// File: @openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

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

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }

    function __Ownable_init_unchained() internal onlyInitializing {
        _transferOwnership(_msgSender());
    }

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

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

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

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

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

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

    /**
     * @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/proxy/utils/Initializable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @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]
 * ```
 * 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. Equivalent to `reinitializer(1)`.
     */
    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.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so 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.
     *
     * 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.
     */
    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.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}

// File: @openzeppelin/contracts-upgradeable/security/PausableUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (security/Pausable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract PausableUpgradeable is Initializable, ContextUpgradeable {
    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    bool private _paused;

    /**
     * @dev Initializes the contract in unpaused state.
     */
    function __Pausable_init() internal onlyInitializing {
        __Pausable_init_unchained();
    }

    function __Pausable_init_unchained() internal onlyInitializing {
        _paused = false;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        _requireNotPaused();
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        _requirePaused();
        _;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Throws if the contract is paused.
     */
    function _requireNotPaused() internal view virtual {
        require(!paused(), "Pausable: paused");
    }

    /**
     * @dev Throws if the contract is not paused.
     */
    function _requirePaused() internal view virtual {
        require(paused(), "Pausable: not paused");
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        _paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        _paused = false;
        emit Unpaused(_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/ReentrancyGuardUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If 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() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

        _;

        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_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: @openzeppelin/contracts-upgradeable/utils/AddressUpgradeable.sol



// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (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
     * ====
     *
     * [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://diligence.consensys.net/posts/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/v0.5.11/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 functionCall(target, data, "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");
        require(isContract(target), "Address: call to non-contract");

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(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) {
        require(isContract(target), "Address: static call to non-contract");

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason 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 {
            // 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/utils/ContextUpgradeable.sol



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

pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";

/**
 * @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/access/Ownable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

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

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

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

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

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

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

    function _setOwner(address newOwner) private {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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

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

// File: contracts/L1/messaging/IL1CrossDomainMessenger.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";

/* Interface Imports */
import { ICrossDomainMessenger } from "../../libraries/bridge/ICrossDomainMessenger.sol";

/**
 * @title IL1CrossDomainMessenger
 */
interface IL1CrossDomainMessenger is ICrossDomainMessenger {
    /*******************
     * Data Structures *
     *******************/

    struct L2MessageInclusionProof {
        bytes32 stateRoot;
        Lib_OVMCodec.ChainBatchHeader stateRootBatchHeader;
        Lib_OVMCodec.ChainInclusionProof stateRootProof;
        bytes stateTrieWitness;
        bytes storageTrieWitness;
    }

    // for batch relay
    struct L2ToL1Message {
        address target;
        address sender;
        bytes message;
        uint256 messageNonce;
        L2MessageInclusionProof proof;
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * Relays a cross domain message to a contract.
     * @param _target Target contract address.
     * @param _sender Message sender address.
     * @param _message Message to send to the target.
     * @param _messageNonce Nonce for the provided message.
     * @param _proof Inclusion proof for the given message.
     */
    function relayMessage(
        address _target,
        address _sender,
        bytes memory _message,
        uint256 _messageNonce,
        L2MessageInclusionProof memory _proof
    ) external;

    /**
     * Replays a cross domain message to the target messenger.
     * @param _target Target contract address.
     * @param _sender Original sender address.
     * @param _message Message to send to the target.
     * @param _queueIndex CTC Queue index for the message to replay.
     * @param _oldGasLimit Original gas limit used to send the message.
     * @param _newGasLimit New gas limit to be used for this message.
     */
    function replayMessage(
        address _target,
        address _sender,
        bytes memory _message,
        uint256 _queueIndex,
        uint32 _oldGasLimit,
        uint32 _newGasLimit
    ) external;

    /**
     * @notice Forwards multiple cross domain messages to the L1 Cross Domain Messenger for relaying
     * @param _messages An array of L2 to L1 messages
     */
    function batchRelayMessages(L2ToL1Message[] calldata _messages) external;
}

// File: contracts/L1/messaging/L1CrossDomainMessengerFast.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_AddressResolver } from "../../libraries/resolver/Lib_AddressResolver.sol";
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";
import { Lib_AddressManager } from "../../libraries/resolver/Lib_AddressManager.sol";
import { Lib_SecureMerkleTrie } from "../../libraries/trie/Lib_SecureMerkleTrie.sol";
import { Lib_DefaultValues } from "../../libraries/constants/Lib_DefaultValues.sol";
import { Lib_PredeployAddresses } from "../../libraries/constants/Lib_PredeployAddresses.sol";
import { Lib_CrossDomainUtils } from "../../libraries/bridge/Lib_CrossDomainUtils.sol";

/* Interface Imports */
import { IL1CrossDomainMessenger } from "./IL1CrossDomainMessenger.sol";
import { IStateCommitmentChain } from "../rollup/IStateCommitmentChain.sol";

/* External Imports */
// for security
import {
    OwnableUpgradeable
} from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import {
    PausableUpgradeable
} from "@openzeppelin/contracts-upgradeable/security/PausableUpgradeable.sol";
import {
    ReentrancyGuardUpgradeable
} from "@openzeppelin/contracts-upgradeable/security/ReentrancyGuardUpgradeable.sol";

/**
 * @title L1CrossDomainMessengerFast
 * @dev The L1 Cross Domain Messenger contract sends messages from L1 to L2, and relays messages
 *  from L2 onto L1. In the event that a message sent from L1 to L2 is rejected for exceeding the L2
 * epoch gas limit, it can be resubmitted via this contract's replay function.
 *
 */
contract L1CrossDomainMessengerFast is
    IL1CrossDomainMessenger,
    Lib_AddressResolver,
    OwnableUpgradeable,
    PausableUpgradeable,
    ReentrancyGuardUpgradeable
{
    /**********
     * Events *
     **********/

    event MessageBlocked(bytes32 indexed _xDomainCalldataHash);

    event MessageAllowed(bytes32 indexed _xDomainCalldataHash);

    /**********************
     * Contract Variables *
     **********************/

    mapping(bytes32 => bool) public blockedMessages;
    mapping(bytes32 => bool) public relayedMessages;
    mapping(bytes32 => bool) public successfulMessages;
    mapping(bytes32 => bool) public failedMessages;

    address internal xDomainMsgSender = Lib_DefaultValues.DEFAULT_XDOMAIN_SENDER;

    /***************
     * Constructor *
     ***************/

    /**
     * This contract is intended to be behind a delegate proxy.
     * We pass the zero address to the address resolver just to satisfy the constructor.
     * We still need to set this value in initialize().
     */
    constructor() Lib_AddressResolver(address(0)) {}

    /**********************
     * Function Modifiers *
     **********************/

    modifier onlyRelayer() {
        require(
            msg.sender == resolve("OVM_FastRelayer"),
            "L1CrossDomainMessengerFast: Function can only be called by the FastRelayer"
        );
        _;
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * @param _libAddressManager Address of the Address Manager.
     */
    function initialize(address _libAddressManager) public initializer {
        require(
            address(libAddressManager) == address(0),
            "L1CrossDomainMessenger already intialized."
        );
        libAddressManager = Lib_AddressManager(_libAddressManager);
        xDomainMsgSender = Lib_DefaultValues.DEFAULT_XDOMAIN_SENDER;

        // Initialize upgradable OZ contracts
        __Context_init_unchained(); // Context is a dependency for both Ownable and Pausable
        __Ownable_init_unchained();
        __Pausable_init_unchained();
        __ReentrancyGuard_init_unchained();
    }

    /**
     * Pause fast exit relays
     */
    function pause() external onlyOwner {
        _pause();
    }

    /**
     * UnPause fast exit relays
     */
    function unpause() external onlyOwner {
        _unpause();
    }

    /**
     * Block a message.
     * @param _xDomainCalldataHash Hash of the message to block.
     */
    function blockMessage(bytes32 _xDomainCalldataHash) external onlyOwner {
        blockedMessages[_xDomainCalldataHash] = true;
        emit MessageBlocked(_xDomainCalldataHash);
    }

    /**
     * Allow a message.
     * @param _xDomainCalldataHash Hash of the message to block.
     */
    function allowMessage(bytes32 _xDomainCalldataHash) external onlyOwner {
        blockedMessages[_xDomainCalldataHash] = false;
        emit MessageAllowed(_xDomainCalldataHash);
    }

    function xDomainMessageSender() public view override returns (address) {
        require(
            xDomainMsgSender != Lib_DefaultValues.DEFAULT_XDOMAIN_SENDER,
            "xDomainMessageSender is not set"
        );
        return xDomainMsgSender;
    }

    /**
     * Sends a cross domain message to the target messenger.
     * @param _target Target contract address.
     * @param _message Message to send to the target.
     * @param _gasLimit Gas limit for the provided message.
     */
    function sendMessage(
        address _target,
        bytes memory _message,
        uint32 _gasLimit
    ) public override {
        // refund gas and restore state
        revert("Sending via this messenger is disabled");
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * Relays a cross domain message to a contract.
     * @inheritdoc IL1CrossDomainMessenger
     */
    function relayMessage(
        address _target,
        address _sender,
        bytes memory _message,
        uint256 _messageNonce,
        L2MessageInclusionProof memory _proof
    ) public override nonReentrant whenNotPaused {
        // generate calldata from params
        bytes memory xDomainCalldata = Lib_CrossDomainUtils.encodeXDomainCalldata(
            _target,
            _sender,
            _message,
            _messageNonce
        );

        // verify message state from xDomainCalldata and _proof
        require(
            _verifyXDomainMessage(xDomainCalldata, _proof) == true,
            "Provided message could not be verified."
        );

        bytes32 xDomainCalldataHash = keccak256(xDomainCalldata);

        require(
            successfulMessages[xDomainCalldataHash] == false,
            "Provided message has already been received."
        );

        require(
            blockedMessages[xDomainCalldataHash] == false,
            "Provided message has been blocked."
        );

        require(
            _target != resolve("CanonicalTransactionChain"),
            "Cannot send L2->L1 messages to L1 system contracts."
        );

        xDomainMsgSender = _sender;
        // direct call from _message
        (bool success, ) = _target.call(_message);
        xDomainMsgSender = Lib_DefaultValues.DEFAULT_XDOMAIN_SENDER;

        // Mark the message as received if the call was successful. Ensures that a message can be
        // relayed multiple times in the case that the call reverted.
        if (success == true) {
            successfulMessages[xDomainCalldataHash] = true;
            emit RelayedFastMessage(_target, _sender, _message, _messageNonce);
        } else {
            failedMessages[xDomainCalldataHash] == true;
            emit FailedRelayedFastMessage(_target, _sender, _message, _messageNonce);
        }

        // Store an identifier that can be used to prove that the given message was relayed by some
        // user. Gives us an easy way to pay relayers for their work.
        bytes32 relayId = keccak256(abi.encodePacked(xDomainCalldata, msg.sender, block.number));
        relayedMessages[relayId] = true;
    }

    /**
     * Replays a cross domain message to the target messenger.
     * @inheritdoc IL1CrossDomainMessenger
     */
    function replayMessage(
        address _target,
        address _sender,
        bytes memory _message,
        uint256 _queueIndex,
        uint32 _oldGasLimit,
        uint32 _newGasLimit
    ) public override {
        revert("Sending via this messenger is disabled");
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Verifies that the given message is valid.
     * @param _xDomainCalldata Calldata to verify.
     * @param _proof Inclusion proof for the message.
     * @return Whether or not the provided message is valid.
     */
    function _verifyXDomainMessage(
        bytes memory _xDomainCalldata,
        L2MessageInclusionProof memory _proof
    ) internal view returns (bool) {
        return (_verifyStateRootProof(_proof) && _verifyStorageProof(_xDomainCalldata, _proof));
    }

    /**
     * Verifies that the state root within an inclusion proof is valid.
     * @param _proof Message inclusion proof.
     * @return Whether or not the provided proof is valid.
     */
    function _verifyStateRootProof(L2MessageInclusionProof memory _proof)
        internal
        view
        returns (bool)
    {
        IStateCommitmentChain ovmStateCommitmentChain = IStateCommitmentChain(
            resolve("StateCommitmentChain")
        );

        // not check time after challenge period
        return (
            ovmStateCommitmentChain.verifyStateCommitment(
                _proof.stateRoot,
                _proof.stateRootBatchHeader,
                _proof.stateRootProof
            )
        );
    }

    /**
     * Verifies that the storage proof within an inclusion proof is valid.
     * @param _xDomainCalldata Encoded message calldata.
     * @param _proof Message inclusion proof.
     * @return Whether or not the provided proof is valid.
     */
    function _verifyStorageProof(
        bytes memory _xDomainCalldata,
        L2MessageInclusionProof memory _proof
    ) internal view returns (bool) {
        bytes32 storageKey = keccak256(
            abi.encodePacked(
                keccak256(
                    abi.encodePacked(
                        _xDomainCalldata,
                        Lib_PredeployAddresses.L2_CROSS_DOMAIN_MESSENGER
                    )
                ),
                uint256(0)
            )
        );

        (bool exists, bytes memory encodedMessagePassingAccount) = Lib_SecureMerkleTrie.get(
            abi.encodePacked(Lib_PredeployAddresses.L2_TO_L1_MESSAGE_PASSER),
            _proof.stateTrieWitness,
            _proof.stateRoot
        );

        require(
            exists == true,
            "Message passing predeploy has not been initialized or invalid proof provided."
        );

        Lib_OVMCodec.EVMAccount memory account = Lib_OVMCodec.decodeEVMAccount(
            encodedMessagePassingAccount
        );

        return
            Lib_SecureMerkleTrie.verifyInclusionProof(
                abi.encodePacked(storageKey),
                abi.encodePacked(uint8(1)),
                _proof.storageTrieWitness,
                account.storageRoot
            );
    }

    /**
     * @notice Forwards multiple cross domain messages to the
     * L1 Cross Domain Messenger Fast for relaying
     * @param _messages An array of L2 to L1 messages
     */
    function batchRelayMessages(L2ToL1Message[] calldata _messages) external onlyRelayer {
        for (uint256 i = 0; i < _messages.length; i++) {
            L2ToL1Message memory message = _messages[i];
            relayMessage(
                message.target,
                message.sender,
                message.message,
                message.messageNonce,
                message.proof
            );
        }
    }
}

// File: contracts/L1/rollup/IStateCommitmentChain.sol



// SPDX-License-Identifier: MIT
pragma solidity >0.5.0 <0.9.0;

/* Library Imports */
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";

/**
 * @title IStateCommitmentChain
 */
interface IStateCommitmentChain {
    /**********
     * Events *
     **********/

    event StateBatchAppended(
        uint256 indexed _batchIndex,
        bytes32 _batchRoot,
        uint256 _batchSize,
        uint256 _prevTotalElements,
        bytes _extraData
    );

    event StateBatchDeleted(uint256 indexed _batchIndex, bytes32 _batchRoot);

    /********************
     * Public Functions *
     ********************/

    /**
     * Retrieves the total number of elements submitted.
     * @return _totalElements Total submitted elements.
     */
    function getTotalElements() external view returns (uint256 _totalElements);

    /**
     * Retrieves the total number of batches submitted.
     * @return _totalBatches Total submitted batches.
     */
    function getTotalBatches() external view returns (uint256 _totalBatches);

    /**
     * Retrieves the timestamp of the last batch submitted by the sequencer.
     * @return _lastSequencerTimestamp Last sequencer batch timestamp.
     */
    function getLastSequencerTimestamp() external view returns (uint256 _lastSequencerTimestamp);

    /**
     * Appends a batch of state roots to the chain.
     * @param _batch Batch of state roots.
     * @param _shouldStartAtElement Index of the element at which this batch should start.
     */
    function appendStateBatch(bytes32[] calldata _batch, uint256 _shouldStartAtElement) external;

    /**
     * Deletes all state roots after (and including) a given batch.
     * @param _batchHeader Header of the batch to start deleting from.
     */
    function deleteStateBatch(Lib_OVMCodec.ChainBatchHeader memory _batchHeader) external;

    /**
     * Verifies a batch inclusion proof.
     * @param _element Hash of the element to verify a proof for.
     * @param _batchHeader Header of the batch in which the element was included.
     * @param _proof Merkle inclusion proof for the element.
     */
    function verifyStateCommitment(
        bytes32 _element,
        Lib_OVMCodec.ChainBatchHeader memory _batchHeader,
        Lib_OVMCodec.ChainInclusionProof memory _proof
    ) external view returns (bool _verified);

    /**
     * Checks whether a given batch is still inside its fraud proof window.
     * @param _batchHeader Header of the batch to check.
     * @return _inside Whether or not the batch is inside the fraud proof window.
     */
    function insideFraudProofWindow(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        external
        view
        returns (bool _inside);
}

// File: contracts/libraries/bridge/ICrossDomainMessenger.sol



// SPDX-License-Identifier: MIT
pragma solidity >0.5.0 <0.9.0;

/**
 * @title ICrossDomainMessenger
 */
interface ICrossDomainMessenger {
    /**********
     * Events *
     **********/

    event SentMessage(
        address indexed target,
        address sender,
        bytes message,
        uint256 messageNonce,
        uint256 gasLimit
    );
    event RelayedMessage(bytes32 indexed msgHash);
    event FailedRelayedMessage(bytes32 indexed msgHash);
    event RelayedFastMessage(
        address indexed target,
        address sender,
        bytes message,
        uint256 messageNonce
    );
    event FailedRelayedFastMessage(
        address indexed target,
        address sender,
        bytes message,
        uint256 messageNonce
    );

    /*************
     * Variables *
     *************/

    function xDomainMessageSender() external view returns (address);

    /********************
     * Public Functions *
     ********************/

    /**
     * Sends a cross domain message to the target messenger.
     * @param _target Target contract address.
     * @param _message Message to send to the target.
     * @param _gasLimit Gas limit for the provided message.
     */
    function sendMessage(
        address _target,
        bytes calldata _message,
        uint32 _gasLimit
    ) external;
}

// File: contracts/libraries/bridge/Lib_CrossDomainUtils.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_CrossDomainUtils
 */
library Lib_CrossDomainUtils {
    /**
     * Generates the correct cross domain calldata for a message.
     * @param _target Target contract address.
     * @param _sender Message sender address.
     * @param _message Message to send to the target.
     * @param _messageNonce Nonce for the provided message.
     * @return ABI encoded cross domain calldata.
     */
    function encodeXDomainCalldata(
        address _target,
        address _sender,
        bytes memory _message,
        uint256 _messageNonce
    ) internal pure returns (bytes memory) {
        return
            abi.encodeWithSignature(
                "relayMessage(address,address,bytes,uint256)",
                _target,
                _sender,
                _message,
                _messageNonce
            );
    }
}

// File: contracts/libraries/codec/Lib_OVMCodec.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_RLPReader } from "../rlp/Lib_RLPReader.sol";
import { Lib_RLPWriter } from "../rlp/Lib_RLPWriter.sol";
import { Lib_BytesUtils } from "../utils/Lib_BytesUtils.sol";
import { Lib_Bytes32Utils } from "../utils/Lib_Bytes32Utils.sol";

/**
 * @title Lib_OVMCodec
 */
library Lib_OVMCodec {
    /*********
     * Enums *
     *********/

    enum QueueOrigin {
        SEQUENCER_QUEUE,
        L1TOL2_QUEUE
    }

    /***********
     * Structs *
     ***********/

    struct EVMAccount {
        uint256 nonce;
        uint256 balance;
        bytes32 storageRoot;
        bytes32 codeHash;
    }

    struct ChainBatchHeader {
        uint256 batchIndex;
        bytes32 batchRoot;
        uint256 batchSize;
        uint256 prevTotalElements;
        bytes extraData;
    }

    struct ChainInclusionProof {
        uint256 index;
        bytes32[] siblings;
    }

    struct Transaction {
        uint256 timestamp;
        uint256 blockNumber;
        QueueOrigin l1QueueOrigin;
        address l1TxOrigin;
        address entrypoint;
        uint256 gasLimit;
        bytes data;
    }

    struct TransactionChainElement {
        bool isSequenced;
        uint256 queueIndex; // QUEUED TX ONLY
        uint256 timestamp; // SEQUENCER TX ONLY
        uint256 blockNumber; // SEQUENCER TX ONLY
        bytes txData; // SEQUENCER TX ONLY
    }

    struct QueueElement {
        bytes32 transactionHash;
        uint40 timestamp;
        uint40 blockNumber;
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Encodes a standard OVM transaction.
     * @param _transaction OVM transaction to encode.
     * @return Encoded transaction bytes.
     */
    function encodeTransaction(Transaction memory _transaction)
        internal
        pure
        returns (bytes memory)
    {
        return
            abi.encodePacked(
                _transaction.timestamp,
                _transaction.blockNumber,
                _transaction.l1QueueOrigin,
                _transaction.l1TxOrigin,
                _transaction.entrypoint,
                _transaction.gasLimit,
                _transaction.data
            );
    }

    /**
     * Hashes a standard OVM transaction.
     * @param _transaction OVM transaction to encode.
     * @return Hashed transaction
     */
    function hashTransaction(Transaction memory _transaction) internal pure returns (bytes32) {
        return keccak256(encodeTransaction(_transaction));
    }

    /**
     * @notice Decodes an RLP-encoded account state into a useful struct.
     * @param _encoded RLP-encoded account state.
     * @return Account state struct.
     */
    function decodeEVMAccount(bytes memory _encoded) internal pure returns (EVMAccount memory) {
        Lib_RLPReader.RLPItem[] memory accountState = Lib_RLPReader.readList(_encoded);

        return
            EVMAccount({
                nonce: Lib_RLPReader.readUint256(accountState[0]),
                balance: Lib_RLPReader.readUint256(accountState[1]),
                storageRoot: Lib_RLPReader.readBytes32(accountState[2]),
                codeHash: Lib_RLPReader.readBytes32(accountState[3])
            });
    }

    /**
     * Calculates a hash for a given batch header.
     * @param _batchHeader Header to hash.
     * @return Hash of the header.
     */
    function hashBatchHeader(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        internal
        pure
        returns (bytes32)
    {
        return
            keccak256(
                abi.encode(
                    _batchHeader.batchRoot,
                    _batchHeader.batchSize,
                    _batchHeader.prevTotalElements,
                    _batchHeader.extraData
                )
            );
    }
}

// File: contracts/libraries/constants/Lib_DefaultValues.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_DefaultValues
 */
library Lib_DefaultValues {
    // The default x-domain message sender being set to a non-zero value makes
    // deployment a bit more expensive, but in exchange the refund on every call to
    // `relayMessage` by the L1 and L2 messengers will be higher.
    address internal constant DEFAULT_XDOMAIN_SENDER = 0x000000000000000000000000000000000000dEaD;
}

// File: contracts/libraries/constants/Lib_PredeployAddresses.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_PredeployAddresses
 */
library Lib_PredeployAddresses {
    address internal constant L2_TO_L1_MESSAGE_PASSER = 0x4200000000000000000000000000000000000000;
    address internal constant L1_MESSAGE_SENDER = 0x4200000000000000000000000000000000000001;
    address internal constant DEPLOYER_WHITELIST = 0x4200000000000000000000000000000000000002;
    address payable internal constant OVM_ETH = payable(0xDeadDeAddeAddEAddeadDEaDDEAdDeaDDeAD0000);
    address internal constant L2_CROSS_DOMAIN_MESSENGER =
        0x4200000000000000000000000000000000000007;
    address internal constant LIB_ADDRESS_MANAGER = 0x4200000000000000000000000000000000000008;
    address internal constant PROXY_EOA = 0x4200000000000000000000000000000000000009;
    address internal constant L2_STANDARD_BRIDGE = 0x4200000000000000000000000000000000000010;
    address internal constant SEQUENCER_FEE_WALLET = 0x4200000000000000000000000000000000000011;
    address internal constant L2_STANDARD_TOKEN_FACTORY =
        0x4200000000000000000000000000000000000012;
    address internal constant L1_BLOCK_NUMBER = 0x4200000000000000000000000000000000000013;
}

// File: contracts/libraries/resolver/Lib_AddressManager.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* External Imports */
import { Ownable } from "@openzeppelin/contracts/access/Ownable.sol";

/**
 * @title Lib_AddressManager
 */
contract Lib_AddressManager is Ownable {
    /**********
     * Events *
     **********/

    event AddressSet(string indexed _name, address _newAddress, address _oldAddress);

    /*************
     * Variables *
     *************/

    mapping(bytes32 => address) private addresses;

    /********************
     * Public Functions *
     ********************/

    /**
     * Changes the address associated with a particular name.
     * @param _name String name to associate an address with.
     * @param _address Address to associate with the name.
     */
    function setAddress(string memory _name, address _address) external onlyOwner {
        bytes32 nameHash = _getNameHash(_name);
        address oldAddress = addresses[nameHash];
        addresses[nameHash] = _address;

        emit AddressSet(_name, _address, oldAddress);
    }

    /**
     * Retrieves the address associated with a given name.
     * @param _name Name to retrieve an address for.
     * @return Address associated with the given name.
     */
    function getAddress(string memory _name) external view returns (address) {
        return addresses[_getNameHash(_name)];
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Computes the hash of a name.
     * @param _name Name to compute a hash for.
     * @return Hash of the given name.
     */
    function _getNameHash(string memory _name) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(_name));
    }
}

// File: contracts/libraries/resolver/Lib_AddressResolver.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_AddressManager } from "./Lib_AddressManager.sol";

/**
 * @title Lib_AddressResolver
 */
abstract contract Lib_AddressResolver {
    /*************
     * Variables *
     *************/

    Lib_AddressManager public libAddressManager;

    /***************
     * Constructor *
     ***************/

    /**
     * @param _libAddressManager Address of the Lib_AddressManager.
     */
    constructor(address _libAddressManager) {
        libAddressManager = Lib_AddressManager(_libAddressManager);
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * Resolves the address associated with a given name.
     * @param _name Name to resolve an address for.
     * @return Address associated with the given name.
     */
    function resolve(string memory _name) public view returns (address) {
        return libAddressManager.getAddress(_name);
    }
}

// File: contracts/libraries/rlp/Lib_RLPReader.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_RLPReader
 * @dev Adapted from "RLPReader" by Hamdi Allam (hamdi.allam97@gmail.com).
 */
library Lib_RLPReader {
    /*************
     * Constants *
     *************/

    uint256 internal constant MAX_LIST_LENGTH = 32;

    /*********
     * Enums *
     *********/

    enum RLPItemType {
        DATA_ITEM,
        LIST_ITEM
    }

    /***********
     * Structs *
     ***********/

    struct RLPItem {
        uint256 length;
        uint256 ptr;
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Converts bytes to a reference to memory position and length.
     * @param _in Input bytes to convert.
     * @return Output memory reference.
     */
    function toRLPItem(bytes memory _in) internal pure returns (RLPItem memory) {
        uint256 ptr;
        assembly {
            ptr := add(_in, 32)
        }

        return RLPItem({ length: _in.length, ptr: ptr });
    }

    /**
     * Reads an RLP list value into a list of RLP items.
     * @param _in RLP list value.
     * @return Decoded RLP list items.
     */
    function readList(RLPItem memory _in) internal pure returns (RLPItem[] memory) {
        (uint256 listOffset, , RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.LIST_ITEM, "Invalid RLP list value.");

        // Solidity in-memory arrays can't be increased in size, but *can* be decreased in size by
        // writing to the length. Since we can't know the number of RLP items without looping over
        // the entire input, we'd have to loop twice to accurately size this array. It's easier to
        // simply set a reasonable maximum list length and decrease the size before we finish.
        RLPItem[] memory out = new RLPItem[](MAX_LIST_LENGTH);

        uint256 itemCount = 0;
        uint256 offset = listOffset;
        while (offset < _in.length) {
            require(itemCount < MAX_LIST_LENGTH, "Provided RLP list exceeds max list length.");

            (uint256 itemOffset, uint256 itemLength, ) = _decodeLength(
                RLPItem({ length: _in.length - offset, ptr: _in.ptr + offset })
            );

            out[itemCount] = RLPItem({ length: itemLength + itemOffset, ptr: _in.ptr + offset });

            itemCount += 1;
            offset += itemOffset + itemLength;
        }

        // Decrease the array size to match the actual item count.
        assembly {
            mstore(out, itemCount)
        }

        return out;
    }

    /**
     * Reads an RLP list value into a list of RLP items.
     * @param _in RLP list value.
     * @return Decoded RLP list items.
     */
    function readList(bytes memory _in) internal pure returns (RLPItem[] memory) {
        return readList(toRLPItem(_in));
    }

    /**
     * Reads an RLP bytes value into bytes.
     * @param _in RLP bytes value.
     * @return Decoded bytes.
     */
    function readBytes(RLPItem memory _in) internal pure returns (bytes memory) {
        (uint256 itemOffset, uint256 itemLength, RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.DATA_ITEM, "Invalid RLP bytes value.");

        return _copy(_in.ptr, itemOffset, itemLength);
    }

    /**
     * Reads an RLP bytes value into bytes.
     * @param _in RLP bytes value.
     * @return Decoded bytes.
     */
    function readBytes(bytes memory _in) internal pure returns (bytes memory) {
        return readBytes(toRLPItem(_in));
    }

    /**
     * Reads an RLP string value into a string.
     * @param _in RLP string value.
     * @return Decoded string.
     */
    function readString(RLPItem memory _in) internal pure returns (string memory) {
        return string(readBytes(_in));
    }

    /**
     * Reads an RLP string value into a string.
     * @param _in RLP string value.
     * @return Decoded string.
     */
    function readString(bytes memory _in) internal pure returns (string memory) {
        return readString(toRLPItem(_in));
    }

    /**
     * Reads an RLP bytes32 value into a bytes32.
     * @param _in RLP bytes32 value.
     * @return Decoded bytes32.
     */
    function readBytes32(RLPItem memory _in) internal pure returns (bytes32) {
        require(_in.length <= 33, "Invalid RLP bytes32 value.");

        (uint256 itemOffset, uint256 itemLength, RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.DATA_ITEM, "Invalid RLP bytes32 value.");

        uint256 ptr = _in.ptr + itemOffset;
        bytes32 out;
        assembly {
            out := mload(ptr)

            // Shift the bytes over to match the item size.
            if lt(itemLength, 32) {
                out := div(out, exp(256, sub(32, itemLength)))
            }
        }

        return out;
    }

    /**
     * Reads an RLP bytes32 value into a bytes32.
     * @param _in RLP bytes32 value.
     * @return Decoded bytes32.
     */
    function readBytes32(bytes memory _in) internal pure returns (bytes32) {
        return readBytes32(toRLPItem(_in));
    }

    /**
     * Reads an RLP uint256 value into a uint256.
     * @param _in RLP uint256 value.
     * @return Decoded uint256.
     */
    function readUint256(RLPItem memory _in) internal pure returns (uint256) {
        return uint256(readBytes32(_in));
    }

    /**
     * Reads an RLP uint256 value into a uint256.
     * @param _in RLP uint256 value.
     * @return Decoded uint256.
     */
    function readUint256(bytes memory _in) internal pure returns (uint256) {
        return readUint256(toRLPItem(_in));
    }

    /**
     * Reads an RLP bool value into a bool.
     * @param _in RLP bool value.
     * @return Decoded bool.
     */
    function readBool(RLPItem memory _in) internal pure returns (bool) {
        require(_in.length == 1, "Invalid RLP boolean value.");

        uint256 ptr = _in.ptr;
        uint256 out;
        assembly {
            out := byte(0, mload(ptr))
        }

        require(out == 0 || out == 1, "Lib_RLPReader: Invalid RLP boolean value, must be 0 or 1");

        return out != 0;
    }

    /**
     * Reads an RLP bool value into a bool.
     * @param _in RLP bool value.
     * @return Decoded bool.
     */
    function readBool(bytes memory _in) internal pure returns (bool) {
        return readBool(toRLPItem(_in));
    }

    /**
     * Reads an RLP address value into a address.
     * @param _in RLP address value.
     * @return Decoded address.
     */
    function readAddress(RLPItem memory _in) internal pure returns (address) {
        if (_in.length == 1) {
            return address(0);
        }

        require(_in.length == 21, "Invalid RLP address value.");

        return address(uint160(readUint256(_in)));
    }

    /**
     * Reads an RLP address value into a address.
     * @param _in RLP address value.
     * @return Decoded address.
     */
    function readAddress(bytes memory _in) internal pure returns (address) {
        return readAddress(toRLPItem(_in));
    }

    /**
     * Reads the raw bytes of an RLP item.
     * @param _in RLP item to read.
     * @return Raw RLP bytes.
     */
    function readRawBytes(RLPItem memory _in) internal pure returns (bytes memory) {
        return _copy(_in);
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Decodes the length of an RLP item.
     * @param _in RLP item to decode.
     * @return Offset of the encoded data.
     * @return Length of the encoded data.
     * @return RLP item type (LIST_ITEM or DATA_ITEM).
     */
    function _decodeLength(RLPItem memory _in)
        private
        pure
        returns (
            uint256,
            uint256,
            RLPItemType
        )
    {
        require(_in.length > 0, "RLP item cannot be null.");

        uint256 ptr = _in.ptr;
        uint256 prefix;
        assembly {
            prefix := byte(0, mload(ptr))
        }

        if (prefix <= 0x7f) {
            // Single byte.

            return (0, 1, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xb7) {
            // Short string.

            // slither-disable-next-line variable-scope
            uint256 strLen = prefix - 0x80;

            require(_in.length > strLen, "Invalid RLP short string.");

            return (1, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xbf) {
            // Long string.
            uint256 lenOfStrLen = prefix - 0xb7;

            require(_in.length > lenOfStrLen, "Invalid RLP long string length.");

            uint256 strLen;
            assembly {
                // Pick out the string length.
                strLen := div(mload(add(ptr, 1)), exp(256, sub(32, lenOfStrLen)))
            }

            require(_in.length > lenOfStrLen + strLen, "Invalid RLP long string.");

            return (1 + lenOfStrLen, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xf7) {
            // Short list.
            // slither-disable-next-line variable-scope
            uint256 listLen = prefix - 0xc0;

            require(_in.length > listLen, "Invalid RLP short list.");

            return (1, listLen, RLPItemType.LIST_ITEM);
        } else {
            // Long list.
            uint256 lenOfListLen = prefix - 0xf7;

            require(_in.length > lenOfListLen, "Invalid RLP long list length.");

            uint256 listLen;
            assembly {
                // Pick out the list length.
                listLen := div(mload(add(ptr, 1)), exp(256, sub(32, lenOfListLen)))
            }

            require(_in.length > lenOfListLen + listLen, "Invalid RLP long list.");

            return (1 + lenOfListLen, listLen, RLPItemType.LIST_ITEM);
        }
    }

    /**
     * Copies the bytes from a memory location.
     * @param _src Pointer to the location to read from.
     * @param _offset Offset to start reading from.
     * @param _length Number of bytes to read.
     * @return Copied bytes.
     */
    function _copy(
        uint256 _src,
        uint256 _offset,
        uint256 _length
    ) private pure returns (bytes memory) {
        bytes memory out = new bytes(_length);
        if (out.length == 0) {
            return out;
        }

        uint256 src = _src + _offset;
        uint256 dest;
        assembly {
            dest := add(out, 32)
        }

        // Copy over as many complete words as we can.
        for (uint256 i = 0; i < _length / 32; i++) {
            assembly {
                mstore(dest, mload(src))
            }

            src += 32;
            dest += 32;
        }

        // Pick out the remaining bytes.
        uint256 mask;
        unchecked {
            mask = 256**(32 - (_length % 32)) - 1;
        }

        assembly {
            mstore(dest, or(and(mload(src), not(mask)), and(mload(dest), mask)))
        }
        return out;
    }

    /**
     * Copies an RLP item into bytes.
     * @param _in RLP item to copy.
     * @return Copied bytes.
     */
    function _copy(RLPItem memory _in) private pure returns (bytes memory) {
        return _copy(_in.ptr, 0, _in.length);
    }
}

// File: contracts/libraries/rlp/Lib_RLPWriter.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_RLPWriter
 * @author Bakaoh (with modifications)
 */
library Lib_RLPWriter {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * RLP encodes a byte string.
     * @param _in The byte string to encode.
     * @return The RLP encoded string in bytes.
     */
    function writeBytes(bytes memory _in) internal pure returns (bytes memory) {
        bytes memory encoded;

        if (_in.length == 1 && uint8(_in[0]) < 128) {
            encoded = _in;
        } else {
            encoded = abi.encodePacked(_writeLength(_in.length, 128), _in);
        }

        return encoded;
    }

    /**
     * RLP encodes a list of RLP encoded byte byte strings.
     * @param _in The list of RLP encoded byte strings.
     * @return The RLP encoded list of items in bytes.
     */
    function writeList(bytes[] memory _in) internal pure returns (bytes memory) {
        bytes memory list = _flatten(_in);
        return abi.encodePacked(_writeLength(list.length, 192), list);
    }

    /**
     * RLP encodes a string.
     * @param _in The string to encode.
     * @return The RLP encoded string in bytes.
     */
    function writeString(string memory _in) internal pure returns (bytes memory) {
        return writeBytes(bytes(_in));
    }

    /**
     * RLP encodes an address.
     * @param _in The address to encode.
     * @return The RLP encoded address in bytes.
     */
    function writeAddress(address _in) internal pure returns (bytes memory) {
        return writeBytes(abi.encodePacked(_in));
    }

    /**
     * RLP encodes a uint.
     * @param _in The uint256 to encode.
     * @return The RLP encoded uint256 in bytes.
     */
    function writeUint(uint256 _in) internal pure returns (bytes memory) {
        return writeBytes(_toBinary(_in));
    }

    /**
     * RLP encodes a bool.
     * @param _in The bool to encode.
     * @return The RLP encoded bool in bytes.
     */
    function writeBool(bool _in) internal pure returns (bytes memory) {
        bytes memory encoded = new bytes(1);
        encoded[0] = (_in ? bytes1(0x01) : bytes1(0x80));
        return encoded;
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Encode the first byte, followed by the `len` in binary form if `length` is more than 55.
     * @param _len The length of the string or the payload.
     * @param _offset 128 if item is string, 192 if item is list.
     * @return RLP encoded bytes.
     */
    function _writeLength(uint256 _len, uint256 _offset) private pure returns (bytes memory) {
        bytes memory encoded;

        if (_len < 56) {
            encoded = new bytes(1);
            encoded[0] = bytes1(uint8(_len) + uint8(_offset));
        } else {
            uint256 lenLen;
            uint256 i = 1;
            while (_len / i != 0) {
                lenLen++;
                i *= 256;
            }

            encoded = new bytes(lenLen + 1);
            encoded[0] = bytes1(uint8(lenLen) + uint8(_offset) + 55);
            for (i = 1; i <= lenLen; i++) {
                encoded[i] = bytes1(uint8((_len / (256**(lenLen - i))) % 256));
            }
        }

        return encoded;
    }

    /**
     * Encode integer in big endian binary form with no leading zeroes.
     * @notice TODO: This should be optimized with assembly to save gas costs.
     * @param _x The integer to encode.
     * @return RLP encoded bytes.
     */
    function _toBinary(uint256 _x) private pure returns (bytes memory) {
        bytes memory b = abi.encodePacked(_x);

        uint256 i = 0;
        for (; i < 32; i++) {
            if (b[i] != 0) {
                break;
            }
        }

        bytes memory res = new bytes(32 - i);
        for (uint256 j = 0; j < res.length; j++) {
            res[j] = b[i++];
        }

        return res;
    }

    /**
     * Copies a piece of memory to another location.
     * @notice From: https://github.com/Arachnid/solidity-stringutils/blob/master/src/strings.sol.
     * @param _dest Destination location.
     * @param _src Source location.
     * @param _len Length of memory to copy.
     */
    function _memcpy(
        uint256 _dest,
        uint256 _src,
        uint256 _len
    ) private pure {
        uint256 dest = _dest;
        uint256 src = _src;
        uint256 len = _len;

        for (; len >= 32; len -= 32) {
            assembly {
                mstore(dest, mload(src))
            }
            dest += 32;
            src += 32;
        }

        uint256 mask;
        unchecked {
            mask = 256**(32 - len) - 1;
        }
        assembly {
            let srcpart := and(mload(src), not(mask))
            let destpart := and(mload(dest), mask)
            mstore(dest, or(destpart, srcpart))
        }
    }

    /**
     * Flattens a list of byte strings into one byte string.
     * @notice From: https://github.com/sammayo/solidity-rlp-encoder/blob/master/RLPEncode.sol.
     * @param _list List of byte strings to flatten.
     * @return The flattened byte string.
     */
    function _flatten(bytes[] memory _list) private pure returns (bytes memory) {
        if (_list.length == 0) {
            return new bytes(0);
        }

        uint256 len;
        uint256 i = 0;
        for (; i < _list.length; i++) {
            len += _list[i].length;
        }

        bytes memory flattened = new bytes(len);
        uint256 flattenedPtr;
        assembly {
            flattenedPtr := add(flattened, 0x20)
        }

        for (i = 0; i < _list.length; i++) {
            bytes memory item = _list[i];

            uint256 listPtr;
            assembly {
                listPtr := add(item, 0x20)
            }

            _memcpy(flattenedPtr, listPtr, item.length);
            flattenedPtr += _list[i].length;
        }

        return flattened;
    }
}

// File: contracts/libraries/trie/Lib_MerkleTrie.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_BytesUtils } from "../utils/Lib_BytesUtils.sol";
import { Lib_RLPReader } from "../rlp/Lib_RLPReader.sol";
import { Lib_RLPWriter } from "../rlp/Lib_RLPWriter.sol";

/**
 * @title Lib_MerkleTrie
 */
library Lib_MerkleTrie {
    /*******************
     * Data Structures *
     *******************/

    enum NodeType {
        BranchNode,
        ExtensionNode,
        LeafNode
    }

    struct TrieNode {
        bytes encoded;
        Lib_RLPReader.RLPItem[] decoded;
    }

    /**********************
     * Contract Constants *
     **********************/

    // TREE_RADIX determines the number of elements per branch node.
    uint256 constant TREE_RADIX = 16;
    // Branch nodes have TREE_RADIX elements plus an additional `value` slot.
    uint256 constant BRANCH_NODE_LENGTH = TREE_RADIX + 1;
    // Leaf nodes and extension nodes always have two elements, a `path` and a `value`.
    uint256 constant LEAF_OR_EXTENSION_NODE_LENGTH = 2;

    // Prefixes are prepended to the `path` within a leaf or extension node and
    // allow us to differentiate between the two node types. `ODD` or `EVEN` is
    // determined by the number of nibbles within the unprefixed `path`. If the
    // number of nibbles if even, we need to insert an extra padding nibble so
    // the resulting prefixed `path` has an even number of nibbles.
    uint8 constant PREFIX_EXTENSION_EVEN = 0;
    uint8 constant PREFIX_EXTENSION_ODD = 1;
    uint8 constant PREFIX_LEAF_EVEN = 2;
    uint8 constant PREFIX_LEAF_ODD = 3;

    // Just a utility constant. RLP represents `NULL` as 0x80.
    bytes1 constant RLP_NULL = bytes1(0x80);

    /**********************
     * Internal Functions *
     **********************/

    /**
     * @notice Verifies a proof that a given key/value pair is present in the
     * Merkle trie.
     * @param _key Key of the node to search for, as a hex string.
     * @param _value Value of the node to search for, as a hex string.
     * @param _proof Merkle trie inclusion proof for the desired node. Unlike
     * traditional Merkle trees, this proof is executed top-down and consists
     * of a list of RLP-encoded nodes that make a path down to the target node.
     * @param _root Known root of the Merkle trie. Used to verify that the
     * included proof is correctly constructed.
     * @return _verified `true` if the k/v pair exists in the trie, `false` otherwise.
     */
    function verifyInclusionProof(
        bytes memory _key,
        bytes memory _value,
        bytes memory _proof,
        bytes32 _root
    ) internal pure returns (bool _verified) {
        (bool exists, bytes memory value) = get(_key, _proof, _root);

        return (exists && Lib_BytesUtils.equal(_value, value));
    }

    /**
     * @notice Retrieves the value associated with a given key.
     * @param _key Key to search for, as hex bytes.
     * @param _proof Merkle trie inclusion proof for the key.
     * @param _root Known root of the Merkle trie.
     * @return _exists Whether or not the key exists.
     * @return _value Value of the key if it exists.
     */
    function get(
        bytes memory _key,
        bytes memory _proof,
        bytes32 _root
    ) internal pure returns (bool _exists, bytes memory _value) {
        TrieNode[] memory proof = _parseProof(_proof);
        (uint256 pathLength, bytes memory keyRemainder, bool isFinalNode) = _walkNodePath(
            proof,
            _key,
            _root
        );

        bool exists = keyRemainder.length == 0;

        require(exists || isFinalNode, "Provided proof is invalid.");

        bytes memory value = exists ? _getNodeValue(proof[pathLength - 1]) : bytes("");

        return (exists, value);
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * @notice Walks through a proof using a provided key.
     * @param _proof Inclusion proof to walk through.
     * @param _key Key to use for the walk.
     * @param _root Known root of the trie.
     * @return _pathLength Length of the final path
     * @return _keyRemainder Portion of the key remaining after the walk.
     * @return _isFinalNode Whether or not we've hit a dead end.
     */
    function _walkNodePath(
        TrieNode[] memory _proof,
        bytes memory _key,
        bytes32 _root
    )
        private
        pure
        returns (
            uint256 _pathLength,
            bytes memory _keyRemainder,
            bool _isFinalNode
        )
    {
        uint256 pathLength = 0;
        bytes memory key = Lib_BytesUtils.toNibbles(_key);

        bytes32 currentNodeID = _root;
        uint256 currentKeyIndex = 0;
        uint256 currentKeyIncrement = 0;
        TrieNode memory currentNode;

        // Proof is top-down, so we start at the first element (root).
        for (uint256 i = 0; i < _proof.length; i++) {
            currentNode = _proof[i];
            currentKeyIndex += currentKeyIncrement;

            // Keep track of the proof elements we actually need.
            // It's expensive to resize arrays, so this simply reduces gas costs.
            pathLength += 1;

            if (currentKeyIndex == 0) {
                // First proof element is always the root node.
                require(keccak256(currentNode.encoded) == currentNodeID, "Invalid root hash");
            } else if (currentNode.encoded.length >= 32) {
                // Nodes 32 bytes or larger are hashed inside branch nodes.
                require(
                    keccak256(currentNode.encoded) == currentNodeID,
                    "Invalid large internal hash"
                );
            } else {
                // Nodes smaller than 31 bytes aren't hashed.
                require(
                    Lib_BytesUtils.toBytes32(currentNode.encoded) == currentNodeID,
                    "Invalid internal node hash"
                );
            }

            if (currentNode.decoded.length == BRANCH_NODE_LENGTH) {
                if (currentKeyIndex == key.length) {
                    // We've hit the end of the key
                    // meaning the value should be within this branch node.
                    break;
                } else {
                    // We're not at the end of the key yet.
                    // Figure out what the next node ID should be and continue.
                    uint8 branchKey = uint8(key[currentKeyIndex]);
                    Lib_RLPReader.RLPItem memory nextNode = currentNode.decoded[branchKey];
                    currentNodeID = _getNodeID(nextNode);
                    currentKeyIncrement = 1;
                    continue;
                }
            } else if (currentNode.decoded.length == LEAF_OR_EXTENSION_NODE_LENGTH) {
                bytes memory path = _getNodePath(currentNode);
                uint8 prefix = uint8(path[0]);
                uint8 offset = 2 - (prefix % 2);
                bytes memory pathRemainder = Lib_BytesUtils.slice(path, offset);
                bytes memory keyRemainder = Lib_BytesUtils.slice(key, currentKeyIndex);
                uint256 sharedNibbleLength = _getSharedNibbleLength(pathRemainder, keyRemainder);

                if (prefix == PREFIX_LEAF_EVEN || prefix == PREFIX_LEAF_ODD) {
                    if (
                        pathRemainder.length == sharedNibbleLength &&
                        keyRemainder.length == sharedNibbleLength
                    ) {
                        // The key within this leaf matches our key exactly.
                        // Increment the key index to reflect that we have no remainder.
                        currentKeyIndex += sharedNibbleLength;
                    }

                    // We've hit a leaf node, so our next node should be NULL.
                    currentNodeID = bytes32(RLP_NULL);
                    break;
                } else if (prefix == PREFIX_EXTENSION_EVEN || prefix == PREFIX_EXTENSION_ODD) {
                    if (sharedNibbleLength != pathRemainder.length) {
                        // Our extension node is not identical to the remainder.
                        // We've hit the end of this path
                        // updates will need to modify this extension.
                        currentNodeID = bytes32(RLP_NULL);
                        break;
                    } else {
                        // Our extension shares some nibbles.
                        // Carry on to the next node.
                        currentNodeID = _getNodeID(currentNode.decoded[1]);
                        currentKeyIncrement = sharedNibbleLength;
                        continue;
                    }
                } else {
                    revert("Received a node with an unknown prefix");
                }
            } else {
                revert("Received an unparseable node.");
            }
        }

        // If our node ID is NULL, then we're at a dead end.
        bool isFinalNode = currentNodeID == bytes32(RLP_NULL);
        return (pathLength, Lib_BytesUtils.slice(key, currentKeyIndex), isFinalNode);
    }

    /**
     * @notice Parses an RLP-encoded proof into something more useful.
     * @param _proof RLP-encoded proof to parse.
     * @return _parsed Proof parsed into easily accessible structs.
     */
    function _parseProof(bytes memory _proof) private pure returns (TrieNode[] memory _parsed) {
        Lib_RLPReader.RLPItem[] memory nodes = Lib_RLPReader.readList(_proof);
        TrieNode[] memory proof = new TrieNode[](nodes.length);

        for (uint256 i = 0; i < nodes.length; i++) {
            bytes memory encoded = Lib_RLPReader.readBytes(nodes[i]);
            proof[i] = TrieNode({ encoded: encoded, decoded: Lib_RLPReader.readList(encoded) });
        }

        return proof;
    }

    /**
     * @notice Picks out the ID for a node. Node ID is referred to as the
     * "hash" within the specification, but nodes < 32 bytes are not actually
     * hashed.
     * @param _node Node to pull an ID for.
     * @return _nodeID ID for the node, depending on the size of its contents.
     */
    function _getNodeID(Lib_RLPReader.RLPItem memory _node) private pure returns (bytes32 _nodeID) {
        bytes memory nodeID;

        if (_node.length < 32) {
            // Nodes smaller than 32 bytes are RLP encoded.
            nodeID = Lib_RLPReader.readRawBytes(_node);
        } else {
            // Nodes 32 bytes or larger are hashed.
            nodeID = Lib_RLPReader.readBytes(_node);
        }

        return Lib_BytesUtils.toBytes32(nodeID);
    }

    /**
     * @notice Gets the path for a leaf or extension node.
     * @param _node Node to get a path for.
     * @return _path Node path, converted to an array of nibbles.
     */
    function _getNodePath(TrieNode memory _node) private pure returns (bytes memory _path) {
        return Lib_BytesUtils.toNibbles(Lib_RLPReader.readBytes(_node.decoded[0]));
    }

    /**
     * @notice Gets the path for a node.
     * @param _node Node to get a value for.
     * @return _value Node value, as hex bytes.
     */
    function _getNodeValue(TrieNode memory _node) private pure returns (bytes memory _value) {
        return Lib_RLPReader.readBytes(_node.decoded[_node.decoded.length - 1]);
    }

    /**
     * @notice Utility; determines the number of nibbles shared between two
     * nibble arrays.
     * @param _a First nibble array.
     * @param _b Second nibble array.
     * @return _shared Number of shared nibbles.
     */
    function _getSharedNibbleLength(bytes memory _a, bytes memory _b)
        private
        pure
        returns (uint256 _shared)
    {
        uint256 i = 0;
        while (_a.length > i && _b.length > i && _a[i] == _b[i]) {
            i++;
        }
        return i;
    }
}

// File: contracts/libraries/trie/Lib_SecureMerkleTrie.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_MerkleTrie } from "./Lib_MerkleTrie.sol";

/**
 * @title Lib_SecureMerkleTrie
 */
library Lib_SecureMerkleTrie {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * @notice Verifies a proof that a given key/value pair is present in the
     * Merkle trie.
     * @param _key Key of the node to search for, as a hex string.
     * @param _value Value of the node to search for, as a hex string.
     * @param _proof Merkle trie inclusion proof for the desired node. Unlike
     * traditional Merkle trees, this proof is executed top-down and consists
     * of a list of RLP-encoded nodes that make a path down to the target node.
     * @param _root Known root of the Merkle trie. Used to verify that the
     * included proof is correctly constructed.
     * @return _verified `true` if the k/v pair exists in the trie, `false` otherwise.
     */
    function verifyInclusionProof(
        bytes memory _key,
        bytes memory _value,
        bytes memory _proof,
        bytes32 _root
    ) internal pure returns (bool _verified) {
        bytes memory key = _getSecureKey(_key);
        return Lib_MerkleTrie.verifyInclusionProof(key, _value, _proof, _root);
    }

    /**
     * @notice Retrieves the value associated with a given key.
     * @param _key Key to search for, as hex bytes.
     * @param _proof Merkle trie inclusion proof for the key.
     * @param _root Known root of the Merkle trie.
     * @return _exists Whether or not the key exists.
     * @return _value Value of the key if it exists.
     */
    function get(
        bytes memory _key,
        bytes memory _proof,
        bytes32 _root
    ) internal pure returns (bool _exists, bytes memory _value) {
        bytes memory key = _getSecureKey(_key);
        return Lib_MerkleTrie.get(key, _proof, _root);
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Computes the secure counterpart to a key.
     * @param _key Key to get a secure key from.
     * @return _secureKey Secure version of the key.
     */
    function _getSecureKey(bytes memory _key) private pure returns (bytes memory _secureKey) {
        return abi.encodePacked(keccak256(_key));
    }
}

// File: contracts/libraries/utils/Lib_Bytes32Utils.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_Byte32Utils
 */
library Lib_Bytes32Utils {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * Converts a bytes32 value to a boolean. Anything non-zero will be converted to "true."
     * @param _in Input bytes32 value.
     * @return Bytes32 as a boolean.
     */
    function toBool(bytes32 _in) internal pure returns (bool) {
        return _in != 0;
    }

    /**
     * Converts a boolean to a bytes32 value.
     * @param _in Input boolean value.
     * @return Boolean as a bytes32.
     */
    function fromBool(bool _in) internal pure returns (bytes32) {
        return bytes32(uint256(_in ? 1 : 0));
    }

    /**
     * Converts a bytes32 value to an address. Takes the *last* 20 bytes.
     * @param _in Input bytes32 value.
     * @return Bytes32 as an address.
     */
    function toAddress(bytes32 _in) internal pure returns (address) {
        return address(uint160(uint256(_in)));
    }

    /**
     * Converts an address to a bytes32.
     * @param _in Input address value.
     * @return Address as a bytes32.
     */
    function fromAddress(address _in) internal pure returns (bytes32) {
        return bytes32(uint256(uint160(_in)));
    }
}

// File: contracts/libraries/utils/Lib_BytesUtils.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_BytesUtils
 */
library Lib_BytesUtils {
    /**********************
     * Internal Functions *
     **********************/

    function slice(
        bytes memory _bytes,
        uint256 _start,
        uint256 _length
    ) internal pure returns (bytes memory) {
        require(_length + 31 >= _length, "slice_overflow");
        require(_start + _length >= _start, "slice_overflow");
        require(_bytes.length >= _start + _length, "slice_outOfBounds");

        bytes memory tempBytes;

        assembly {
            switch iszero(_length)
            case 0 {
                // Get a location of some free memory and store it in tempBytes as
                // Solidity does for memory variables.
                tempBytes := mload(0x40)

                // The first word of the slice result is potentially a partial
                // word read from the original array. To read it, we calculate
                // the length of that partial word and start copying that many
                // bytes into the array. The first word we copy will start with
                // data we don't care about, but the last `lengthmod` bytes will
                // land at the beginning of the contents of the new array. When
                // we're done copying, we overwrite the full first word with
                // the actual length of the slice.
                let lengthmod := and(_length, 31)

                // The multiplication in the next line is necessary
                // because when slicing multiples of 32 bytes (lengthmod == 0)
                // the following copy loop was copying the origin's length
                // and then ending prematurely not copying everything it should.
                let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                let end := add(mc, _length)

                for {
                    // The multiplication in the next line has the same exact purpose
                    // as the one above.
                    let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                } lt(mc, end) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } {
                    mstore(mc, mload(cc))
                }

                mstore(tempBytes, _length)

                //update free-memory pointer
                //allocating the array padded to 32 bytes like the compiler does now
                mstore(0x40, and(add(mc, 31), not(31)))
            }
            //if we want a zero-length slice let's just return a zero-length array
            default {
                tempBytes := mload(0x40)

                //zero out the 32 bytes slice we are about to return
                //we need to do it because Solidity does not garbage collect
                mstore(tempBytes, 0)

                mstore(0x40, add(tempBytes, 0x20))
            }
        }

        return tempBytes;
    }

    function slice(bytes memory _bytes, uint256 _start) internal pure returns (bytes memory) {
        if (_start >= _bytes.length) {
            return bytes("");
        }

        return slice(_bytes, _start, _bytes.length - _start);
    }

    function toBytes32(bytes memory _bytes) internal pure returns (bytes32) {
        if (_bytes.length < 32) {
            bytes32 ret;
            assembly {
                ret := mload(add(_bytes, 32))
            }
            return ret;
        }

        return abi.decode(_bytes, (bytes32)); // will truncate if input length > 32 bytes
    }

    function toUint256(bytes memory _bytes) internal pure returns (uint256) {
        return uint256(toBytes32(_bytes));
    }

    function toNibbles(bytes memory _bytes) internal pure returns (bytes memory) {
        bytes memory nibbles = new bytes(_bytes.length * 2);

        for (uint256 i = 0; i < _bytes.length; i++) {
            nibbles[i * 2] = _bytes[i] >> 4;
            nibbles[i * 2 + 1] = bytes1(uint8(_bytes[i]) % 16);
        }

        return nibbles;
    }

    function fromNibbles(bytes memory _bytes) internal pure returns (bytes memory) {
        bytes memory ret = new bytes(_bytes.length / 2);

        for (uint256 i = 0; i < ret.length; i++) {
            ret[i] = (_bytes[i * 2] << 4) | (_bytes[i * 2 + 1]);
        }

        return ret;
    }

    function equal(bytes memory _bytes, bytes memory _other) internal pure returns (bool) {
        return keccak256(_bytes) == keccak256(_other);
    }
}