uint256 _amount) external onlyRole(RATE_LIMIT_SETTER_ROLE) {
    uint256 usedLimitAmountToSet;
    bool amountUsedLoweredToLimit;
    bool usedAmountResetToZero;

    if (currentPeriodEnd < block.timestamp) {
      currentPeriodEnd = block.timestamp + periodInSeconds;
      usedAmountResetToZero = true;
    } else {
      if (_amount < currentPeriodAmountInWei) {
        usedLimitAmountToSet = _amount;
        amountUsedLoweredToLimit = true;
      }
    }

    limitInWei = _amount;

    if (usedAmountResetToZero || amountUsedLoweredToLimit) {
      currentPeriodAmountInWei = usedLimitAmountToSet;
    }

    emit LimitAmountChanged(_msgSender(), _amount, amountUsedLoweredToLimit, usedAmountResetToZero);
  }

  /**
   * @notice Resets the amount used to zero.
   * @dev Only the RATE_LIMIT_SETTER_ROLE is allowed to execute this function.
   * @dev Emits the AmountUsedInPeriodReset event.
   **/
  function resetAmountUsedInPeriod() external onlyRole(RATE_LIMIT_SETTER_ROLE) {
    currentPeriodAmountInWei = 0;

    emit AmountUsedInPeriodReset(_msgSender());
  }
}


// File contracts/messageService/l2/L2MessageService.sol


pragma solidity ^0.8.19;







/**
 * @title Contract to manage cross-chain messaging on L2.
 * @author ConsenSys Software Inc.
 */
contract L2MessageService is
  Initializable,
  RateLimiter,
  L2MessageManager,
  ReentrancyGuardUpgradeable,
  IMessageService,
  IGenericErrors
{
  // Keep free storage slots for future implementation updates to avoid storage collision.
  uint256[50] private __gap_L2MessageService;

  bytes32 public constant MINIMUM_FEE_SETTER_ROLE = keccak256("MINIMUM_FEE_SETTER_ROLE");

  address private _messageSender;

  // @dev initialise to save user cost with existing slot.
  uint256 public nextMessageNumber;

  // @dev initialise minimumFeeInWei variable.
  uint256 public minimumFeeInWei;

  // @dev adding these should not affect storage as they are constants and are store in bytecode
  uint256 private constant REFUND_OVERHEAD_IN_GAS = 47500;

  /// @custom:oz-upgrades-unsafe-allow constructor
  constructor() {
    _disableInitializers();
  }

  /**
   * @notice Initialises underlying message service dependencies.
   * @param _securityCouncil The address owning the security council role.
   * @param _l1l2MessageSetter The address owning the add L1L2MessageHashes functionality.
   * @param _rateLimitPeriod The period to rate limit against.
   * @param _rateLimitAmount The limit allowed for withdrawing the period.
   **/
  function initialize(
    address _securityCouncil,
    address _l1l2MessageSetter,
    uint256 _rateLimitPeriod,
    uint256 _rateLimitAmount
  ) public initializer {
    if (_securityCouncil == address(0)) {
      revert ZeroAddressNotAllowed();
    }

    if (_l1l2MessageSetter == address(0)) {
      revert ZeroAddressNotAllowed();
    }

    __ERC165_init();
    __Context_init();
    __AccessControl_init();
    __RateLimiter_init(_rateLimitPeriod, _rateLimitAmount);
    __L2MessageManager_init(_l1l2MessageSetter);

    nextMessageNumber = 1;

    _grantRole(DEFAULT_ADMIN_ROLE, _securityCouncil);
    _grantRole(MINIMUM_FEE_SETTER_ROLE, _securityCouncil);
    _grantRole(RATE_LIMIT_SETTER_ROLE, _securityCouncil);
    _grantRole(PAUSE_MANAGER_ROLE, _securityCouncil);

    _messageSender = address(123456789);
  }

  /**
   * @notice Adds a message for sending cross-chain and emits a relevant event.
   * @dev The message number is preset and only incremented at the end if successful for the next caller.
   * @param _to The address the message is intended for.
   * @param _fee The fee being paid for the message delivery.
   * @param _calldata The calldata to pass to the recipient.
   **/
  function sendMessage(address _to, uint256 _fee, bytes calldata _calldata) external payable {
    _requireTypeNotPaused(L2_L1_PAUSE_TYPE);
    _requireTypeNotPaused(GENERAL_PAUSE_TYPE);

    if (_to == address(0)) {
      revert ZeroAddressNotAllowed();
    }

    if (_fee > msg.value) {
      revert ValueSentTooLow();
    }

    uint256 coinbaseFee = minimumFeeInWei;

    if (_fee < coinbaseFee) {
      revert FeeTooLow();
    }

    uint256 postmanFee;
    uint256 valueSent;

    unchecked {
      postmanFee = _fee - coinbaseFee;
      valueSent = msg.value - _fee;
    }

    uint256 messageNumber = nextMessageNumber;
    /// @dev Rate limit and revert is in the rate limiter.
    _addUsedAmount(valueSent + postmanFee);

    bytes32 messageHash = keccak256(abi.encode(msg.sender, _to, postmanFee, valueSent, messageNumber, _calldata));

    nextMessageNumber++;

    (bool success, ) = block.coinbase.call{ value: coinbaseFee }("");
    if (!success) {
      revert FeePaymentFailed(block.coinbase);
    }

    emit MessageSent(msg.sender, _to, postmanFee, valueSent, messageNumber, _calldata, messageHash);
  }

  /**
   * @notice Claims and delivers a cross-chain message.
   * @dev _feeRecipient Can be set to address(0) to receive as msg.sender.
   * @dev messageSender Is set temporarily when claiming and reset post.
   * @param _from The address of the original sender.
   * @param _to The address the message is intended for.
   * @param _fee The fee being paid for the message delivery.
   * @param _value The value to be transferred to the destination address.
   * @param _feeRecipient The recipient for the fee.
   * @param _calldata The calldata to pass to the recipient.
   * @param _nonce The unique auto generated message number used when sending the message.
   **/
  function claimMessage(
    address _from,
    address _to,
    uint256 _fee,
    uint256 _value,
    address payable _feeRecipient,
    bytes calldata _calldata,
    uint256 _nonce
  ) external nonReentrant distributeFees(_fee, _to, _calldata, _feeRecipient) {
    _requireTypeNotPaused(L1_L2_PAUSE_TYPE);
    _requireTypeNotPaused(GENERAL_PAUSE_TYPE);

    bytes32 messageHash = keccak256(abi.encode(_from, _to, _fee, _value, _nonce, _calldata));

    /// @dev Status check and revert is in the message manager.
    _updateL1L2MessageStatusToClaimed(messageHash);

    _messageSender = _from;

    (bool callSuccess, bytes memory returnData) = _to.call{ value: _value }(_calldata);
    if (!callSuccess) {
      if (returnData.length > 0) {
        assembly {
          let data_size := mload(returnData)
          revert(add(32, returnData), data_size)
        }
      } else {
        revert MessageSendingFailed(_to);
      }
    }

    _messageSender = address(123456789);
    emit MessageClaimed(messageHash);
  }

  /**
   * @notice The Fee Manager sets a minimum fee to address DOS protection.
   * @param _feeInWei New minimum fee in Wei.
   **/
  function setMinimumFee(uint256 _feeInWei) external onlyRole(MINIMUM_FEE_SETTER_ROLE) {
    minimumFeeInWei = _feeInWei;
  }

  /**
   * @dev The _messageSender address is set temporarily when claiming.
   * @return _messageSender address.
   **/
  function sender() external view returns (address) {
    return _messageSender;
  }

  /**
   * @notice Function to receive funds for liquidity purposes.
   **/
  receive() external payable virtual {}

  /**
   * @notice The unspent fee is refunded if applicable.
   * @param _feeInWei The fee paid for delivery in Wei.
   * @param _to The recipient of the message and gas refund.
   * @param _calldata The calldata of the message.
   **/
  modifier distributeFees(
    uint256 _feeInWei,
    address _to,
    bytes calldata _calldata,
    address _feeRecipient
  ) {
    //pre-execution
    uint256 startingGas = gasleft();
    _;
    //post-execution

    // we have a fee
    if (_feeInWei > 0) {
      // default postman fee
      uint256 deliveryFee = _feeInWei;

      // do we have empty calldata?
      if (_calldata.length == 0) {
        bool isDestinationEOA;

        assembly {
          isDestinationEOA := iszero(extcodesize(_to))
        }

        // are we calling an EOA
        if (isDestinationEOA) {
          // initial + cost to call and refund minus gasleft
          deliveryFee = (startingGas + REFUND_OVERHEAD_IN_GAS - gasleft()) * tx.gasprice;

          if (_feeInWei > deliveryFee) {
            payable(_to).send(_feeInWei - deliveryFee);
          } else {
            deliveryFee = _feeInWei;
          }
        }
      }

      address feeReceiver = _feeRecipient == address(0) ? msg.sender : _feeRecipient;

      bool callSuccess = payable(feeReceiver).send(deliveryFee);
      if (!callSuccess) {
        revert FeePaymentFailed(feeReceiver);
      }
    }
  }
}

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