Cryo Explorer Ethereum Mainnet

// SPDX-License-Identifier: Apache-2.0
pragma solidity >=0.8.0;

import {TokenRouter} from "./libs/TokenRouter.sol";
import {TokenMessage} from "./libs/TokenMessage.sol";
import {Address} from "@openzeppelin/contracts/utils/Address.sol";

/**
 * @title Hyperlane Native Token Router that extends ERC20 with remote transfer functionality.
 * @author Abacus Works
 * @dev Supply on each chain is not constant but the aggregate supply across all chains is.
 */
contract HypNative is TokenRouter {
    /**
     * @dev Emitted when native tokens are donated to the contract.
     * @param sender The address of the sender.
     * @param amount The amount of native tokens donated.
     */
    event Donation(address indexed sender, uint256 amount);

    constructor(address _mailbox) TokenRouter(_mailbox) {}

    /**
     * @notice Initializes the Hyperlane router
     * @param _hook The post-dispatch hook contract.
       @param _interchainSecurityModule The interchain security module contract.
       @param _owner The this contract.
     */
    function initialize(
        address _hook,
        address _interchainSecurityModule,
        address _owner
    ) public initializer {
        _MailboxClient_initialize(_hook, _interchainSecurityModule, _owner);
    }

    /**
     * @inheritdoc TokenRouter
     * @dev uses (`msg.value` - `_amount`) as hook payment and `msg.sender` as refund address.
     */
    function transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amount
    ) external payable virtual override returns (bytes32 messageId) {
        require(msg.value >= _amount, "Native: amount exceeds msg.value");
        uint256 _hookPayment = msg.value - _amount;
        return _transferRemote(_destination, _recipient, _amount, _hookPayment);
    }

    /**
     * @inheritdoc TokenRouter
     * @dev uses (`msg.value` - `_amount`) as hook payment.
     */
    function transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amount,
        bytes calldata _hookMetadata,
        address _hook
    ) external payable virtual override returns (bytes32 messageId) {
        require(msg.value >= _amount, "Native: amount exceeds msg.value");
        uint256 _hookPayment = msg.value - _amount;
        return
            _transferRemote(
                _destination,
                _recipient,
                _amount,
                _hookPayment,
                _hookMetadata,
                _hook
            );
    }

    function balanceOf(
        address _account
    ) external view override returns (uint256) {
        return _account.balance;
    }

    /**
     * @inheritdoc TokenRouter
     * @dev No-op because native amount is transferred in `msg.value`
     * @dev Compiler will not include this in the bytecode.
     */
    function _transferFromSender(
        uint256
    ) internal pure override returns (bytes memory) {
        return bytes(""); // no metadata
    }

    /**
     * @dev Sends `_amount` of native token to `_recipient` balance.
     * @inheritdoc TokenRouter
     */
    function _transferTo(
        address _recipient,
        uint256 _amount,
        bytes calldata // no metadata
    ) internal virtual override {
        Address.sendValue(payable(_recipient), _amount);
    }

    receive() external payable {
        emit Donation(msg.sender, msg.value);
    }
}

// SPDX-License-Identifier: Apache-2.0
pragma solidity >=0.8.0;

import {IPostDispatchHook} from "../../interfaces/hooks/IPostDispatchHook.sol";
import {GasRouter} from "../../client/GasRouter.sol";
import {MailboxClient} from "../../client/MailboxClient.sol";
import {TypeCasts} from "../../libs/TypeCasts.sol";
import {TokenMessage} from "./TokenMessage.sol";

/**
 * @title Hyperlane Token Router that extends Router with abstract token (ERC20/ERC721) remote transfer functionality.
 * @author Abacus Works
 */
abstract contract TokenRouter is GasRouter {
    using TypeCasts for bytes32;
    using TypeCasts for address;
    using TokenMessage for bytes;

    /**
     * @dev Emitted on `transferRemote` when a transfer message is dispatched.
     * @param destination The identifier of the destination chain.
     * @param recipient The address of the recipient on the destination chain.
     * @param amount The amount of tokens burnt on the origin chain.
     */
    event SentTransferRemote(
        uint32 indexed destination,
        bytes32 indexed recipient,
        uint256 amount
    );

    /**
     * @dev Emitted on `_handle` when a transfer message is processed.
     * @param origin The identifier of the origin chain.
     * @param recipient The address of the recipient on the destination chain.
     * @param amount The amount of tokens minted on the destination chain.
     */
    event ReceivedTransferRemote(
        uint32 indexed origin,
        bytes32 indexed recipient,
        uint256 amount
    );

    constructor(address _mailbox) GasRouter(_mailbox) {}

    /**
     * @notice Transfers `_amountOrId` token to `_recipient` on `_destination` domain.
     * @dev Delegates transfer logic to `_transferFromSender` implementation.
     * @dev Emits `SentTransferRemote` event on the origin chain.
     * @param _destination The identifier of the destination chain.
     * @param _recipient The address of the recipient on the destination chain.
     * @param _amountOrId The amount or identifier of tokens to be sent to the remote recipient.
     * @return messageId The identifier of the dispatched message.
     */
    function transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amountOrId
    ) external payable virtual returns (bytes32 messageId) {
        return
            _transferRemote(_destination, _recipient, _amountOrId, msg.value);
    }

    /**
     * @notice Transfers `_amountOrId` token to `_recipient` on `_destination` domain with a specified hook
     * @dev Delegates transfer logic to `_transferFromSender` implementation.
     * @dev The metadata is the token metadata, and is DIFFERENT than the hook metadata.
     * @dev Emits `SentTransferRemote` event on the origin chain.
     * @param _destination The identifier of the destination chain.
     * @param _recipient The address of the recipient on the destination chain.
     * @param _amountOrId The amount or identifier of tokens to be sent to the remote recipient.
     * @param _hookMetadata The metadata passed into the hook
     * @param _hook The post dispatch hook to be called by the Mailbox
     * @return messageId The identifier of the dispatched message.
     */
    function transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amountOrId,
        bytes calldata _hookMetadata,
        address _hook
    ) external payable virtual returns (bytes32 messageId) {
        return
            _transferRemote(
                _destination,
                _recipient,
                _amountOrId,
                msg.value,
                _hookMetadata,
                _hook
            );
    }

    function _transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amountOrId,
        uint256 _value
    ) internal returns (bytes32 messageId) {
        return
            _transferRemote(
                _destination,
                _recipient,
                _amountOrId,
                _value,
                _GasRouter_hookMetadata(_destination),
                address(hook)
            );
    }

    function _transferRemote(
        uint32 _destination,
        bytes32 _recipient,
        uint256 _amountOrId,
        uint256 _value,
        bytes memory _hookMetadata,
        address _hook
    ) internal virtual returns (bytes32 messageId) {
        bytes memory _tokenMetadata = _transferFromSender(_amountOrId);
        bytes memory _tokenMessage = TokenMessage.format(
            _recipient,
            _amountOrId,
            _tokenMetadata
        );

        messageId = _Router_dispatch(
            _destination,
            _value,
            _tokenMessage,
            _hookMetadata,
            _hook
        );

        emit SentTransferRemote(_destination, _recipient, _amountOrId);
    }

    /**
     * @dev Should transfer `_amountOrId` of tokens from `msg.sender` to this token router.
     * @dev Called by `transferRemote` before message dispatch.
     * @dev Optionally returns `metadata` associated with the transfer to be passed in message.
     */
    function _transferFromSender(
        uint256 _amountOrId
    ) internal virtual returns (bytes memory metadata);

    /**
     * @notice Returns the balance of `account` on this token router.
     * @param account The address to query the balance of.
     * @return The balance of `account`.
     */
    function balanceOf(address account) external virtual returns (uint256);

    /**
     * @dev Mints tokens to recipient when router receives transfer message.
     * @dev Emits `ReceivedTransferRemote` event on the destination chain.
     * @param _origin The identifier of the origin chain.
     * @param _message The encoded remote transfer message containing the recipient address and amount.
     */
    function _handle(
        uint32 _origin,
        bytes32,
        bytes calldata _message
    ) internal virtual override {
        bytes32 recipient = _message.recipient();
        uint256 amount = _message.amount();
        bytes calldata metadata = _message.metadata();
        _transferTo(recipient.bytes32ToAddress(), amount, metadata);
        emit ReceivedTransferRemote(_origin, recipient, amount);
    }

    /**
     * @dev Should transfer `_amountOrId` of tokens from this token router to `_recipient`.
     * @dev Called by `handle` after message decoding.
     * @dev Optionally handles `metadata` associated with transfer passed in message.
     */
    function _transferTo(
        address _recipient,
        uint256 _amountOrId,
        bytes calldata metadata
    ) internal virtual;
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.8.0;

library TokenMessage {
    function format(
        bytes32 _recipient,
        uint256 _amount,
        bytes memory _metadata
    ) internal pure returns (bytes memory) {
        return abi.encodePacked(_recipient, _amount, _metadata);
    }

    function recipient(bytes calldata message) internal pure returns (bytes32) {
        return bytes32(message[0:32]);
    }

    function amount(bytes calldata message) internal pure returns (uint256) {
        return uint256(bytes32(message[32:64]));
    }

    // alias for ERC721
    function tokenId(bytes calldata message) internal pure returns (uint256) {
        return amount(message);
    }

    function metadata(
        bytes calldata message
    ) internal pure returns (bytes calldata) {
        return message[64:];
    }
}

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

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.8.0;

/*@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
     @@@@@  HYPERLANE  @@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
@@@@@@@@@       @@@@@@@@*/

interface IPostDispatchHook {
    enum Types {
        UNUSED,
        ROUTING,
        AGGREGATION,
        MERKLE_TREE,
        INTERCHAIN_GAS_PAYMASTER,
        FALLBACK_ROUTING,
        ID_AUTH_ISM,
        PAUSABLE,
        PROTOCOL_FEE,
        LAYER_ZERO_V1,
        RATE_LIMITED,
        ARB_L2_TO_L1,
        OP_L2_TO_L1
    }

    /**
     * @notice Returns an enum that represents the type of hook
     */
    function hookType() external view returns (uint8);

    /**
     * @notice Returns whether the hook supports metadata
     * @param metadata metadata
     * @return Whether the hook supports metadata
     */
    function supportsMetadata(
        bytes calldata metadata
    ) external view returns (bool);

    /**
     * @notice Post action after a message is dispatched via the Mailbox
     * @param metadata The metadata required for the hook
     * @param message The message passed from the Mailbox.dispatch() call
     */
    function postDispatch(
        bytes calldata metadata,
        bytes calldata message
    ) external payable;

    /**
     * @notice Compute the payment required by the postDispatch call
     * @param metadata The metadata required for the hook
     * @param message The message passed from the Mailbox.dispatch() call
     * @return Quoted payment for the postDispatch call
     */
    function quoteDispatch(
        bytes calldata metadata,
        bytes calldata message
    ) external view returns (uint256);
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

/*@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
     @@@@@  HYPERLANE  @@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
@@@@@@@@@       @@@@@@@@*/

// ============ Internal Imports ============
import {Router} from "./Router.sol";
import {StandardHookMetadata} from "../hooks/libs/StandardHookMetadata.sol";

abstract contract GasRouter is Router {
    event GasSet(uint32 domain, uint256 gas);

    // ============ Mutable Storage ============
    mapping(uint32 => uint256) public destinationGas;

    struct GasRouterConfig {
        uint32 domain;
        uint256 gas;
    }

    constructor(address _mailbox) Router(_mailbox) {}

    /**
     * @notice Sets the gas amount dispatched for each configured domain.
     * @param gasConfigs The array of GasRouterConfig structs
     */
    function setDestinationGas(
        GasRouterConfig[] calldata gasConfigs
    ) external onlyOwner {
        for (uint256 i = 0; i < gasConfigs.length; i += 1) {
            _setDestinationGas(gasConfigs[i].domain, gasConfigs[i].gas);
        }
    }

    /**
     * @notice Sets the gas amount dispatched for each configured domain.
     * @param domain The destination domain ID
     * @param gas The gas limit
     */
    function setDestinationGas(uint32 domain, uint256 gas) external onlyOwner {
        _setDestinationGas(domain, gas);
    }

    /**
     * @notice Returns the gas payment required to dispatch a message to the given domain's router.
     * @param _destinationDomain The domain of the router.
     * @return _gasPayment Payment computed by the registered InterchainGasPaymaster.
     */
    function quoteGasPayment(
        uint32 _destinationDomain
    ) external view returns (uint256) {
        return _GasRouter_quoteDispatch(_destinationDomain, "", address(hook));
    }

    function _GasRouter_hookMetadata(
        uint32 _destination
    ) internal view returns (bytes memory) {
        return
            StandardHookMetadata.overrideGasLimit(destinationGas[_destination]);
    }

    function _setDestinationGas(uint32 domain, uint256 gas) internal {
        destinationGas[domain] = gas;
        emit GasSet(domain, gas);
    }

    function _GasRouter_dispatch(
        uint32 _destination,
        uint256 _value,
        bytes memory _messageBody,
        address _hook
    ) internal returns (bytes32) {
        return
            _Router_dispatch(
                _destination,
                _value,
                _messageBody,
                _GasRouter_hookMetadata(_destination),
                _hook
            );
    }

    function _GasRouter_quoteDispatch(
        uint32 _destination,
        bytes memory _messageBody,
        address _hook
    ) internal view returns (uint256) {
        return
            _Router_quoteDispatch(
                _destination,
                _messageBody,
                _GasRouter_hookMetadata(_destination),
                _hook
            );
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

/*@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
     @@@@@  HYPERLANE  @@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
@@@@@@@@@       @@@@@@@@*/

// ============ Internal Imports ============
import {IMailbox} from "../interfaces/IMailbox.sol";
import {IPostDispatchHook} from "../interfaces/hooks/IPostDispatchHook.sol";
import {IInterchainSecurityModule} from "../interfaces/IInterchainSecurityModule.sol";
import {Message} from "../libs/Message.sol";
import {PackageVersioned} from "../PackageVersioned.sol";

// ============ External Imports ============
import {Address} from "@openzeppelin/contracts/utils/Address.sol";
import {OwnableUpgradeable} from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";

abstract contract MailboxClient is OwnableUpgradeable, PackageVersioned {
    using Message for bytes;

    event HookSet(address _hook);
    event IsmSet(address _ism);

    IMailbox public immutable mailbox;

    uint32 public immutable localDomain;

    IPostDispatchHook public hook;

    IInterchainSecurityModule public interchainSecurityModule;

    uint256[48] private __GAP; // gap for upgrade safety

    // ============ Modifiers ============
    modifier onlyContract(address _contract) {
        require(
            Address.isContract(_contract),
            "MailboxClient: invalid mailbox"
        );
        _;
    }

    modifier onlyContractOrNull(address _contract) {
        require(
            Address.isContract(_contract) || _contract == address(0),
            "MailboxClient: invalid contract setting"
        );
        _;
    }

    /**
     * @notice Only accept messages from a Hyperlane Mailbox contract
     */
    modifier onlyMailbox() {
        require(
            msg.sender == address(mailbox),
            "MailboxClient: sender not mailbox"
        );
        _;
    }

    constructor(address _mailbox) onlyContract(_mailbox) {
        mailbox = IMailbox(_mailbox);
        localDomain = mailbox.localDomain();
        _transferOwnership(msg.sender);
    }

    /**
     * @notice Sets the address of the application's custom hook.
     * @param _hook The address of the hook contract.
     */
    function setHook(
        address _hook
    ) public virtual onlyContractOrNull(_hook) onlyOwner {
        hook = IPostDispatchHook(_hook);
        emit HookSet(_hook);
    }

    /**
     * @notice Sets the address of the application's custom interchain security module.
     * @param _module The address of the interchain security module contract.
     */
    function setInterchainSecurityModule(
        address _module
    ) public onlyContractOrNull(_module) onlyOwner {
        interchainSecurityModule = IInterchainSecurityModule(_module);
        emit IsmSet(_module);
    }

    // ======== Initializer =========
    function _MailboxClient_initialize(
        address _hook,
        address _interchainSecurityModule,
        address _owner
    ) internal onlyInitializing {
        __Ownable_init();
        setHook(_hook);
        setInterchainSecurityModule(_interchainSecurityModule);
        _transferOwnership(_owner);
    }

    function _isLatestDispatched(bytes32 id) internal view returns (bool) {
        return mailbox.latestDispatchedId() == id;
    }

    function _isDelivered(bytes32 id) internal view returns (bool) {
        return mailbox.delivered(id);
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

library TypeCasts {
    // alignment preserving cast
    function addressToBytes32(address _addr) internal pure returns (bytes32) {
        return bytes32(uint256(uint160(_addr)));
    }

    // alignment preserving cast
    function bytes32ToAddress(bytes32 _buf) internal pure returns (address) {
        require(
            uint256(_buf) <= uint256(type(uint160).max),
            "TypeCasts: bytes32ToAddress overflow"
        );
        return address(uint160(uint256(_buf)));
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

// ============ Internal Imports ============
import {IMessageRecipient} from "../interfaces/IMessageRecipient.sol";
import {IPostDispatchHook} from "../interfaces/hooks/IPostDispatchHook.sol";
import {IInterchainSecurityModule} from "../interfaces/IInterchainSecurityModule.sol";
import {MailboxClient} from "./MailboxClient.sol";
import {EnumerableMapExtended} from "../libs/EnumerableMapExtended.sol";

// ============ External Imports ============
import {Strings} from "@openzeppelin/contracts/utils/Strings.sol";

abstract contract Router is MailboxClient, IMessageRecipient {
    using EnumerableMapExtended for EnumerableMapExtended.UintToBytes32Map;
    using Strings for uint32;

    // ============ Mutable Storage ============
    EnumerableMapExtended.UintToBytes32Map internal _routers;

    uint256[48] private __GAP; // gap for upgrade safety

    constructor(address _mailbox) MailboxClient(_mailbox) {}

    // ============ External functions ============
    function domains() external view returns (uint32[] memory) {
        return _routers.uint32Keys();
    }

    /**
     * @notice Returns the address of the Router contract for the given domain
     * @param _domain The remote domain ID.
     * @dev Returns 0 address if no router is enrolled for the given domain
     * @return router The address of the Router contract for the given domain
     */
    function routers(uint32 _domain) public view virtual returns (bytes32) {
        (, bytes32 _router) = _routers.tryGet(_domain);
        return _router;
    }

    /**
     * @notice Unregister the domain
     * @param _domain The domain of the remote Application Router
     */
    function unenrollRemoteRouter(uint32 _domain) external virtual onlyOwner {
        _unenrollRemoteRouter(_domain);
    }

    /**
     * @notice Register the address of a Router contract for the same Application on a remote chain
     * @param _domain The domain of the remote Application Router
     * @param _router The address of the remote Application Router
     */
    function enrollRemoteRouter(
        uint32 _domain,
        bytes32 _router
    ) external virtual onlyOwner {
        _enrollRemoteRouter(_domain, _router);
    }

    /**
     * @notice Batch version of `enrollRemoteRouter`
     * @param _domains The domains of the remote Application Routers
     * @param _addresses The addresses of the remote Application Routers
     */
    function enrollRemoteRouters(
        uint32[] calldata _domains,
        bytes32[] calldata _addresses
    ) external virtual onlyOwner {
        require(_domains.length == _addresses.length, "!length");
        uint256 length = _domains.length;
        for (uint256 i = 0; i < length; i += 1) {
            _enrollRemoteRouter(_domains[i], _addresses[i]);
        }
    }

    /**
     * @notice Batch version of `unenrollRemoteRouter`
     * @param _domains The domains of the remote Application Routers
     */
    function unenrollRemoteRouters(
        uint32[] calldata _domains
    ) external virtual onlyOwner {
        uint256 length = _domains.length;
        for (uint256 i = 0; i < length; i += 1) {
            _unenrollRemoteRouter(_domains[i]);
        }
    }

    /**
     * @notice Handles an incoming message
     * @param _origin The origin domain
     * @param _sender The sender address
     * @param _message The message
     */
    function handle(
        uint32 _origin,
        bytes32 _sender,
        bytes calldata _message
    ) external payable virtual override onlyMailbox {
        bytes32 _router = _mustHaveRemoteRouter(_origin);
        require(_router == _sender, "Enrolled router does not match sender");
        _handle(_origin, _sender, _message);
    }

    // ============ Virtual functions ============
    function _handle(
        uint32 _origin,
        bytes32 _sender,
        bytes calldata _message
    ) internal virtual;

    // ============ Internal functions ============

    /**
     * @notice Set the router for a given domain
     * @param _domain The domain
     * @param _address The new router
     */
    function _enrollRemoteRouter(
        uint32 _domain,
        bytes32 _address
    ) internal virtual {
        _routers.set(_domain, _address);
    }

    /**
     * @notice Remove the router for a given domain
     * @param _domain The domain
     */
    function _unenrollRemoteRouter(uint32 _domain) internal virtual {
        require(_routers.remove(_domain), _domainNotFoundError(_domain));
    }

    /**
     * @notice Return true if the given domain / router is the address of a remote Application Router
     * @param _domain The domain of the potential remote Application Router
     * @param _address The address of the potential remote Application Router
     */
    function _isRemoteRouter(
        uint32 _domain,
        bytes32 _address
    ) internal view returns (bool) {
        return routers(_domain) == _address;
    }

    /**
     * @notice Assert that the given domain has an Application Router registered and return its address
     * @param _domain The domain of the chain for which to get the Application Router
     * @return _router The address of the remote Application Router on _domain
     */
    function _mustHaveRemoteRouter(
        uint32 _domain
    ) internal view returns (bytes32) {
        (bool contained, bytes32 _router) = _routers.tryGet(_domain);
        if (contained) {
            return _router;
        }
        revert(_domainNotFoundError(_domain));
    }

    function _domainNotFoundError(
        uint32 _domain
    ) internal pure returns (string memory) {
        return
            string.concat(
                "No router enrolled for domain: ",
                _domain.toString()
            );
    }

    function _Router_dispatch(
        uint32 _destinationDomain,
        uint256 _value,
        bytes memory _messageBody,
        bytes memory _hookMetadata,
        address _hook
    ) internal returns (bytes32) {
        bytes32 _router = _mustHaveRemoteRouter(_destinationDomain);
        return
            mailbox.dispatch{value: _value}(
                _destinationDomain,
                _router,
                _messageBody,
                _hookMetadata,
                IPostDispatchHook(_hook)
            );
    }

    /**
     * DEPRECATED: Use `_Router_dispatch` instead
     * @dev For backward compatibility with v2 client contracts
     */
    function _dispatch(
        uint32 _destinationDomain,
        bytes memory _messageBody
    ) internal returns (bytes32) {
        return
            _Router_dispatch(
                _destinationDomain,
                msg.value,
                _messageBody,
                "",
                address(hook)
            );
    }

    function _Router_quoteDispatch(
        uint32 _destinationDomain,
        bytes memory _messageBody,
        bytes memory _hookMetadata,
        address _hook
    ) internal view returns (uint256) {
        bytes32 _router = _mustHaveRemoteRouter(_destinationDomain);
        return
            mailbox.quoteDispatch(
                _destinationDomain,
                _router,
                _messageBody,
                _hookMetadata,
                IPostDispatchHook(_hook)
            );
    }

    /**
     * DEPRECATED: Use `_Router_quoteDispatch` instead
     * @dev For backward compatibility with v2 client contracts
     */
    function _quoteDispatch(
        uint32 _destinationDomain,
        bytes memory _messageBody
    ) internal view returns (uint256) {
        return
            _Router_quoteDispatch(
                _destinationDomain,
                _messageBody,
                "",
                address(hook)
            );
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.8.0;

/*@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
     @@@@@  HYPERLANE  @@@@@@@
    @@@@@@@@@@@@@@@@@@@@@@@@@
   @@@@@@@@@       @@@@@@@@@
  @@@@@@@@@       @@@@@@@@@
 @@@@@@@@@       @@@@@@@@@
@@@@@@@@@       @@@@@@@@*/

/**
 * Format of metadata:
 *
 * [0:2] variant
 * [2:34] msg.value
 * [34:66] Gas limit for message (IGP)
 * [66:86] Refund address for message (IGP)
 * [86:] Custom metadata
 */
library StandardHookMetadata {
    struct Metadata {
        uint16 variant;
        uint256 msgValue;
        uint256 gasLimit;
        address refundAddress;
    }

    uint8 private constant VARIANT_OFFSET = 0;
    uint8 private constant MSG_VALUE_OFFSET = 2;
    uint8 private constant GAS_LIMIT_OFFSET = 34;
    uint8 private constant REFUND_ADDRESS_OFFSET = 66;
    uint256 private constant MIN_METADATA_LENGTH = 86;

    uint16 public constant VARIANT = 1;

    /**
     * @notice Returns the variant of the metadata.
     * @param _metadata ABI encoded standard hook metadata.
     * @return variant of the metadata as uint8.
     */
    function variant(bytes calldata _metadata) internal pure returns (uint16) {
        if (_metadata.length < VARIANT_OFFSET + 2) return 0;
        return uint16(bytes2(_metadata[VARIANT_OFFSET:VARIANT_OFFSET + 2]));
    }

    /**
     * @notice Returns the specified value for the message.
     * @param _metadata ABI encoded standard hook metadata.
     * @param _default Default fallback value.
     * @return Value for the message as uint256.
     */
    function msgValue(
        bytes calldata _metadata,
        uint256 _default
    ) internal pure returns (uint256) {
        if (_metadata.length < MSG_VALUE_OFFSET + 32) return _default;
        return
            uint256(bytes32(_metadata[MSG_VALUE_OFFSET:MSG_VALUE_OFFSET + 32]));
    }

    /**
     * @notice Returns the specified gas limit for the message.
     * @param _metadata ABI encoded standard hook metadata.
     * @param _default Default fallback gas limit.
     * @return Gas limit for the message as uint256.
     */
    function gasLimit(
        bytes calldata _metadata,
        uint256 _default
    ) internal pure returns (uint256) {
        if (_metadata.length < GAS_LIMIT_OFFSET + 32) return _default;
        return
            uint256(bytes32(_metadata[GAS_LIMIT_OFFSET:GAS_LIMIT_OFFSET + 32]));
    }

    /**
     * @notice Returns the specified refund address for the message.
     * @param _metadata ABI encoded standard hook metadata.
     * @param _default Default fallback refund address.
     * @return Refund address for the message as address.
     */
    function refundAddress(
        bytes calldata _metadata,
        address _default
    ) internal pure returns (address) {
        if (_metadata.length < REFUND_ADDRESS_OFFSET + 20) return _default;
        return
            address(
                bytes20(
                    _metadata[REFUND_ADDRESS_OFFSET:REFUND_ADDRESS_OFFSET + 20]
                )
            );
    }

    /**
     * @notice Returns any custom metadata.
     * @param _metadata ABI encoded standard hook metadata.
     * @return Custom metadata.
     */
    function getCustomMetadata(
        bytes calldata _metadata
    ) internal pure returns (bytes calldata) {
        if (_metadata.length < MIN_METADATA_LENGTH) return _metadata[0:0];
        return _metadata[MIN_METADATA_LENGTH:];
    }

    /**
     * @notice Formats the specified gas limit and refund address into standard hook metadata.
     * @param _msgValue msg.value for the message.
     * @param _gasLimit Gas limit for the message.
     * @param _refundAddress Refund address for the message.
     * @param _customMetadata Additional metadata to include in the standard hook metadata.
     * @return ABI encoded standard hook metadata.
     */
    function formatMetadata(
        uint256 _msgValue,
        uint256 _gasLimit,
        address _refundAddress,
        bytes memory _customMetadata
    ) internal pure returns (bytes memory) {
        return
            abi.encodePacked(
                VARIANT,
                _msgValue,
                _gasLimit,
                _refundAddress,
                _customMetadata
            );
    }

    /**
     * @notice Formats the specified gas limit and refund address into standard hook metadata.
     * @param _msgValue msg.value for the message.
     * @return ABI encoded standard hook metadata.
     */
    function overrideMsgValue(
        uint256 _msgValue
    ) internal view returns (bytes memory) {
        return formatMetadata(_msgValue, uint256(0), msg.sender, "");
    }

    /**
     * @notice Formats the specified gas limit and refund address into standard hook metadata.
     * @param _gasLimit Gas limit for the message.
     * @return ABI encoded standard hook metadata.
     */
    function overrideGasLimit(
        uint256 _gasLimit
    ) internal view returns (bytes memory) {
        return formatMetadata(uint256(0), _gasLimit, msg.sender, "");
    }

    /**
     * @notice Formats the specified refund address into standard hook metadata.
     * @param _refundAddress Refund address for the message.
     * @return ABI encoded standard hook metadata.
     */
    function overrideRefundAddress(
        address _refundAddress
    ) internal pure returns (bytes memory) {
        return formatMetadata(uint256(0), uint256(0), _refundAddress, "");
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.8.0;

import {IInterchainSecurityModule} from "./IInterchainSecurityModule.sol";
import {IPostDispatchHook} from "./hooks/IPostDispatchHook.sol";

interface IMailbox {
    // ============ Events ============
    /**
     * @notice Emitted when a new message is dispatched via Hyperlane
     * @param sender The address that dispatched the message
     * @param destination The destination domain of the message
     * @param recipient The message recipient address on `destination`
     * @param message Raw bytes of message
     */
    event Dispatch(
        address indexed sender,
        uint32 indexed destination,
        bytes32 indexed recipient,
        bytes message
    );

    /**
     * @notice Emitted when a new message is dispatched via Hyperlane
     * @param messageId The unique message identifier
     */
    event DispatchId(bytes32 indexed messageId);

    /**
     * @notice Emitted when a Hyperlane message is processed
     * @param messageId The unique message identifier
     */
    event ProcessId(bytes32 indexed messageId);

    /**
     * @notice Emitted when a Hyperlane message is delivered
     * @param origin The origin domain of the message
     * @param sender The message sender address on `origin`
     * @param recipient The address that handled the message
     */
    event Process(
        uint32 indexed origin,
        bytes32 indexed sender,
        address indexed recipient
    );

    function localDomain() external view returns (uint32);

    function delivered(bytes32 messageId) external view returns (bool);

    function defaultIsm() external view returns (IInterchainSecurityModule);

    function defaultHook() external view returns (IPostDispatchHook);

    function requiredHook() external view returns (IPostDispatchHook);

    function latestDispatchedId() external view returns (bytes32);

    function dispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata messageBody
    ) external payable returns (bytes32 messageId);

    function quoteDispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata messageBody
    ) external view returns (uint256 fee);

    function dispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata body,
        bytes calldata defaultHookMetadata
    ) external payable returns (bytes32 messageId);

    function quoteDispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata messageBody,
        bytes calldata defaultHookMetadata
    ) external view returns (uint256 fee);

    function dispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata body,
        bytes calldata customHookMetadata,
        IPostDispatchHook customHook
    ) external payable returns (bytes32 messageId);

    function quoteDispatch(
        uint32 destinationDomain,
        bytes32 recipientAddress,
        bytes calldata messageBody,
        bytes calldata customHookMetadata,
        IPostDispatchHook customHook
    ) external view returns (uint256 fee);

    function process(
        bytes calldata metadata,
        bytes calldata message
    ) external payable;

    function recipientIsm(
        address recipient
    ) external view returns (IInterchainSecurityModule module);
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

interface IInterchainSecurityModule {
    enum Types {
        UNUSED,
        ROUTING,
        AGGREGATION,
        LEGACY_MULTISIG,
        MERKLE_ROOT_MULTISIG,
        MESSAGE_ID_MULTISIG,
        NULL, // used with relayer carrying no metadata
        CCIP_READ,
        ARB_L2_TO_L1,
        WEIGHTED_MERKLE_ROOT_MULTISIG,
        WEIGHTED_MESSAGE_ID_MULTISIG,
        OP_L2_TO_L1
    }

    /**
     * @notice Returns an enum that represents the type of security model
     * encoded by this ISM.
     * @dev Relayers infer how to fetch and format metadata.
     */
    function moduleType() external view returns (uint8);

    /**
     * @notice Defines a security model responsible for verifying interchain
     * messages based on the provided metadata.
     * @param _metadata Off-chain metadata provided by a relayer, specific to
     * the security model encoded by the module (e.g. validator signatures)
     * @param _message Hyperlane encoded interchain message
     * @return True if the message was verified
     */
    function verify(
        bytes calldata _metadata,
        bytes calldata _message
    ) external returns (bool);
}

interface ISpecifiesInterchainSecurityModule {
    function interchainSecurityModule()
        external
        view
        returns (IInterchainSecurityModule);
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.8.0;

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

/**
 * @title Hyperlane Message Library
 * @notice Library for formatted messages used by Mailbox
 **/
library Message {
    using TypeCasts for bytes32;

    uint256 private constant VERSION_OFFSET = 0;
    uint256 private constant NONCE_OFFSET = 1;
    uint256 private constant ORIGIN_OFFSET = 5;
    uint256 private constant SENDER_OFFSET = 9;
    uint256 private constant DESTINATION_OFFSET = 41;
    uint256 private constant RECIPIENT_OFFSET = 45;
    uint256 private constant BODY_OFFSET = 77;

    /**
     * @notice Returns formatted (packed) Hyperlane message with provided fields
     * @dev This function should only be used in memory message construction.
     * @param _version The version of the origin and destination Mailboxes
     * @param _nonce A nonce to uniquely identify the message on its origin chain
     * @param _originDomain Domain of origin chain
     * @param _sender Address of sender as bytes32
     * @param _destinationDomain Domain of destination chain
     * @param _recipient Address of recipient on destination chain as bytes32
     * @param _messageBody Raw bytes of message body
     * @return Formatted message
     */
    function formatMessage(
        uint8 _version,
        uint32 _nonce,
        uint32 _originDomain,
        bytes32 _sender,
        uint32 _destinationDomain,
        bytes32 _recipient,
        bytes calldata _messageBody
    ) internal pure returns (bytes memory) {
        return
            abi.encodePacked(
                _version,
                _nonce,
                _originDomain,
                _sender,
                _destinationDomain,
                _recipient,
                _messageBody
            );
    }

    /**
     * @notice Returns the message ID.
     * @param _message ABI encoded Hyperlane message.
     * @return ID of `_message`
     */
    function id(bytes memory _message) internal pure returns (bytes32) {
        return keccak256(_message);
    }

    /**
     * @notice Returns the message version.
     * @param _message ABI encoded Hyperlane message.
     * @return Version of `_message`
     */
    function version(bytes calldata _message) internal pure returns (uint8) {
        return uint8(bytes1(_message[VERSION_OFFSET:NONCE_OFFSET]));
    }

    /**
     * @notice Returns the message nonce.
     * @param _message ABI encoded Hyperlane message.
     * @return Nonce of `_message`
     */
    function nonce(bytes calldata _message) internal pure returns (uint32) {
        return uint32(bytes4(_message[NONCE_OFFSET:ORIGIN_OFFSET]));
    }

    /**
     * @notice Returns the message origin domain.
     * @param _message ABI encoded Hyperlane message.
     * @return Origin domain of `_message`
     */
    function origin(bytes calldata _message) internal pure returns (uint32) {
        return uint32(bytes4(_message[ORIGIN_OFFSET:SENDER_OFFSET]));
    }

    /**
     * @notice Returns the message sender as bytes32.
     * @param _message ABI encoded Hyperlane message.
     * @return Sender of `_message` as bytes32
     */
    function sender(bytes calldata _message) internal pure returns (bytes32) {
        return bytes32(_message[SENDER_OFFSET:DESTINATION_OFFSET]);
    }

    /**
     * @notice Returns the message sender as address.
     * @param _message ABI encoded Hyperlane message.
     * @return Sender of `_message` as address
     */
    function senderAddress(
        bytes calldata _message
    ) internal pure returns (address) {
        return sender(_message).bytes32ToAddress();
    }

    /**
     * @notice Returns the message destination domain.
     * @param _message ABI encoded Hyperlane message.
     * @return Destination domain of `_message`
     */
    function destination(
        bytes calldata _message
    ) internal pure returns (uint32) {
        return uint32(bytes4(_message[DESTINATION_OFFSET:RECIPIENT_OFFSET]));
    }

    /**
     * @notice Returns the message recipient as bytes32.
     * @param _message ABI encoded Hyperlane message.
     * @return Recipient of `_message` as bytes32
     */
    function recipient(
        bytes calldata _message
    ) internal pure returns (bytes32) {
        return bytes32(_message[RECIPIENT_OFFSET:BODY_OFFSET]);
    }

    /**
     * @notice Returns the message recipient as address.
     * @param _message ABI encoded Hyperlane message.
     * @return Recipient of `_message` as address
     */
    function recipientAddress(
        bytes calldata _message
    ) internal pure returns (address) {
        return recipient(_message).bytes32ToAddress();
    }

    /**
     * @notice Returns the message body.
     * @param _message ABI encoded Hyperlane message.
     * @return Body of `_message`
     */
    function body(
        bytes calldata _message
    ) internal pure returns (bytes calldata) {
        return bytes(_message[BODY_OFFSET:]);
    }
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

/**
 * @title PackageVersioned
 * @notice Package version getter for contracts
 **/
abstract contract PackageVersioned {
    // GENERATED CODE - DO NOT EDIT
    string public constant PACKAGE_VERSION = "5.11.3";
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (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. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

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

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

interface IMessageRecipient {
    function handle(
        uint32 _origin,
        bytes32 _sender,
        bytes calldata _message
    ) external payable;
}

// SPDX-License-Identifier: MIT OR Apache-2.0
pragma solidity >=0.6.11;

// ============ External Imports ============
import "@openzeppelin/contracts/utils/structs/EnumerableMap.sol";
import "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";

// extends EnumerableMap with uint256 => bytes32 type
// modelled after https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.0/contracts/utils/structs/EnumerableMap.sol
library EnumerableMapExtended {
    using EnumerableMap for EnumerableMap.Bytes32ToBytes32Map;
    using EnumerableSet for EnumerableSet.Bytes32Set;

    struct UintToBytes32Map {
        EnumerableMap.Bytes32ToBytes32Map _inner;
    }

    // ============ Library Functions ============
    function keys(
        UintToBytes32Map storage map
    ) internal view returns (uint256[] memory _keys) {
        uint256 _length = map._inner.length();
        _keys = new uint256[](_length);
        for (uint256 i = 0; i < _length; i++) {
            _keys[i] = uint256(map._inner._keys.at(i));
        }
    }

    function uint32Keys(
        UintToBytes32Map storage map
    ) internal view returns (uint32[] memory _keys) {
        uint256[] memory uint256keys = keys(map);
        _keys = new uint32[](uint256keys.length);
        for (uint256 i = 0; i < uint256keys.length; i++) {
            _keys[i] = uint32(uint256keys[i]);
        }
    }

    function set(
        UintToBytes32Map storage map,
        uint256 key,
        bytes32 value
    ) internal {
        map._inner.set(bytes32(key), value);
    }

    function get(
        UintToBytes32Map storage map,
        uint256 key
    ) internal view returns (bytes32) {
        return map._inner.get(bytes32(key));
    }

    function tryGet(
        UintToBytes32Map storage map,
        uint256 key
    ) internal view returns (bool, bytes32) {
        return map._inner.tryGet(bytes32(key));
    }

    function remove(
        UintToBytes32Map storage map,
        uint256 key
    ) internal returns (bool) {
        return map._inner.remove(bytes32(key));
    }

    function contains(
        UintToBytes32Map storage map,
        uint256 key
    ) internal view returns (bool) {
        return map._inner.contains(bytes32(key));
    }

    function length(
        UintToBytes32Map storage map
    ) internal view returns (uint256) {
        return map._inner.length();
    }

    function at(
        UintToBytes32Map storage map,
        uint256 index
    ) internal view returns (uint256, bytes32) {
        (bytes32 key, bytes32 value) = map._inner.at(index);
        return (uint256(key), value);
    }
}

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

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

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

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

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

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

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

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

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

// 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;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (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]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

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

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized != type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/structs/EnumerableMap.sol)
// This file was procedurally generated from scripts/generate/templates/EnumerableMap.js.

pragma solidity ^0.8.0;

import "./EnumerableSet.sol";

/**
 * @dev Library for managing an enumerable variant of Solidity's
 * https://solidity.readthedocs.io/en/latest/types.html#mapping-types[`mapping`]
 * type.
 *
 * Maps have the following properties:
 *
 * - Entries are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Entries are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using EnumerableMap for EnumerableMap.UintToAddressMap;
 *
 *     // Declare a set state variable
 *     EnumerableMap.UintToAddressMap private myMap;
 * }
 * ```
 *
 * The following map types are supported:
 *
 * - `uint256 -> address` (`UintToAddressMap`) since v3.0.0
 * - `address -> uint256` (`AddressToUintMap`) since v4.6.0
 * - `bytes32 -> bytes32` (`Bytes32ToBytes32Map`) since v4.6.0
 * - `uint256 -> uint256` (`UintToUintMap`) since v4.7.0
 * - `bytes32 -> uint256` (`Bytes32ToUintMap`) since v4.7.0
 *
 * [WARNING]
 * ====
 * Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
 * unusable.
 * See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 * In order to clean an EnumerableMap, you can either remove all elements one by one or create a fresh instance using an
 * array of EnumerableMap.
 * ====
 */
library EnumerableMap {
    using EnumerableSet for EnumerableSet.Bytes32Set;

    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Map type with
    // bytes32 keys and values.
    // The Map implementation uses private functions, and user-facing
    // implementations (such as Uint256ToAddressMap) are just wrappers around
    // the underlying Map.
    // This means that we can only create new EnumerableMaps for types that fit
    // in bytes32.

    struct Bytes32ToBytes32Map {
        // Storage of keys
        EnumerableSet.Bytes32Set _keys;
        mapping(bytes32 => bytes32) _values;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(Bytes32ToBytes32Map storage map, bytes32 key, bytes32 value) internal returns (bool) {
        map._values[key] = value;
        return map._keys.add(key);
    }

    /**
     * @dev Removes a key-value pair from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(Bytes32ToBytes32Map storage map, bytes32 key) internal returns (bool) {
        delete map._values[key];
        return map._keys.remove(key);
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(Bytes32ToBytes32Map storage map, bytes32 key) internal view returns (bool) {
        return map._keys.contains(key);
    }

    /**
     * @dev Returns the number of key-value pairs in the map. O(1).
     */
    function length(Bytes32ToBytes32Map storage map) internal view returns (uint256) {
        return map._keys.length();
    }

    /**
     * @dev Returns the key-value pair stored at position `index` in the map. O(1).
     *
     * Note that there are no guarantees on the ordering of entries inside the
     * array, and it may change when more entries are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32ToBytes32Map storage map, uint256 index) internal view returns (bytes32, bytes32) {
        bytes32 key = map._keys.at(index);
        return (key, map._values[key]);
    }

    /**
     * @dev Tries to returns the value associated with `key`. O(1).
     * Does not revert if `key` is not in the map.
     */
    function tryGet(Bytes32ToBytes32Map storage map, bytes32 key) internal view returns (bool, bytes32) {
        bytes32 value = map._values[key];
        if (value == bytes32(0)) {
            return (contains(map, key), bytes32(0));
        } else {
            return (true, value);
        }
    }

    /**
     * @dev Returns the value associated with `key`. O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(Bytes32ToBytes32Map storage map, bytes32 key) internal view returns (bytes32) {
        bytes32 value = map._values[key];
        require(value != 0 || contains(map, key), "EnumerableMap: nonexistent key");
        return value;
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(
        Bytes32ToBytes32Map storage map,
        bytes32 key,
        string memory errorMessage
    ) internal view returns (bytes32) {
        bytes32 value = map._values[key];
        require(value != 0 || contains(map, key), errorMessage);
        return value;
    }

    /**
     * @dev Return the an array containing all the keys
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the map grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function keys(Bytes32ToBytes32Map storage map) internal view returns (bytes32[] memory) {
        return map._keys.values();
    }

    // UintToUintMap

    struct UintToUintMap {
        Bytes32ToBytes32Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(UintToUintMap storage map, uint256 key, uint256 value) internal returns (bool) {
        return set(map._inner, bytes32(key), bytes32(value));
    }

    /**
     * @dev Removes a value from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(UintToUintMap storage map, uint256 key) internal returns (bool) {
        return remove(map._inner, bytes32(key));
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(UintToUintMap storage map, uint256 key) internal view returns (bool) {
        return contains(map._inner, bytes32(key));
    }

    /**
     * @dev Returns the number of elements in the map. O(1).
     */
    function length(UintToUintMap storage map) internal view returns (uint256) {
        return length(map._inner);
    }

    /**
     * @dev Returns the element stored at position `index` in the map. O(1).
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintToUintMap storage map, uint256 index) internal view returns (uint256, uint256) {
        (bytes32 key, bytes32 value) = at(map._inner, index);
        return (uint256(key), uint256(value));
    }

    /**
     * @dev Tries to returns the value associated with `key`. O(1).
     * Does not revert if `key` is not in the map.
     */
    function tryGet(UintToUintMap storage map, uint256 key) internal view returns (bool, uint256) {
        (bool success, bytes32 value) = tryGet(map._inner, bytes32(key));
        return (success, uint256(value));
    }

    /**
     * @dev Returns the value associated with `key`. O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(UintToUintMap storage map, uint256 key) internal view returns (uint256) {
        return uint256(get(map._inner, bytes32(key)));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(UintToUintMap storage map, uint256 key, string memory errorMessage) internal view returns (uint256) {
        return uint256(get(map._inner, bytes32(key), errorMessage));
    }

    /**
     * @dev Return the an array containing all the keys
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the map grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function keys(UintToUintMap storage map) internal view returns (uint256[] memory) {
        bytes32[] memory store = keys(map._inner);
        uint256[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // UintToAddressMap

    struct UintToAddressMap {
        Bytes32ToBytes32Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(UintToAddressMap storage map, uint256 key, address value) internal returns (bool) {
        return set(map._inner, bytes32(key), bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(UintToAddressMap storage map, uint256 key) internal returns (bool) {
        return remove(map._inner, bytes32(key));
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(UintToAddressMap storage map, uint256 key) internal view returns (bool) {
        return contains(map._inner, bytes32(key));
    }

    /**
     * @dev Returns the number of elements in the map. O(1).
     */
    function length(UintToAddressMap storage map) internal view returns (uint256) {
        return length(map._inner);
    }

    /**
     * @dev Returns the element stored at position `index` in the map. O(1).
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintToAddressMap storage map, uint256 index) internal view returns (uint256, address) {
        (bytes32 key, bytes32 value) = at(map._inner, index);
        return (uint256(key), address(uint160(uint256(value))));
    }

    /**
     * @dev Tries to returns the value associated with `key`. O(1).
     * Does not revert if `key` is not in the map.
     */
    function tryGet(UintToAddressMap storage map, uint256 key) internal view returns (bool, address) {
        (bool success, bytes32 value) = tryGet(map._inner, bytes32(key));
        return (success, address(uint160(uint256(value))));
    }

    /**
     * @dev Returns the value associated with `key`. O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(UintToAddressMap storage map, uint256 key) internal view returns (address) {
        return address(uint160(uint256(get(map._inner, bytes32(key)))));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(
        UintToAddressMap storage map,
        uint256 key,
        string memory errorMessage
    ) internal view returns (address) {
        return address(uint160(uint256(get(map._inner, bytes32(key), errorMessage))));
    }

    /**
     * @dev Return the an array containing all the keys
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the map grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function keys(UintToAddressMap storage map) internal view returns (uint256[] memory) {
        bytes32[] memory store = keys(map._inner);
        uint256[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // AddressToUintMap

    struct AddressToUintMap {
        Bytes32ToBytes32Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(AddressToUintMap storage map, address key, uint256 value) internal returns (bool) {
        return set(map._inner, bytes32(uint256(uint160(key))), bytes32(value));
    }

    /**
     * @dev Removes a value from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(AddressToUintMap storage map, address key) internal returns (bool) {
        return remove(map._inner, bytes32(uint256(uint160(key))));
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(AddressToUintMap storage map, address key) internal view returns (bool) {
        return contains(map._inner, bytes32(uint256(uint160(key))));
    }

    /**
     * @dev Returns the number of elements in the map. O(1).
     */
    function length(AddressToUintMap storage map) internal view returns (uint256) {
        return length(map._inner);
    }

    /**
     * @dev Returns the element stored at position `index` in the map. O(1).
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressToUintMap storage map, uint256 index) internal view returns (address, uint256) {
        (bytes32 key, bytes32 value) = at(map._inner, index);
        return (address(uint160(uint256(key))), uint256(value));
    }

    /**
     * @dev Tries to returns the value associated with `key`. O(1).
     * Does not revert if `key` is not in the map.
     */
    function tryGet(AddressToUintMap storage map, address key) internal view returns (bool, uint256) {
        (bool success, bytes32 value) = tryGet(map._inner, bytes32(uint256(uint160(key))));
        return (success, uint256(value));
    }

    /**
     * @dev Returns the value associated with `key`. O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(AddressToUintMap storage map, address key) internal view returns (uint256) {
        return uint256(get(map._inner, bytes32(uint256(uint160(key)))));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(
        AddressToUintMap storage map,
        address key,
        string memory errorMessage
    ) internal view returns (uint256) {
        return uint256(get(map._inner, bytes32(uint256(uint160(key))), errorMessage));
    }

    /**
     * @dev Return the an array containing all the keys
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the map grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function keys(AddressToUintMap storage map) internal view returns (address[] memory) {
        bytes32[] memory store = keys(map._inner);
        address[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // Bytes32ToUintMap

    struct Bytes32ToUintMap {
        Bytes32ToBytes32Map _inner;
    }

    /**
     * @dev Adds a key-value pair to a map, or updates the value for an existing
     * key. O(1).
     *
     * Returns true if the key was added to the map, that is if it was not
     * already present.
     */
    function set(Bytes32ToUintMap storage map, bytes32 key, uint256 value) internal returns (bool) {
        return set(map._inner, key, bytes32(value));
    }

    /**
     * @dev Removes a value from a map. O(1).
     *
     * Returns true if the key was removed from the map, that is if it was present.
     */
    function remove(Bytes32ToUintMap storage map, bytes32 key) internal returns (bool) {
        return remove(map._inner, key);
    }

    /**
     * @dev Returns true if the key is in the map. O(1).
     */
    function contains(Bytes32ToUintMap storage map, bytes32 key) internal view returns (bool) {
        return contains(map._inner, key);
    }

    /**
     * @dev Returns the number of elements in the map. O(1).
     */
    function length(Bytes32ToUintMap storage map) internal view returns (uint256) {
        return length(map._inner);
    }

    /**
     * @dev Returns the element stored at position `index` in the map. O(1).
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32ToUintMap storage map, uint256 index) internal view returns (bytes32, uint256) {
        (bytes32 key, bytes32 value) = at(map._inner, index);
        return (key, uint256(value));
    }

    /**
     * @dev Tries to returns the value associated with `key`. O(1).
     * Does not revert if `key` is not in the map.
     */
    function tryGet(Bytes32ToUintMap storage map, bytes32 key) internal view returns (bool, uint256) {
        (bool success, bytes32 value) = tryGet(map._inner, key);
        return (success, uint256(value));
    }

    /**
     * @dev Returns the value associated with `key`. O(1).
     *
     * Requirements:
     *
     * - `key` must be in the map.
     */
    function get(Bytes32ToUintMap storage map, bytes32 key) internal view returns (uint256) {
        return uint256(get(map._inner, key));
    }

    /**
     * @dev Same as {get}, with a custom error message when `key` is not in the map.
     *
     * CAUTION: This function is deprecated because it requires allocating memory for the error
     * message unnecessarily. For custom revert reasons use {tryGet}.
     */
    function get(
        Bytes32ToUintMap storage map,
        bytes32 key,
        string memory errorMessage
    ) internal view returns (uint256) {
        return uint256(get(map._inner, key, errorMessage));
    }

    /**
     * @dev Return the an array containing all the keys
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the map grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function keys(Bytes32ToUintMap storage map) internal view returns (bytes32[] memory) {
        bytes32[] memory store = keys(map._inner);
        bytes32[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/structs/EnumerableSet.sol)
// This file was procedurally generated from scripts/generate/templates/EnumerableSet.js.

pragma solidity ^0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```solidity
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 *
 * [WARNING]
 * ====
 * Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
 * unusable.
 * See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 * In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an
 * array of EnumerableSet.
 * ====
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            if (lastIndex != toDeleteIndex) {
                bytes32 lastValue = set._values[lastIndex];

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastValue;
                // Update the index for the moved value
                set._indexes[lastValue] = valueIndex; // Replace lastValue's index to valueIndex
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        bytes32[] memory store = _values(set._inner);
        bytes32[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

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

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

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

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

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

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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