Contract Address Details

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "../based/TaikoL2.sol";

/// @title HeklaTaikoL2
/// @custom:security-contact security@taiko.xyz
contract HeklaTaikoL2 is TaikoL2 {
    function ontakeForkHeight() public pure override returns (uint64) {
        return 840_512;
    }
}
        

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

library LibSharedData {
    /// @dev Struct that represents L2 basefee configurations
    struct BaseFeeConfig {
        uint8 adjustmentQuotient;
        uint8 sharingPctg;
        uint32 gasIssuancePerSecond;
        uint64 minGasExcess;
        uint32 maxGasIssuancePerBlock;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title ISignalService
/// @notice The SignalService contract serves as a secure cross-chain message
/// passing system. It defines methods for sending and verifying signals with
/// merkle proofs. The trust assumption is that the target chain has secure
/// access to the merkle root (such as Taiko injects it in the anchor
/// transaction). With this, verifying a signal is reduced to simply verifying
/// a merkle proof.
/// @custom:security-contact security@taiko.xyz
interface ISignalService {
    enum CacheOption {
        CACHE_NOTHING,
        CACHE_SIGNAL_ROOT,
        CACHE_STATE_ROOT,
        CACHE_BOTH
    }

    struct HopProof {
        /// @notice This hop's destination chain ID. If there is a next hop, this ID is the next
        /// hop's source chain ID.
        uint64 chainId;
        /// @notice The ID of a source chain block whose state root has been synced to the hop's
        /// destination chain.
        /// Note that this block ID must be greater than or equal to the block ID where the signal
        /// was sent on the source chain.
        uint64 blockId;
        /// @notice The state root or signal root of the source chain at the above blockId. This
        /// value has been synced to the destination chain.
        /// @dev To get both the blockId and the rootHash, apps should subscribe to the
        /// ChainDataSynced event or query `topBlockId` first using the source chain's ID and
        /// LibStrings.H_STATE_ROOT to get the most recent block ID synced, then call
        /// `getSyncedChainData` to read the synchronized data.
        bytes32 rootHash;
        /// @notice Options to cache either the state roots or signal roots of middle-hops to the
        /// current chain.
        CacheOption cacheOption;
        /// @notice The signal service's account proof. If this value is empty, then `rootHash` will
        /// be used as the signal root, otherwise, `rootHash` will be used as the state root.
        bytes[] accountProof;
        /// @notice The signal service's storage proof.
        bytes[] storageProof;
    }

    /// @notice Emitted when a remote chain's state root or signal root is
    /// synced locally as a signal.
    /// @param chainId The remote chainId.
    /// @param blockId The chain data's corresponding blockId.
    /// @param kind A value to mark the data type.
    /// @param data The remote data.
    /// @param signal The signal for this chain data.
    event ChainDataSynced(
        uint64 indexed chainId,
        uint64 indexed blockId,
        bytes32 indexed kind,
        bytes32 data,
        bytes32 signal
    );

    /// @notice Emitted when a signal is sent.
    /// @param app The address that initiated the signal.
    /// @param signal The signal (message) that was sent.
    /// @param slot The location in storage where this signal is stored.
    /// @param value The value of the signal.
    event SignalSent(address app, bytes32 signal, bytes32 slot, bytes32 value);

    /// @notice Emitted when an address is authorized or deauthorized.
    /// @param addr The address to be authorized or deauthorized.
    /// @param authorized True if authorized, false otherwise.
    event Authorized(address indexed addr, bool authorized);

    /// @notice Send a signal (message) by setting the storage slot to the same value as the signal
    /// itself.
    /// @param _signal The signal (message) to send.
    /// @return slot_ The location in storage where this signal is stored.
    function sendSignal(bytes32 _signal) external returns (bytes32 slot_);

    /// @notice Sync a data from a remote chain locally as a signal. The signal is calculated
    /// uniquely from chainId, kind, and data.
    /// @param _chainId The remote chainId.
    /// @param _kind A value to mark the data type.
    /// @param _blockId The chain data's corresponding blockId
    /// @param _chainData The remote data.
    /// @return signal_ The signal for this chain data.
    function syncChainData(
        uint64 _chainId,
        bytes32 _kind,
        uint64 _blockId,
        bytes32 _chainData
    )
        external
        returns (bytes32 signal_);

    /// @notice Verifies if a signal has been received on the target chain.
    /// @param _chainId The identifier for the source chain from which the
    /// signal originated.
    /// @param _app The address that initiated the signal.
    /// @param _signal The signal (message) to send.
    /// @param _proof Merkle proof that the signal was persisted on the
    /// source chain.
    /// @return numCacheOps_ The number of newly cached items.
    function proveSignalReceived(
        uint64 _chainId,
        address _app,
        bytes32 _signal,
        bytes calldata _proof
    )
        external
        returns (uint256 numCacheOps_);

    /// @notice Verifies if a signal has been received on the target chain.
    /// This is the "readonly" version of proveSignalReceived.
    /// @param _chainId The identifier for the source chain from which the
    /// signal originated.
    /// @param _app The address that initiated the signal.
    /// @param _signal The signal (message) to send.
    /// @param _proof Merkle proof that the signal was persisted on the
    /// source chain.
    function verifySignalReceived(
        uint64 _chainId,
        address _app,
        bytes32 _signal,
        bytes calldata _proof
    )
        external
        view;

    /// @notice Verifies if a particular signal has already been sent.
    /// @param _app The address that initiated the signal.
    /// @param _signal The signal (message) that was sent.
    /// @return true if the signal has been sent, otherwise false.
    function isSignalSent(address _app, bytes32 _signal) external view returns (bool);

    /// @notice Checks if a chain data has been synced.
    /// @param _chainId The remote chainId.
    /// @param _kind A value to mark the data type.
    /// @param _blockId The chain data's corresponding blockId
    /// @param _chainData The remote data.
    /// @return true if the data has been synced, otherwise false.
    function isChainDataSynced(
        uint64 _chainId,
        bytes32 _kind,
        uint64 _blockId,
        bytes32 _chainData
    )
        external
        view
        returns (bool);

    /// @notice Returns the given block's  chain data.
    /// @param _chainId Identifier of the chainId.
    /// @param _kind A value to mark the data type.
    /// @param _blockId The chain data's corresponding block id. If this value is 0, use the top
    /// block id.
    /// @return blockId_ The actual block id.
    /// @return chainData_ The synced chain data.
    function getSyncedChainData(
        uint64 _chainId,
        bytes32 _kind,
        uint64 _blockId
    )
        external
        view
        returns (uint64 blockId_, bytes32 chainData_);

    /// @notice Returns the data to be used for caching slot generation.
    /// @param _chainId Identifier of the chainId.
    /// @param _kind A value to mark the data type.
    /// @param _blockId The chain data's corresponding block id. If this value is 0, use the top
    /// block id.
    /// @return signal_ The signal used for caching slot creation.
    function signalForChainData(
        uint64 _chainId,
        bytes32 _kind,
        uint64 _blockId
    )
        external
        pure
        returns (bytes32 signal_);
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title IBlockHash
/// @notice Interface for retrieving block hashes.
interface IBlockHash {
    /// @notice Retrieves the block hash for a given block ID.
    /// @param _blockId The ID of the block whose hash is being requested.
    /// @return The block hash of the specified block ID, or 0 if no hash is found.
    function getBlockHash(uint256 _blockId) external view returns (bytes32);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.0;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {BeaconProxy} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}
          

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

pragma solidity ^0.8.0;

import "../../interfaces/draft-IERC1822.sol";
import "../ERC1967/ERC1967Upgrade.sol";

/**
 * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
 * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
 *
 * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
 * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
 * `UUPSUpgradeable` with a custom implementation of upgrades.
 *
 * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
 *
 * _Available since v4.1._
 */
abstract contract UUPSUpgradeable is IERC1822Proxiable, ERC1967Upgrade {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
    address private immutable __self = address(this);

    /**
     * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
     * a proxy contract with an implementation (as defined in ERC1967) pointing to self. This should only be the case
     * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
     * function through ERC1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
     * fail.
     */
    modifier onlyProxy() {
        require(address(this) != __self, "Function must be called through delegatecall");
        require(_getImplementation() == __self, "Function must be called through active proxy");
        _;
    }

    /**
     * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
     * callable on the implementing contract but not through proxies.
     */
    modifier notDelegated() {
        require(address(this) == __self, "UUPSUpgradeable: must not be called through delegatecall");
        _;
    }

    /**
     * @dev Implementation of the ERC1822 {proxiableUUID} function. This returns the storage slot used by the
     * implementation. It is used to validate the implementation's compatibility when performing an upgrade.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
     */
    function proxiableUUID() external view virtual override notDelegated returns (bytes32) {
        return _IMPLEMENTATION_SLOT;
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeTo(address newImplementation) public virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, new bytes(0), false);
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
     * encoded in `data`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) public payable virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, data, true);
    }

    /**
     * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
     * {upgradeTo} and {upgradeToAndCall}.
     *
     * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
     *
     * ```solidity
     * function _authorizeUpgrade(address) internal override onlyOwner {}
     * ```
     */
    function _authorizeUpgrade(address newImplementation) internal virtual;
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts-upgradeable/proxy/utils/Initializable.sol";
import "./IAddressManager.sol";
import "./IAddressResolver.sol";

/// @title AddressResolver
/// @notice See the documentation in {IAddressResolver}.
/// @custom:security-contact security@taiko.xyz
abstract contract AddressResolver is IAddressResolver, Initializable {
    /// @notice Address of the AddressManager.
    address public addressManager;
    uint256[49] private __gap;

    error RESOLVER_DENIED();
    error RESOLVER_INVALID_MANAGER();
    error RESOLVER_UNEXPECTED_CHAINID();
    error RESOLVER_ZERO_ADDR(uint64 chainId, bytes32 name);

    /// @dev Modifier that ensures the caller is the resolved address of a given
    /// name.
    /// @param _name The name to check against.
    modifier onlyFromNamed(bytes32 _name) {
        if (msg.sender != resolve(_name, true)) revert RESOLVER_DENIED();
        _;
    }

    /// @dev Modifier that ensures the caller is the resolved address of a given
    /// name, if the name is set.
    /// @param _name The name to check against.
    modifier onlyFromOptionalNamed(bytes32 _name) {
        address addr = resolve(_name, true);
        if (addr != address(0) && msg.sender != addr) revert RESOLVER_DENIED();
        _;
    }

    /// @dev Modifier that ensures the caller is a resolved address to either _name1 or _name2
    /// name.
    /// @param _name1 The first name to check against.
    /// @param _name2 The second name to check against.
    modifier onlyFromNamedEither(bytes32 _name1, bytes32 _name2) {
        if (msg.sender != resolve(_name1, true) && msg.sender != resolve(_name2, true)) {
            revert RESOLVER_DENIED();
        }
        _;
    }

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

    /// @inheritdoc IAddressResolver
    function resolve(bytes32 _name, bool _allowZeroAddress) public view virtual returns (address) {
        return _resolve(uint64(block.chainid), _name, _allowZeroAddress);
    }

    /// @inheritdoc IAddressResolver
    function resolve(
        uint64 _chainId,
        bytes32 _name,
        bool _allowZeroAddress
    )
        public
        view
        virtual
        returns (address)
    {
        return _resolve(_chainId, _name, _allowZeroAddress);
    }

    /// @dev Initialization method for setting up AddressManager reference.
    /// @param _addressManager Address of the AddressManager.
    function __AddressResolver_init(address _addressManager) internal virtual onlyInitializing {
        if (block.chainid > type(uint64).max) {
            revert RESOLVER_UNEXPECTED_CHAINID();
        }
        addressManager = _addressManager;
    }

    /// @dev Helper method to resolve name-to-address.
    /// @param _chainId The chainId of interest.
    /// @param _name Name whose address is to be resolved.
    /// @param _allowZeroAddress If set to true, does not throw if the resolved
    /// address is `address(0)`.
    /// @return addr_ Address associated with the given name on the specified
    /// chain.
    function _resolve(
        uint64 _chainId,
        bytes32 _name,
        bool _allowZeroAddress
    )
        internal
        view
        returns (address addr_)
    {
        addr_ = _getAddress(_chainId, _name);

        if (!_allowZeroAddress && addr_ == address(0)) {
            revert RESOLVER_ZERO_ADDR(_chainId, _name);
        }
    }

    function _getAddress(uint64 _chainId, bytes32 _name) internal view virtual returns (address) {
        address _addressManager = addressManager;
        if (_addressManager == address(0)) revert RESOLVER_INVALID_MANAGER();

        return IAddressManager(_addressManager).getAddress(_chainId, _name);
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@solady/src/utils/FixedPointMathLib.sol";
import "../../shared/common/LibMath.sol";

/// @title Lib1559Math
/// @notice Implements e^(x) based bonding curve for EIP-1559
/// @dev See https://ethresear.ch/t/make-eip-1559-more-like-an-amm-curve/9082 but some minor
/// difference as stated in docs/eip1559_on_l2.md.
/// @custom:security-contact security@taiko.xyz
library Lib1559Math {
    using LibMath for uint256;

    uint128 public constant MAX_EXP_INPUT = 135_305_999_368_893_231_588;

    error EIP1559_INVALID_PARAMS();

    function calc1559BaseFee(
        uint256 _gasTarget,
        uint64 _gasExcess,
        uint64 _gasIssuance,
        uint32 _parentGasUsed,
        uint64 _minGasExcess
    )
        internal
        pure
        returns (uint256 basefee_, uint64 gasExcess_)
    {
        // We always add the gas used by parent block to the gas excess
        // value as this has already happened
        uint256 excess = uint256(_gasExcess) + _parentGasUsed;
        excess = excess > _gasIssuance ? excess - _gasIssuance : 1;
        gasExcess_ = uint64(excess.max(_minGasExcess).min(type(uint64).max));

        // The base fee per gas used by this block is the spot price at the
        // bonding curve, regardless the actual amount of gas used by this
        // block, however, this block's gas used will affect the next
        // block's base fee.
        basefee_ = basefee(gasExcess_, _gasTarget);
    }

    /// @dev Returns the new gas excess that will keep the basefee the same.
    /// `_newGasTarget * ln(_newGasTarget / _target) + _gasExcess * _newGasTarget / _target`
    function adjustExcess(
        uint64 _gasExcess,
        uint64 _gasTarget,
        uint64 _newGasTarget
    )
        internal
        pure
        returns (uint64)
    {
        if (_gasTarget == 0) {
            return _newGasTarget;
        }

        uint256 f = FixedPointMathLib.WAD;
        uint256 ratio = f * _newGasTarget / _gasTarget;
        if (ratio > uint256(type(int256).max)) revert EIP1559_INVALID_PARAMS();

        int256 lnRatio = FixedPointMathLib.lnWad(int256(ratio)); // may be negative

        uint256 newGasExcess;

        assembly {
            // compute x = (_newGasTarget * lnRatio + _gasExcess * ratio)
            let x := add(mul(_newGasTarget, lnRatio), mul(_gasExcess, ratio))

            // If x < 0, set newGasExcess to 0, otherwise calculate newGasExcess = x / f
            switch slt(x, 0)
            case 1 { newGasExcess := 0 }
            default { newGasExcess := div(x, f) }
        }

        return uint64(newGasExcess.min(type(uint64).max));
    }

    /// @dev exp(_gasExcess / _gasTarget) / _gasTarget
    function basefee(uint256 _gasExcess, uint256 _gasTarget) internal pure returns (uint256) {
        uint256 fee = ethQty(_gasExcess, _gasTarget) / _gasTarget;
        return fee == 0 ? 1 : fee;
    }

    /// @dev exp(_gasExcess / _gasTarget)
    function ethQty(uint256 _gasExcess, uint256 _gasTarget) internal pure returns (uint256) {
        if (_gasTarget == 0) revert EIP1559_INVALID_PARAMS();

        uint256 input = FixedPointMathLib.WAD * _gasExcess / _gasTarget;
        if (input > MAX_EXP_INPUT) {
            input = MAX_EXP_INPUT;
        }
        return uint256(FixedPointMathLib.expWad(int256(input))) / FixedPointMathLib.WAD;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title LibL2Config
library LibL2Config {
    struct Config {
        uint32 gasTargetPerL1Block;
        uint8 basefeeAdjustmentQuotient;
    }

    /// @notice Returns EIP1559 related configurations.
    /// @return config_ struct containing configuration parameters.
    function get() internal pure returns (Config memory config_) {
        // Assuming we sell 3x more blockspace than Ethereum: 15_000_000 * 4
        // Note that Brecht's concern is that this value may be too large.
        // We need to monitor L2 state growth and lower this value when necessary.
        config_.gasTargetPerL1Block = 60_000_000;
        config_.basefeeAdjustmentQuotient = 8;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "../../shared/data/LibSharedData.sol";
import "../../shared/common/EssentialContract.sol";
import "../../shared/common/LibStrings.sol";
import "../../shared/common/LibAddress.sol";
import "../../shared/signal/ISignalService.sol";
import "./Lib1559Math.sol";
import "./LibL2Config.sol";
import "./IBlockHash.sol";

/// @title TaikoL2
/// @notice Taiko L2 is a smart contract that handles cross-layer message
/// verification and manages EIP-1559 gas pricing for Layer 2 (L2) operations.
/// It is used to anchor the latest L1 block details to L2 for cross-layer
/// communication, manage EIP-1559 parameters for gas pricing, and store
/// verified L1 block information.
/// @custom:security-contact security@taiko.xyz
contract TaikoL2 is EssentialContract, IBlockHash {
    using LibAddress for address;
    using SafeERC20 for IERC20;

    /// @notice Golden touch address is the only address that can do the anchor transaction.
    address public constant GOLDEN_TOUCH_ADDRESS = 0x0000777735367b36bC9B61C50022d9D0700dB4Ec;

    /// @notice Mapping from L2 block numbers to their block hashes. All L2 block hashes will
    /// be saved in this mapping.
    mapping(uint256 blockId => bytes32 blockHash) private _blockhashes;

    /// @notice A hash to check the integrity of public inputs.
    /// @dev Slot 2.
    bytes32 public publicInputHash;

    /// @notice The gas excess value used to calculate the base fee.
    /// @dev Slot 3.
    uint64 public parentGasExcess;

    /// @notice The last synced L1 block height.
    uint64 public lastSyncedBlock;
    uint64 public parentTimestamp;
    uint64 public parentGasTarget;

    /// @notice The L1's chain ID.
    uint64 public l1ChainId;

    uint256[46] private __gap;

    /// @notice Emitted when the latest L1 block details are anchored to L2.
    /// @param parentHash The hash of the parent block.
    /// @param parentGasExcess The gas excess value used to calculate the base fee.
    event Anchored(bytes32 parentHash, uint64 parentGasExcess);

    error L2_BASEFEE_MISMATCH();
    error L2_FORK_ERROR();
    error L2_INVALID_L1_CHAIN_ID();
    error L2_INVALID_L2_CHAIN_ID();
    error L2_INVALID_PARAM();
    error L2_INVALID_SENDER();
    error L2_PUBLIC_INPUT_HASH_MISMATCH();
    error L2_TOO_LATE();

    modifier onlyGoldenTouch() {
        if (msg.sender != GOLDEN_TOUCH_ADDRESS) revert L2_INVALID_SENDER();
        _;
    }

    /// @notice Initializes the contract.
    /// @param _owner The owner of this contract. msg.sender will be used if this value is zero.
    /// @param _rollupAddressManager The address of the {AddressManager} contract.
    /// @param _l1ChainId The ID of the base layer.
    /// @param _initialGasExcess The initial parentGasExcess.
    function init(
        address _owner,
        address _rollupAddressManager,
        uint64 _l1ChainId,
        uint64 _initialGasExcess
    )
        external
        initializer
    {
        __Essential_init(_owner, _rollupAddressManager);

        if (_l1ChainId == 0 || _l1ChainId == block.chainid) {
            revert L2_INVALID_L1_CHAIN_ID();
        }
        if (block.chainid <= 1 || block.chainid > type(uint64).max) {
            revert L2_INVALID_L2_CHAIN_ID();
        }

        if (block.number == 0) {
            // This is the case in real L2 genesis
        } else if (block.number == 1) {
            // This is the case in tests
            uint256 parentHeight = block.number - 1;
            _blockhashes[parentHeight] = blockhash(parentHeight);
        } else {
            revert L2_TOO_LATE();
        }

        l1ChainId = _l1ChainId;
        parentGasExcess = _initialGasExcess;
        (publicInputHash,) = _calcPublicInputHash(block.number);
    }

    /// @notice Anchors the latest L1 block details to L2 for cross-layer
    /// message verification.
    /// @dev This function can be called freely as the golden touch private key is publicly known,
    /// but the Taiko node guarantees the first transaction of each block is always this anchor
    /// transaction, and any subsequent calls will revert with L2_PUBLIC_INPUT_HASH_MISMATCH.
    /// @param _l1StateRoot The state root for the L1 block with id equals `_anchorBlockId`
    /// @param _l1BlockId The `anchorBlockId` value in this block's metadata.
    /// @param _parentGasUsed The gas used in the parent block.
    function anchor(
        bytes32, /*_l1BlockHash*/
        bytes32 _l1StateRoot,
        uint64 _l1BlockId,
        uint32 _parentGasUsed
    )
        external
        nonZeroValue(uint256(_l1StateRoot))
        nonZeroValue(uint256(_l1BlockId))
        onlyGoldenTouch
        nonReentrant
    {
        if (block.number >= ontakeForkHeight()) revert L2_FORK_ERROR();

        // Verify ancestor hashes
        uint256 parentId = block.number - 1;
        (bytes32 currentPublicInputHash, bytes32 newPublicInputHash) =
            _calcPublicInputHash(parentId);
        if (publicInputHash != currentPublicInputHash) revert L2_PUBLIC_INPUT_HASH_MISMATCH();

        // Verify the base fee per gas is correct
        (uint256 basefee, uint64 newGasExcess) = getBasefee(_l1BlockId, _parentGasUsed);

        if (!skipFeeCheck() && block.basefee != basefee) revert L2_BASEFEE_MISMATCH();

        if (_l1BlockId > lastSyncedBlock) {
            // Store the L1's state root as a signal to the local signal service to
            // allow for multi-hop bridging.
            ISignalService(resolve(LibStrings.B_SIGNAL_SERVICE, false)).syncChainData(
                l1ChainId, LibStrings.H_STATE_ROOT, _l1BlockId, _l1StateRoot
            );

            lastSyncedBlock = _l1BlockId;
        }

        // Update state variables
        bytes32 parentHash = blockhash(parentId);
        _blockhashes[parentId] = parentHash;

        publicInputHash = newPublicInputHash;
        parentGasExcess = newGasExcess;
        parentTimestamp = uint64(block.timestamp);

        emit Anchored(parentHash, newGasExcess);
    }

    function anchorV2(
        uint64 _anchorBlockId,
        bytes32 _anchorStateRoot,
        uint32 _parentGasUsed,
        LibSharedData.BaseFeeConfig calldata _baseFeeConfig
    )
        external
        nonZeroValue(uint256(_anchorStateRoot))
        nonZeroValue(uint256(_anchorBlockId))
        nonZeroValue(uint256(_baseFeeConfig.gasIssuancePerSecond))
        nonZeroValue(uint256(_baseFeeConfig.adjustmentQuotient))
        onlyGoldenTouch
        nonReentrant
    {
        if (block.number < ontakeForkHeight()) revert L2_FORK_ERROR();

        uint256 parentId = block.number - 1;

        // Verify ancestor hashes
        {
            (bytes32 currentPublicInputHash, bytes32 newPublicInputHash) =
                _calcPublicInputHash(parentId);
            if (publicInputHash != currentPublicInputHash) revert L2_PUBLIC_INPUT_HASH_MISMATCH();
            publicInputHash = newPublicInputHash;
        }

        // Check if the gas settings has changed
        {
            uint64 newGasTarget =
                uint64(_baseFeeConfig.gasIssuancePerSecond) * _baseFeeConfig.adjustmentQuotient;

            if (parentGasTarget != newGasTarget) {
                if (parentGasTarget != 0) {
                    parentGasExcess = adjustExcess(parentGasExcess, parentGasTarget, newGasTarget);
                }
                parentGasTarget = newGasTarget;
            }
        }

        // Verify the base fee per gas is correct
        {
            (uint256 basefee, uint64 newGasExcess) = calculateBaseFee(
                _baseFeeConfig,
                uint64(block.timestamp - parentTimestamp),
                parentGasExcess,
                _parentGasUsed
            );

            if (!skipFeeCheck() && block.basefee != basefee) revert L2_BASEFEE_MISMATCH();
            parentGasExcess = newGasExcess;
        }

        if (_anchorBlockId > lastSyncedBlock) {
            // Store the L1's state root as a signal to the local signal service to
            // allow for multi-hop bridging.
            ISignalService(resolve(LibStrings.B_SIGNAL_SERVICE, false)).syncChainData(
                l1ChainId, LibStrings.H_STATE_ROOT, _anchorBlockId, _anchorStateRoot
            );

            lastSyncedBlock = _anchorBlockId;
        }

        // Update state variables
        bytes32 parentHash = blockhash(parentId);
        _blockhashes[parentId] = parentHash;
        parentTimestamp = uint64(block.timestamp);

        emit Anchored(parentHash, parentGasExcess);
    }

    /// @notice Withdraw token or Ether from this address
    /// @param _token Token address or address(0) if Ether.
    /// @param _to Withdraw to address.
    function withdraw(
        address _token,
        address _to
    )
        external
        whenNotPaused
        onlyFromOwnerOrNamed(LibStrings.B_WITHDRAWER)
        nonReentrant
    {
        if (_to == address(0)) revert L2_INVALID_PARAM();
        if (_token == address(0)) {
            _to.sendEtherAndVerify(address(this).balance);
        } else {
            IERC20(_token).safeTransfer(_to, IERC20(_token).balanceOf(address(this)));
        }
    }

    /// @notice Gets the basefee and gas excess using EIP-1559 configuration for
    /// the given parameters.
    /// @dev This function will deprecate after Ontake fork, node/client shall use calculateBaseFee
    /// instead for base fee prediction.
    /// @param _anchorBlockId The synced L1 height in the next Taiko block
    /// @param _parentGasUsed Gas used in the parent block.
    /// @return basefee_ The calculated EIP-1559 base fee per gas.
    /// @return parentGasExcess_ The new parentGasExcess value.
    function getBasefee(
        uint64 _anchorBlockId,
        uint32 _parentGasUsed
    )
        public
        view
        returns (uint256 basefee_, uint64 parentGasExcess_)
    {
        LibL2Config.Config memory config = getConfig();

        (basefee_, parentGasExcess_) = Lib1559Math.calc1559BaseFee(
            uint256(config.gasTargetPerL1Block) * config.basefeeAdjustmentQuotient,
            parentGasExcess,
            uint64(_anchorBlockId - lastSyncedBlock) * config.gasTargetPerL1Block,
            _parentGasUsed,
            0
        );
    }

    /// @inheritdoc IBlockHash
    function getBlockHash(uint256 _blockId) public view returns (bytes32) {
        if (_blockId >= block.number) return 0;
        if (_blockId + 256 >= block.number) return blockhash(_blockId);
        return _blockhashes[_blockId];
    }

    /// @notice Returns EIP1559 related configurations.
    /// @return config_ struct containing configuration parameters.
    function getConfig() public view virtual returns (LibL2Config.Config memory) {
        return LibL2Config.get();
    }

    /// @notice Returns the new gas excess that will keep the basefee the same.
    /// @param _currGasExcess The current gas excess value.
    /// @param _currGasTarget The current gas target.
    /// @param _newGasTarget The new gas target.
    /// @return newGasExcess_ The new gas excess value.
    function adjustExcess(
        uint64 _currGasExcess,
        uint64 _currGasTarget,
        uint64 _newGasTarget
    )
        public
        pure
        returns (uint64 newGasExcess_)
    {
        return Lib1559Math.adjustExcess(_currGasExcess, _currGasTarget, _newGasTarget);
    }

    /// @notice Tells if we need to validate basefee (for simulation).
    /// @return Returns true to skip checking basefee mismatch.
    function skipFeeCheck() public pure virtual returns (bool) {
        return false;
    }

    function ontakeForkHeight() public pure virtual returns (uint64) {
        return 0;
    }

    /// @notice Calculates the basefee and the new gas excess value based on parent gas used and gas
    /// excess.
    /// @param _baseFeeConfig The base fee config object.
    /// @param _blocktime The time between this block and the parent block.
    /// @param _parentGasExcess The current gas excess value.
    /// @param _parentGasUsed Total gas used by the parent block.
    /// @return basefee_ Next block's base fee.
    /// @return parentGasExcess_ The new gas excess value.
    function calculateBaseFee(
        LibSharedData.BaseFeeConfig calldata _baseFeeConfig,
        uint64 _blocktime,
        uint64 _parentGasExcess,
        uint32 _parentGasUsed
    )
        public
        pure
        returns (uint256 basefee_, uint64 parentGasExcess_)
    {
        uint64 gasIssuance = _blocktime * _baseFeeConfig.gasIssuancePerSecond;
        if (
            _baseFeeConfig.maxGasIssuancePerBlock != 0
                && gasIssuance > _baseFeeConfig.maxGasIssuancePerBlock
        ) {
            gasIssuance = _baseFeeConfig.maxGasIssuancePerBlock;
        }

        uint256 gasTarget =
            uint256(_baseFeeConfig.gasIssuancePerSecond) * _baseFeeConfig.adjustmentQuotient;

        return Lib1559Math.calc1559BaseFee(
            gasTarget, _parentGasExcess, gasIssuance, _parentGasUsed, _baseFeeConfig.minGasExcess
        );
    }

    function _calcPublicInputHash(uint256 _blockId)
        private
        view
        returns (bytes32 publicInputHashOld, bytes32 publicInputHashNew)
    {
        bytes32[256] memory inputs;

        // Unchecked is safe because it cannot overflow.
        unchecked {
            // Put the previous 255 blockhashes (excluding the parent's) into a
            // ring buffer.
            for (uint256 i; i < 255 && _blockId >= i + 1; ++i) {
                uint256 j = _blockId - i - 1;
                inputs[j % 255] = blockhash(j);
            }
        }

        inputs[255] = bytes32(block.chainid);

        assembly {
            publicInputHashOld := keccak256(inputs, 8192 /*mul(256, 32)*/ )
        }

        inputs[_blockId % 255] = blockhash(_blockId);
        assembly {
            publicInputHashNew := keccak256(inputs, 8192 /*mul(256, 32)*/ )
        }
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts/proxy/utils/UUPSUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/access/Ownable2StepUpgradeable.sol";
import "./AddressResolver.sol";

/// @title EssentialContract
/// @custom:security-contact security@taiko.xyz
abstract contract EssentialContract is UUPSUpgradeable, Ownable2StepUpgradeable, AddressResolver {
    uint8 private constant _FALSE = 1;
    uint8 private constant _TRUE = 2;

    /// @dev Slot 1.
    uint8 private __reentry;
    uint8 private __paused;
    uint64 public lastUnpausedAt;

    uint256[49] private __gap;

    /// @notice Emitted when the contract is paused.
    /// @param account The account that paused the contract.
    event Paused(address account);

    /// @notice Emitted when the contract is unpaused.
    /// @param account The account that unpaused the contract.
    event Unpaused(address account);

    error INVALID_PAUSE_STATUS();
    error FUNC_NOT_IMPLEMENTED();
    error REENTRANT_CALL();
    error ZERO_ADDRESS();
    error ZERO_VALUE();

    /// @dev Modifier that ensures the caller is the owner or resolved address of a given name.
    /// @param _name The name to check against.
    modifier onlyFromOwnerOrNamed(bytes32 _name) {
        if (msg.sender != owner() && msg.sender != resolve(_name, true)) revert RESOLVER_DENIED();
        _;
    }

    modifier notImplemented() {
        revert FUNC_NOT_IMPLEMENTED();
        _;
    }

    modifier nonReentrant() {
        if (_loadReentryLock() == _TRUE) revert REENTRANT_CALL();
        _storeReentryLock(_TRUE);
        _;
        _storeReentryLock(_FALSE);
    }

    modifier whenPaused() {
        if (!paused()) revert INVALID_PAUSE_STATUS();
        _;
    }

    modifier whenNotPaused() {
        if (paused()) revert INVALID_PAUSE_STATUS();
        _;
    }

    modifier nonZeroAddr(address _addr) {
        if (_addr == address(0)) revert ZERO_ADDRESS();
        _;
    }

    modifier nonZeroValue(uint256 _value) {
        if (_value == 0) revert ZERO_VALUE();
        _;
    }

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

    /// @notice Pauses the contract.
    function pause() public virtual {
        _pause();
        // We call the authorize function here to avoid:
        // Warning (5740): Unreachable code.
        _authorizePause(msg.sender, true);
    }

    /// @notice Unpauses the contract.
    function unpause() public virtual {
        _unpause();
        // We call the authorize function here to avoid:
        // Warning (5740): Unreachable code.
        _authorizePause(msg.sender, false);
    }

    function impl() public view returns (address) {
        return _getImplementation();
    }

    /// @notice Returns true if the contract is paused, and false otherwise.
    /// @return true if paused, false otherwise.
    function paused() public view returns (bool) {
        return __paused == _TRUE;
    }

    function inNonReentrant() public view returns (bool) {
        return _loadReentryLock() == _TRUE;
    }

    /// @notice Initializes the contract.
    /// @param _owner The owner of this contract. msg.sender will be used if this value is zero.
    /// @param _addressManager The address of the {AddressManager} contract.
    function __Essential_init(
        address _owner,
        address _addressManager
    )
        internal
        nonZeroAddr(_addressManager)
    {
        __Essential_init(_owner);
        __AddressResolver_init(_addressManager);
    }

    function __Essential_init(address _owner) internal virtual onlyInitializing {
        __Context_init();
        _transferOwnership(_owner == address(0) ? msg.sender : _owner);
        __paused = _FALSE;
    }

    function _pause() internal whenNotPaused {
        __paused = _TRUE;
        emit Paused(msg.sender);
    }

    function _unpause() internal whenPaused {
        __paused = _FALSE;
        lastUnpausedAt = uint64(block.timestamp);
        emit Unpaused(msg.sender);
    }

    function _authorizeUpgrade(address) internal virtual override onlyOwner { }

    function _authorizePause(address, bool) internal virtual onlyOwner { }

    // Stores the reentry lock
    function _storeReentryLock(uint8 _reentry) internal virtual {
        __reentry = _reentry;
    }

    // Loads the reentry lock
    function _loadReentryLock() internal view virtual returns (uint8 reentry_) {
        reentry_ = __reentry;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title IAddressManager
/// @notice Manages a mapping of (chainId, name) pairs to Ethereum addresses.
/// @custom:security-contact security@taiko.xyz
interface IAddressManager {
    /// @notice Gets the address mapped to a specific chainId-name pair.
    /// @dev Note that in production, this method shall be a pure function
    /// without any storage access.
    /// @param _chainId The chainId for which the address needs to be fetched.
    /// @param _name The name for which the address needs to be fetched.
    /// @return Address associated with the chainId-name pair.
    function getAddress(uint64 _chainId, bytes32 _name) external view returns (address);
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title IAddressResolver
/// @notice This contract acts as a bridge for name-to-address resolution.
/// It delegates the resolution to the AddressManager. By separating the logic,
/// we can maintain flexibility in address management without affecting the
/// resolving process.
/// @dev Note that the address manager should be changed using upgradability, there
/// is no setAddressManager() function to guarantee atomicity across all
/// contracts that are resolvers.
/// @custom:security-contact security@taiko.xyz
interface IAddressResolver {
    /// @notice Resolves a name to its address deployed on this chain.
    /// @param _name Name whose address is to be resolved.
    /// @param _allowZeroAddress If set to true, does not throw if the resolved
    /// address is `address(0)`.
    /// @return Address associated with the given name.
    function resolve(bytes32 _name, bool _allowZeroAddress) external view returns (address);

    /// @notice Resolves a name to its address deployed on a specified chain.
    /// @param _chainId The chainId of interest.
    /// @param _name Name whose address is to be resolved.
    /// @param _allowZeroAddress If set to true, does not throw if the resolved
    /// address is `address(0)`.
    /// @return Address associated with the given name on the specified
    /// chain.
    function resolve(
        uint64 _chainId,
        bytes32 _name,
        bool _allowZeroAddress
    )
        external
        view
        returns (address);
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts/utils/Address.sol";
import "@openzeppelin/contracts/utils/introspection/IERC165.sol";
import "@openzeppelin/contracts/interfaces/IERC1271.sol";

/// @title LibAddress
/// @dev Provides utilities for address-related operations.
/// @custom:security-contact security@taiko.xyz
library LibAddress {
    error ETH_TRANSFER_FAILED();

    /// @dev Sends Ether to the specified address. This method will not revert even if sending ether
    /// fails.
    /// This function is inspired by
    /// https://github.com/nomad-xyz/ExcessivelySafeCall/blob/main/src/ExcessivelySafeCall.sol
    /// @param _to The recipient address.
    /// @param _amount The amount of Ether to send in wei.
    /// @param _gasLimit The max amount gas to pay for this transaction.
    /// @return success_ true if the call is successful, false otherwise.
    function sendEther(
        address _to,
        uint256 _amount,
        uint256 _gasLimit,
        bytes memory _calldata
    )
        internal
        returns (bool success_)
    {
        // Check for zero-address transactions
        if (_to == address(0)) revert ETH_TRANSFER_FAILED();
        // dispatch message to recipient
        // by assembly calling "handle" function
        // we call via assembly to avoid memcopying a very large returndata
        // returned by a malicious contract
        assembly {
            success_ :=
                call(
                    _gasLimit, // gas
                    _to, // recipient
                    _amount, // ether value
                    add(_calldata, 0x20), // inloc
                    mload(_calldata), // inlen
                    0, // outloc
                    0 // outlen
                )
        }
    }

    /// @dev Sends Ether to the specified address. This method will revert if sending ether fails.
    /// @param _to The recipient address.
    /// @param _amount The amount of Ether to send in wei.
    /// @param _gasLimit The max amount gas to pay for this transaction.
    function sendEtherAndVerify(address _to, uint256 _amount, uint256 _gasLimit) internal {
        if (_amount == 0) return;
        if (!sendEther(_to, _amount, _gasLimit, "")) {
            revert ETH_TRANSFER_FAILED();
        }
    }

    /// @dev Sends Ether to the specified address. This method will revert if sending ether fails.
    /// @param _to The recipient address.
    /// @param _amount The amount of Ether to send in wei.
    function sendEtherAndVerify(address _to, uint256 _amount) internal {
        sendEtherAndVerify(_to, _amount, gasleft());
    }

    function supportsInterface(
        address _addr,
        bytes4 _interfaceId
    )
        internal
        view
        returns (bool result_)
    {
        if (!Address.isContract(_addr)) return false;

        try IERC165(_addr).supportsInterface(_interfaceId) returns (bool _result) {
            result_ = _result;
        } catch { }
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title LibMath
/// @dev This library offers additional math functions for uint256.
/// @custom:security-contact security@taiko.xyz
library LibMath {
    /// @dev Returns the smaller of the two given values.
    /// @param _a The first number to compare.
    /// @param _b The second number to compare.
    /// @return The smaller of the two numbers.
    function min(uint256 _a, uint256 _b) internal pure returns (uint256) {
        return _a > _b ? _b : _a;
    }

    /// @dev Returns the larger of the two given values.
    /// @param _a The first number to compare.
    /// @param _b The second number to compare.
    /// @return The larger of the two numbers.
    function max(uint256 _a, uint256 _b) internal pure returns (uint256) {
        return _a > _b ? _a : _b;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title LibStrings
/// @custom:security-contact security@taiko.xyz
library LibStrings {
    bytes32 internal constant B_AUTOMATA_DCAP_ATTESTATION = bytes32("automata_dcap_attestation");
    bytes32 internal constant B_BLOCK_PROPOSER = bytes32("block_proposer");
    bytes32 internal constant B_BRIDGE = bytes32("bridge");
    bytes32 internal constant B_BRIDGE_WATCHDOG = bytes32("bridge_watchdog");
    bytes32 internal constant B_BRIDGED_ERC1155 = bytes32("bridged_erc1155");
    bytes32 internal constant B_BRIDGED_ERC20 = bytes32("bridged_erc20");
    bytes32 internal constant B_BRIDGED_ERC721 = bytes32("bridged_erc721");
    bytes32 internal constant B_CHAIN_WATCHDOG = bytes32("chain_watchdog");
    bytes32 internal constant B_ERC1155_VAULT = bytes32("erc1155_vault");
    bytes32 internal constant B_ERC20_VAULT = bytes32("erc20_vault");
    bytes32 internal constant B_ERC721_VAULT = bytes32("erc721_vault");
    bytes32 internal constant B_PROVER_ASSIGNMENT = bytes32("PROVER_ASSIGNMENT");
    bytes32 internal constant B_PROVER_SET = bytes32("prover_set");
    bytes32 internal constant B_QUOTA_MANAGER = bytes32("quota_manager");
    bytes32 internal constant B_SGX_WATCHDOG = bytes32("sgx_watchdog");
    bytes32 internal constant B_SIGNAL_SERVICE = bytes32("signal_service");
    bytes32 internal constant B_SP1_REMOTE_VERIFIER = bytes32("sp1_remote_verifier");
    bytes32 internal constant B_TAIKO = bytes32("taiko");
    bytes32 internal constant B_TAIKO_TOKEN = bytes32("taiko_token");
    bytes32 internal constant B_TIER_GUARDIAN = bytes32("tier_guardian");
    bytes32 internal constant B_TIER_GUARDIAN_MINORITY = bytes32("tier_guardian_minority");
    bytes32 internal constant B_TIER_ROUTER = bytes32("tier_router");
    bytes32 internal constant B_TIER_SGX = bytes32("tier_sgx");
    bytes32 internal constant B_TIER_TDX = bytes32("tier_tdx");
    bytes32 internal constant B_TIER_TEE_ANY = bytes32("tier_tee_any");
    bytes32 internal constant B_TIER_ZKVM_RISC0 = bytes32("tier_zkvm_risc0");
    bytes32 internal constant B_TIER_ZKVM_SP1 = bytes32("tier_zkvm_sp1");
    bytes32 internal constant B_TIER_ZKVM_ANY = bytes32("tier_zkvm_any");
    bytes32 internal constant B_TIER_ZKVM_AND_TEE = bytes32("tier_zkvm_and_tee");
    bytes32 internal constant B_RISCZERO_GROTH16_VERIFIER = bytes32("risc0_groth16_verifier");
    bytes32 internal constant B_WITHDRAWER = bytes32("withdrawer");
    bytes32 internal constant H_RETURN_LIVENESS_BOND = keccak256("RETURN_LIVENESS_BOND");
    bytes32 internal constant H_SIGNAL_ROOT = keccak256("SIGNAL_ROOT");
    bytes32 internal constant H_STATE_ROOT = keccak256("STATE_ROOT");
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.0;

import "./OwnableUpgradeable.sol";
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which provides 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} and {acceptOwnership}.
 *
 * This module is used through inheritance. It will make available all functions
 * from parent (Ownable).
 */
abstract contract Ownable2StepUpgradeable is Initializable, OwnableUpgradeable {
    address private _pendingOwner;

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

    function __Ownable2Step_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }

    function __Ownable2Step_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev Returns the address of the pending owner.
     */
    function pendingOwner() public view virtual returns (address) {
        return _pendingOwner;
    }

    /**
     * @dev Starts the ownership transfer of the contract to a new account. Replaces the pending transfer if there is one.
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual override onlyOwner {
        _pendingOwner = newOwner;
        emit OwnershipTransferStarted(owner(), newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`) and deletes any pending owner.
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual override {
        delete _pendingOwner;
        super._transferOwnership(newOwner);
    }

    /**
     * @dev The new owner accepts the ownership transfer.
     */
    function acceptOwnership() public virtual {
        address sender = _msgSender();
        require(pendingOwner() == sender, "Ownable2Step: caller is not the new owner");
        _transferOwnership(sender);
    }

    /**
     * @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
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import {Initializable} from "../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
// 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/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);
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.4) (utils/Context.sol)

pragma solidity ^0.8.0;
import {Initializable} from "../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;
    }

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

    /**
     * @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 v4.4.1 (interfaces/IERC1271.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC1271 standard signature validation method for
 * contracts as defined in https://eips.ethereum.org/EIPS/eip-1271[ERC-1271].
 *
 * _Available since v4.1._
 */
interface IERC1271 {
    /**
     * @dev Should return whether the signature provided is valid for the provided data
     * @param hash      Hash of the data to be signed
     * @param signature Signature byte array associated with _data
     */
    function isValidSignature(bytes32 hash, bytes memory signature) external view returns (bytes4 magicValue);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (interfaces/IERC1967.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
 *
 * _Available since v4.8.3._
 */
interface IERC1967 {
    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Emitted when the beacon is changed.
     */
    event BeaconUpgraded(address indexed beacon);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (proxy/ERC1967/ERC1967Upgrade.sol)

pragma solidity ^0.8.2;

import "../beacon/IBeacon.sol";
import "../../interfaces/IERC1967.sol";
import "../../interfaces/draft-IERC1822.sol";
import "../../utils/Address.sol";
import "../../utils/StorageSlot.sol";

/**
 * @dev This abstract contract provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
 *
 * _Available since v4.1._
 */
abstract contract ERC1967Upgrade is IERC1967 {
    // This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
    bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;

    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev Returns the current implementation address.
     */
    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Perform implementation upgrade
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeTo(address newImplementation) internal {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }

    /**
     * @dev Perform implementation upgrade with additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCall(address newImplementation, bytes memory data, bool forceCall) internal {
        _upgradeTo(newImplementation);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(newImplementation, data);
        }
    }

    /**
     * @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCallUUPS(address newImplementation, bytes memory data, bool forceCall) internal {
        // Upgrades from old implementations will perform a rollback test. This test requires the new
        // implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
        // this special case will break upgrade paths from old UUPS implementation to new ones.
        if (StorageSlot.getBooleanSlot(_ROLLBACK_SLOT).value) {
            _setImplementation(newImplementation);
        } else {
            try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
                require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
            } catch {
                revert("ERC1967Upgrade: new implementation is not UUPS");
            }
            _upgradeToAndCall(newImplementation, data, forceCall);
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Returns the current admin.
     */
    function _getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(_ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        require(newAdmin != address(0), "ERC1967: new admin is the zero address");
        StorageSlot.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _changeAdmin(address newAdmin) internal {
        emit AdminChanged(_getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
     */
    bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Returns the current beacon.
     */
    function _getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(_BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the EIP1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        require(Address.isContract(newBeacon), "ERC1967: new beacon is not a contract");
        require(
            Address.isContract(IBeacon(newBeacon).implementation()),
            "ERC1967: beacon implementation is not a contract"
        );
        StorageSlot.getAddressSlot(_BEACON_SLOT).value = newBeacon;
    }

    /**
     * @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
     * not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
     *
     * Emits a {BeaconUpgraded} event.
     */
    function _upgradeBeaconToAndCall(address newBeacon, bytes memory data, bool forceCall) internal {
        _setBeacon(newBeacon);
        emit BeaconUpgraded(newBeacon);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.4) (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * ==== Security Considerations
 *
 * There are two important considerations concerning the use of `permit`. The first is that a valid permit signature
 * expresses an allowance, and it should not be assumed to convey additional meaning. In particular, it should not be
 * considered as an intention to spend the allowance in any specific way. The second is that because permits have
 * built-in replay protection and can be submitted by anyone, they can be frontrun. A protocol that uses permits should
 * take this into consideration and allow a `permit` call to fail. Combining these two aspects, a pattern that may be
 * generally recommended is:
 *
 * ```solidity
 * function doThingWithPermit(..., uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public {
 *     try token.permit(msg.sender, address(this), value, deadline, v, r, s) {} catch {}
 *     doThing(..., value);
 * }
 *
 * function doThing(..., uint256 value) public {
 *     token.safeTransferFrom(msg.sender, address(this), value);
 *     ...
 * }
 * ```
 *
 * Observe that: 1) `msg.sender` is used as the owner, leaving no ambiguity as to the signer intent, and 2) the use of
 * `try/catch` allows the permit to fail and makes the code tolerant to frontrunning. (See also
 * {SafeERC20-safeTransferFrom}).
 *
 * Additionally, note that smart contract wallets (such as Argent or Safe) are not able to produce permit signatures, so
 * contracts should have entry points that don't rely on permit.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     *
     * CAUTION: See Security Considerations above.
     */
    function permit(
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.3) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/IERC20Permit.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    /**
     * @dev Transfer `value` amount of `token` from the calling contract to `to`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    /**
     * @dev Transfer `value` amount of `token` from `from` to `to`, spending the approval given by `from` to the
     * calling contract. If `token` returns no value, non-reverting calls are assumed to be successful.
     */
    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        require(
            (value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    /**
     * @dev Increase the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 oldAllowance = token.allowance(address(this), spender);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, oldAllowance + value));
    }

    /**
     * @dev Decrease the calling contract's allowance toward `spender` by `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful.
     */
    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, oldAllowance - value));
        }
    }

    /**
     * @dev Set the calling contract's allowance toward `spender` to `value`. If `token` returns no value,
     * non-reverting calls are assumed to be successful. Meant to be used with tokens that require the approval
     * to be set to zero before setting it to a non-zero value, such as USDT.
     */
    function forceApprove(IERC20 token, address spender, uint256 value) internal {
        bytes memory approvalCall = abi.encodeWithSelector(token.approve.selector, spender, value);

        if (!_callOptionalReturnBool(token, approvalCall)) {
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, 0));
            _callOptionalReturn(token, approvalCall);
        }
    }

    /**
     * @dev Use a ERC-2612 signature to set the `owner` approval toward `spender` on `token`.
     * Revert on invalid signature.
     */
    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address-functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        require(returndata.length == 0 || abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     *
     * This is a variant of {_callOptionalReturn} that silents catches all reverts and returns a bool instead.
     */
    function _callOptionalReturnBool(IERC20 token, bytes memory data) private returns (bool) {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We cannot use {Address-functionCall} here since this should return false
        // and not revert is the subcall reverts.

        (bool success, bytes memory returndata) = address(token).call(data);
        return
            success && (returndata.length == 0 || abi.decode(returndata, (bool))) && Address.isContract(address(token));
    }
}
          

// 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
// OpenZeppelin Contracts (last updated v4.9.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.0;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, `uint256`._
 * _Available since v4.9 for `string`, `bytes`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;

/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/FixedPointMathLib.sol)
/// @author Modified from Solmate (https://github.com/transmissions11/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error ExpOverflow();

    /// @dev The operation failed, as the output exceeds the maximum value of uint256.
    error FactorialOverflow();

    /// @dev The operation failed, due to an overflow.
    error RPowOverflow();

    /// @dev The mantissa is too big to fit.
    error MantissaOverflow();

    /// @dev The operation failed, due to an multiplication overflow.
    error MulWadFailed();

    /// @dev The operation failed, due to an multiplication overflow.
    error SMulWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error DivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error SDivWadFailed();

    /// @dev The operation failed, either due to a multiplication overflow, or a division by a zero.
    error MulDivFailed();

    /// @dev The division failed, as the denominator is zero.
    error DivFailed();

    /// @dev The full precision multiply-divide operation failed, either due
    /// to the result being larger than 256 bits, or a division by a zero.
    error FullMulDivFailed();

    /// @dev The output is undefined, as the input is less-than-or-equal to zero.
    error LnWadUndefined();

    /// @dev The input outside the acceptable domain.
    error OutOfDomain();

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                         CONSTANTS                          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev The scalar of ETH and most ERC20s.
    uint256 internal constant WAD = 1e18;

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              SIMPLIFIED FIXED POINT OPERATIONS             */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function mulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if mul(y, gt(x, div(not(0), y))) {
                mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down.
    function sMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require((x == 0 || z / x == y) && !(x == -1 && y == type(int256).min))`.
            if iszero(gt(or(iszero(x), eq(sdiv(z, x), y)), lt(not(x), eq(y, shl(255, 1))))) {
                mstore(0x00, 0xedcd4dd4) // `SMulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(z, WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawMulWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded down, but without overflow checks.
    function rawSMulWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, y), WAD)
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up.
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y == 0 || x <= type(uint256).max / y)`.
            if mul(y, gt(x, div(not(0), y))) {
                mstore(0x00, 0xbac65e5b) // `MulWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * y) / WAD` rounded up, but without overflow checks.
    function rawMulWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, y), WAD))), div(mul(x, y), WAD))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function divWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
            if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down.
    function sDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, WAD)
            // Equivalent to `require(y != 0 && ((x * WAD) / WAD == x))`.
            if iszero(and(iszero(iszero(y)), eq(sdiv(z, WAD), x))) {
                mstore(0x00, 0x5c43740d) // `SDivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawDivWad(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded down, but without overflow and divide by zero checks.
    function rawSDivWad(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(mul(x, WAD), y)
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up.
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // Equivalent to `require(y != 0 && (WAD == 0 || x <= type(uint256).max / WAD))`.
            if iszero(mul(y, iszero(mul(WAD, gt(x, div(not(0), WAD)))))) {
                mstore(0x00, 0x7c5f487d) // `DivWadFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `(x * WAD) / y` rounded up, but without overflow and divide by zero checks.
    function rawDivWadUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := add(iszero(iszero(mod(mul(x, WAD), y))), div(mul(x, WAD), y))
        }
    }

    /// @dev Equivalent to `x` to the power of `y`.
    /// because `x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)`.
    /// Note: This function is an approximation.
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Using `ln(x)` means `x` must be greater than 0.
        return expWad((lnWad(x) * y) / int256(WAD));
    }

    /// @dev Returns `exp(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is less than 0.5 we return zero.
            // This happens when `x <= (log(1e-18) * 1e18) ~ -4.15e19`.
            if (x <= -41446531673892822313) return r;

            /// @solidity memory-safe-assembly
            assembly {
                // When the result is greater than `(2**255 - 1) / 1e18` we can not represent it as
                // an int. This happens when `x >= floor(log((2**255 - 1) / 1e18) * 1e18) ≈ 135`.
                if iszero(slt(x, 135305999368893231589)) {
                    mstore(0x00, 0xa37bfec9) // `ExpOverflow()`.
                    revert(0x1c, 0x04)
                }
            }

            // `x` is now in the range `(-42, 136) * 1e18`. Convert to `(-42, 136) * 2**96`
            // for more intermediate precision and a binary basis. This base conversion
            // is a multiplication by 1e18 / 2**96 = 5**18 / 2**78.
            x = (x << 78) / 5 ** 18;

            // Reduce range of x to (-½ ln 2, ½ ln 2) * 2**96 by factoring out powers
            // of two such that exp(x) = exp(x') * 2**k, where k is an integer.
            // Solving this gives k = round(x / log(2)) and x' = x - k * log(2).
            int256 k = ((x << 96) / 54916777467707473351141471128 + 2 ** 95) >> 96;
            x = x - k * 54916777467707473351141471128;

            // `k` is in the range `[-61, 195]`.

            // Evaluate using a (6, 7)-term rational approximation.
            // `p` is made monic, we'll multiply by a scale factor later.
            int256 y = x + 1346386616545796478920950773328;
            y = ((y * x) >> 96) + 57155421227552351082224309758442;
            int256 p = y + x - 94201549194550492254356042504812;
            p = ((p * y) >> 96) + 28719021644029726153956944680412240;
            p = p * x + (4385272521454847904659076985693276 << 96);

            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.
            int256 q = x - 2855989394907223263936484059900;
            q = ((q * x) >> 96) + 50020603652535783019961831881945;
            q = ((q * x) >> 96) - 533845033583426703283633433725380;
            q = ((q * x) >> 96) + 3604857256930695427073651918091429;
            q = ((q * x) >> 96) - 14423608567350463180887372962807573;
            q = ((q * x) >> 96) + 26449188498355588339934803723976023;

            /// @solidity memory-safe-assembly
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial won't have zeros in the domain as all its roots are complex.
                // No scaling is necessary because p is already `2**96` too large.
                r := sdiv(p, q)
            }

            // r should be in the range `(0.09, 0.25) * 2**96`.

            // We now need to multiply r by:
            // - The scale factor `s ≈ 6.031367120`.
            // - The `2**k` factor from the range reduction.
            // - The `1e18 / 2**96` factor for base conversion.
            // We do this all at once, with an intermediate result in `2**213`
            // basis, so the final right shift is always by a positive amount.
            r = int256(
                (uint256(r) * 3822833074963236453042738258902158003155416615667) >> uint256(195 - k)
            );
        }
    }

    /// @dev Returns `ln(x)`, denominated in `WAD`.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/22/exp-ln
    /// Note: This function is an approximation. Monotonically increasing.
    function lnWad(int256 x) internal pure returns (int256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            // We want to convert `x` from `10**18` fixed point to `2**96` fixed point.
            // We do this by multiplying by `2**96 / 10**18`. But since
            // `ln(x * C) = ln(x) + ln(C)`, we can simply do nothing here
            // and add `ln(2**96 / 10**18)` at the end.

            // Compute `k = log2(x) - 96`, `r = 159 - k = 255 - log2(x) = 255 ^ log2(x)`.
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // We place the check here for more optimal stack operations.
            if iszero(sgt(x, 0)) {
                mstore(0x00, 0x1615e638) // `LnWadUndefined()`.
                revert(0x1c, 0x04)
            }
            // forgefmt: disable-next-item
            r := xor(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0xf8f9f9faf9fdfafbf9fdfcfdfafbfcfef9fafdfafcfcfbfefafafcfbffffffff))

            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            x := shr(159, shl(r, x))

            // Evaluate using a (8, 8)-term rational approximation.
            // `p` is made monic, we will multiply by a scale factor later.
            // forgefmt: disable-next-item
            let p := sub( // This heavily nested expression is to avoid stack-too-deep for via-ir.
                sar(96, mul(add(43456485725739037958740375743393,
                sar(96, mul(add(24828157081833163892658089445524,
                sar(96, mul(add(3273285459638523848632254066296,
                    x), x))), x))), x)), 11111509109440967052023855526967)
            p := sub(sar(96, mul(p, x)), 45023709667254063763336534515857)
            p := sub(sar(96, mul(p, x)), 14706773417378608786704636184526)
            p := sub(mul(p, x), shl(96, 795164235651350426258249787498))
            // We leave `p` in `2**192` basis so we don't need to scale it back up for the division.

            // `q` is monic by convention.
            let q := add(5573035233440673466300451813936, x)
            q := add(71694874799317883764090561454958, sar(96, mul(x, q)))
            q := add(283447036172924575727196451306956, sar(96, mul(x, q)))
            q := add(401686690394027663651624208769553, sar(96, mul(x, q)))
            q := add(204048457590392012362485061816622, sar(96, mul(x, q)))
            q := add(31853899698501571402653359427138, sar(96, mul(x, q)))
            q := add(909429971244387300277376558375, sar(96, mul(x, q)))

            // `p / q` is in the range `(0, 0.125) * 2**96`.

            // Finalization, we need to:
            // - Multiply by the scale factor `s = 5.549…`.
            // - Add `ln(2**96 / 10**18)`.
            // - Add `k * ln(2)`.
            // - Multiply by `10**18 / 2**96 = 5**18 >> 78`.

            // The q polynomial is known not to have zeros in the domain.
            // No scaling required because p is already `2**96` too large.
            p := sdiv(p, q)
            // Multiply by the scaling factor: `s * 5**18 * 2**96`, base is now `5**18 * 2**192`.
            p := mul(1677202110996718588342820967067443963516166, p)
            // Add `ln(2) * k * 5**18 * 2**192`.
            // forgefmt: disable-next-item
            p := add(mul(16597577552685614221487285958193947469193820559219878177908093499208371, sub(159, r)), p)
            // Add `ln(2**96 / 10**18) * 5**18 * 2**192`.
            p := add(600920179829731861736702779321621459595472258049074101567377883020018308, p)
            // Base conversion: mul `2**18 / 2**192`.
            r := sar(174, p)
        }
    }

    /// @dev Returns `W_0(x)`, denominated in `WAD`.
    /// See: https://en.wikipedia.org/wiki/Lambert_W_function
    /// a.k.a. Product log function. This is an approximation of the principal branch.
    /// Note: This function is an approximation. Monotonically increasing.
    function lambertW0Wad(int256 x) internal pure returns (int256 w) {
        // forgefmt: disable-next-item
        unchecked {
            if ((w = x) <= -367879441171442322) revert OutOfDomain(); // `x` less than `-1/e`.
            int256 wad = int256(WAD);
            int256 p = x;
            uint256 c; // Whether we need to avoid catastrophic cancellation.
            uint256 i = 4; // Number of iterations.
            if (w <= 0x1ffffffffffff) {
                if (-0x4000000000000 <= w) {
                    i = 1; // Inputs near zero only take one step to converge.
                } else if (w <= -0x3ffffffffffffff) {
                    i = 32; // Inputs near `-1/e` take very long to converge.
                }
            } else if (uint256(w >> 63) == uint256(0)) {
                /// @solidity memory-safe-assembly
                assembly {
                    // Inline log2 for more performance, since the range is small.
                    let v := shr(49, w)
                    let l := shl(3, lt(0xff, v))
                    l := add(or(l, byte(and(0x1f, shr(shr(l, v), 0x8421084210842108cc6318c6db6d54be)),
                        0x0706060506020504060203020504030106050205030304010505030400000000)), 49)
                    w := sdiv(shl(l, 7), byte(sub(l, 31), 0x0303030303030303040506080c13))
                    c := gt(l, 60)
                    i := add(2, add(gt(l, 53), c))
                }
            } else {
                int256 ll = lnWad(w = lnWad(w));
                /// @solidity memory-safe-assembly
                assembly {
                    // `w = ln(x) - ln(ln(x)) + b * ln(ln(x)) / ln(x)`.
                    w := add(sdiv(mul(ll, 1023715080943847266), w), sub(w, ll))
                    i := add(3, iszero(shr(68, x)))
                    c := iszero(shr(143, x))
                }
                if (c == uint256(0)) {
                    do { // If `x` is big, use Newton's so that intermediate values won't overflow.
                        int256 e = expWad(w);
                        /// @solidity memory-safe-assembly
                        assembly {
                            let t := mul(w, div(e, wad))
                            w := sub(w, sdiv(sub(t, x), div(add(e, t), wad)))
                        }
                        if (p <= w) break;
                        p = w;
                    } while (--i != uint256(0));
                    /// @solidity memory-safe-assembly
                    assembly {
                        w := sub(w, sgt(w, 2))
                    }
                    return w;
                }
            }
            do { // Otherwise, use Halley's for faster convergence.
                int256 e = expWad(w);
                /// @solidity memory-safe-assembly
                assembly {
                    let t := add(w, wad)
                    let s := sub(mul(w, e), mul(x, wad))
                    w := sub(w, sdiv(mul(s, wad), sub(mul(e, t), sdiv(mul(add(t, wad), s), add(t, t)))))
                }
                if (p <= w) break;
                p = w;
            } while (--i != c);
            /// @solidity memory-safe-assembly
            assembly {
                w := sub(w, sgt(w, 2))
            }
            // For certain ranges of `x`, we'll use the quadratic-rate recursive formula of
            // R. Iacono and J.P. Boyd for the last iteration, to avoid catastrophic cancellation.
            if (c == uint256(0)) return w;
            int256 t = w | 1;
            /// @solidity memory-safe-assembly
            assembly {
                x := sdiv(mul(x, wad), t)
            }
            x = (t * (wad + lnWad(x)));
            /// @solidity memory-safe-assembly
            assembly {
                w := sdiv(x, add(wad, t))
            }
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  GENERAL NUMBER UTILITIES                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Remco Bloemen under MIT license: https://2π.com/21/muldiv
    function fullMulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            // 512-bit multiply `[p1 p0] = x * y`.
            // Compute the product mod `2**256` and mod `2**256 - 1`
            // then use the Chinese Remainder Theorem to reconstruct
            // the 512 bit result. The result is stored in two 256
            // variables such that `product = p1 * 2**256 + p0`.

            // Temporarily use `result` as `p0` to save gas.
            result := mul(x, y) // Lower 256 bits of `x * y`.
            for {} 1 {} {
                // If overflows.
                if iszero(mul(or(iszero(x), eq(div(result, x), y)), d)) {
                    let mm := mulmod(x, y, not(0))
                    let p1 := sub(mm, add(result, lt(mm, result))) // Upper 256 bits of `x * y`.

                    /*------------------- 512 by 256 division --------------------*/

                    // Make division exact by subtracting the remainder from `[p1 p0]`.
                    let r := mulmod(x, y, d) // Compute remainder using mulmod.
                    let t := and(d, sub(0, d)) // The least significant bit of `d`. `t >= 1`.
                    // Make sure the result is less than `2**256`. Also prevents `d == 0`.
                    // Placing the check here seems to give more optimal stack operations.
                    if iszero(gt(d, p1)) {
                        mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                        revert(0x1c, 0x04)
                    }
                    d := div(d, t) // Divide `d` by `t`, which is a power of two.
                    // Invert `d mod 2**256`
                    // Now that `d` is an odd number, it has an inverse
                    // modulo `2**256` such that `d * inv = 1 mod 2**256`.
                    // Compute the inverse by starting with a seed that is correct
                    // correct for four bits. That is, `d * inv = 1 mod 2**4`.
                    let inv := xor(2, mul(3, d))
                    // Now use 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.
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**8
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**16
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**32
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**64
                    inv := mul(inv, sub(2, mul(d, inv))) // inverse mod 2**128
                    result :=
                        mul(
                            // Divide [p1 p0] by the factors of two.
                            // Shift in bits from `p1` into `p0`. For this we need
                            // to flip `t` such that it is `2**256 / t`.
                            or(
                                mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)),
                                div(sub(result, r), t)
                            ),
                            mul(sub(2, mul(d, inv)), inv) // inverse mod 2**256
                        )
                    break
                }
                result := div(result, d)
                break
            }
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision.
    /// Behavior is undefined if `d` is zero or the final result cannot fit in 256 bits.
    /// Performs the full 512 bit calculation regardless.
    function fullMulDivUnchecked(uint256 x, uint256 y, uint256 d)
        internal
        pure
        returns (uint256 result)
    {
        /// @solidity memory-safe-assembly
        assembly {
            result := mul(x, y)
            let mm := mulmod(x, y, not(0))
            let p1 := sub(mm, add(result, lt(mm, result)))
            let t := and(d, sub(0, d))
            let r := mulmod(x, y, d)
            d := div(d, t)
            let inv := xor(2, mul(3, d))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            inv := mul(inv, sub(2, mul(d, inv)))
            result :=
                mul(
                    or(mul(sub(p1, gt(r, result)), add(div(sub(0, t), t), 1)), div(sub(result, r), t)),
                    mul(sub(2, mul(d, inv)), inv)
                )
        }
    }

    /// @dev Calculates `floor(x * y / d)` with full precision, rounded up.
    /// Throws if result overflows a uint256 or when `d` is zero.
    /// Credit to Uniswap-v3-core under MIT license:
    /// https://github.com/Uniswap/v3-core/blob/main/contracts/libraries/FullMath.sol
    function fullMulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 result) {
        result = fullMulDiv(x, y, d);
        /// @solidity memory-safe-assembly
        assembly {
            if mulmod(x, y, d) {
                result := add(result, 1)
                if iszero(result) {
                    mstore(0x00, 0xae47f702) // `FullMulDivFailed()`.
                    revert(0x1c, 0x04)
                }
            }
        }
    }

    /// @dev Returns `floor(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDiv(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := div(z, d)
        }
    }

    /// @dev Returns `ceil(x * y / d)`.
    /// Reverts if `x * y` overflows, or `d` is zero.
    function mulDivUp(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(x, y)
            // Equivalent to `require(d != 0 && (y == 0 || x <= type(uint256).max / y))`.
            if iszero(mul(or(iszero(x), eq(div(z, x), y)), d)) {
                mstore(0x00, 0xad251c27) // `MulDivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(z, d))), div(z, d))
        }
    }

    /// @dev Returns `ceil(x / d)`.
    /// Reverts if `d` is zero.
    function divUp(uint256 x, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(d) {
                mstore(0x00, 0x65244e4e) // `DivFailed()`.
                revert(0x1c, 0x04)
            }
            z := add(iszero(iszero(mod(x, d))), div(x, d))
        }
    }

    /// @dev Returns `max(0, x - y)`.
    function zeroFloorSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(gt(x, y), sub(x, y))
        }
    }

    /// @dev Returns `condition ? x : y`, without branching.
    function ternary(bool condition, uint256 x, uint256 y) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := xor(x, mul(xor(x, y), iszero(condition)))
        }
    }

    /// @dev Exponentiate `x` to `y` by squaring, denominated in base `b`.
    /// Reverts if the computation overflows.
    function rpow(uint256 x, uint256 y, uint256 b) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mul(b, iszero(y)) // `0 ** 0 = 1`. Otherwise, `0 ** n = 0`.
            if x {
                z := xor(b, mul(xor(b, x), and(y, 1))) // `z = isEven(y) ? scale : x`
                let half := shr(1, b) // Divide `b` by 2.
                // Divide `y` by 2 every iteration.
                for { y := shr(1, y) } y { y := shr(1, y) } {
                    let xx := mul(x, x) // Store x squared.
                    let xxRound := add(xx, half) // Round to the nearest number.
                    // Revert if `xx + half` overflowed, or if `x ** 2` overflows.
                    if or(lt(xxRound, xx), shr(128, x)) {
                        mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                        revert(0x1c, 0x04)
                    }
                    x := div(xxRound, b) // Set `x` to scaled `xxRound`.
                    // If `y` is odd:
                    if and(y, 1) {
                        let zx := mul(z, x) // Compute `z * x`.
                        let zxRound := add(zx, half) // Round to the nearest number.
                        // If `z * x` overflowed or `zx + half` overflowed:
                        if or(xor(div(zx, x), z), lt(zxRound, zx)) {
                            // Revert if `x` is non-zero.
                            if x {
                                mstore(0x00, 0x49f7642b) // `RPowOverflow()`.
                                revert(0x1c, 0x04)
                            }
                        }
                        z := div(zxRound, b) // Return properly scaled `zxRound`.
                    }
                }
            }
        }
    }

    /// @dev Returns the square root of `x`, rounded down.
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            // `floor(sqrt(2**15)) = 181`. `sqrt(2**15) - 181 = 2.84`.
            z := 181 // The "correct" value is 1, but this saves a multiplication later.

            // This segment is to get a reasonable initial estimate for the Babylonian method. With a bad
            // start, the correct # of bits increases ~linearly each iteration instead of ~quadratically.

            // Let `y = x / 2**r`. We check `y >= 2**(k + 8)`
            // but shift right by `k` bits to ensure that if `x >= 256`, then `y >= 256`.
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffffff, shr(r, x))))
            z := shl(shr(1, r), z)

            // Goal was to get `z*z*y` within a small factor of `x`. More iterations could
            // get y in a tighter range. Currently, we will have y in `[256, 256*(2**16))`.
            // We ensured `y >= 256` so that the relative difference between `y` and `y+1` is small.
            // That's not possible if `x < 256` but we can just verify those cases exhaustively.

            // Now, `z*z*y <= x < z*z*(y+1)`, and `y <= 2**(16+8)`, and either `y >= 256`, or `x < 256`.
            // Correctness can be checked exhaustively for `x < 256`, so we assume `y >= 256`.
            // Then `z*sqrt(y)` is within `sqrt(257)/sqrt(256)` of `sqrt(x)`, or about 20bps.

            // For `s` in the range `[1/256, 256]`, the estimate `f(s) = (181/1024) * (s+1)`
            // is in the range `(1/2.84 * sqrt(s), 2.84 * sqrt(s))`,
            // with largest error when `s = 1` and when `s = 256` or `1/256`.

            // Since `y` is in `[256, 256*(2**16))`, let `a = y/65536`, so that `a` is in `[1/256, 256)`.
            // Then we can estimate `sqrt(y)` using
            // `sqrt(65536) * 181/1024 * (a + 1) = 181/4 * (y + 65536)/65536 = 181 * (y + 65536)/2**18`.

            // There is no overflow risk here since `y < 2**136` after the first branch above.
            z := shr(18, mul(z, add(shr(r, x), 65536))) // A `mul()` is saved from starting `z` at 181.

            // Given the worst case multiplicative error of 2.84 above, 7 iterations should be enough.
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))
            z := shr(1, add(z, div(x, z)))

            // If `x+1` is a perfect square, the Babylonian method cycles between
            // `floor(sqrt(x))` and `ceil(sqrt(x))`. This statement ensures we return floor.
            // See: https://en.wikipedia.org/wiki/Integer_square_root#Using_only_integer_division
            z := sub(z, lt(div(x, z), z))
        }
    }

    /// @dev Returns the cube root of `x`, rounded down.
    /// Credit to bout3fiddy and pcaversaccio under AGPLv3 license:
    /// https://github.com/pcaversaccio/snekmate/blob/main/src/utils/Math.vy
    /// Formally verified by xuwinnie:
    /// https://github.com/vectorized/solady/blob/main/audits/xuwinnie-solady-cbrt-proof.pdf
    function cbrt(uint256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            let r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // Makeshift lookup table to nudge the approximate log2 result.
            z := div(shl(div(r, 3), shl(lt(0xf, shr(r, x)), 0xf)), xor(7, mod(r, 3)))
            // Newton-Raphson's.
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            z := div(add(add(div(x, mul(z, z)), z), z), 3)
            // Round down.
            z := sub(z, lt(div(x, mul(z, z)), z))
        }
    }

    /// @dev Returns the square root of `x`, denominated in `WAD`, rounded down.
    function sqrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 18) return sqrt(x * 10 ** 18);
            z = (1 + sqrt(x)) * 10 ** 9;
            z = (fullMulDivUnchecked(x, 10 ** 18, z) + z) >> 1;
        }
        /// @solidity memory-safe-assembly
        assembly {
            z := sub(z, gt(999999999999999999, sub(mulmod(z, z, x), 1))) // Round down.
        }
    }

    /// @dev Returns the cube root of `x`, denominated in `WAD`, rounded down.
    /// Formally verified by xuwinnie:
    /// https://github.com/vectorized/solady/blob/main/audits/xuwinnie-solady-cbrt-proof.pdf
    function cbrtWad(uint256 x) internal pure returns (uint256 z) {
        unchecked {
            if (x <= type(uint256).max / 10 ** 36) return cbrt(x * 10 ** 36);
            z = (1 + cbrt(x)) * 10 ** 12;
            z = (fullMulDivUnchecked(x, 10 ** 36, z * z) + z + z) / 3;
        }
        /// @solidity memory-safe-assembly
        assembly {
            let p := x
            for {} 1 {} {
                if iszero(shr(229, p)) {
                    if iszero(shr(199, p)) {
                        p := mul(p, 100000000000000000) // 10 ** 17.
                        break
                    }
                    p := mul(p, 100000000) // 10 ** 8.
                    break
                }
                if iszero(shr(249, p)) { p := mul(p, 100) }
                break
            }
            let t := mulmod(mul(z, z), z, p)
            z := sub(z, gt(lt(t, shr(1, p)), iszero(t))) // Round down.
        }
    }

    /// @dev Returns the factorial of `x`.
    function factorial(uint256 x) internal pure returns (uint256 result) {
        /// @solidity memory-safe-assembly
        assembly {
            result := 1
            if iszero(lt(x, 58)) {
                mstore(0x00, 0xaba0f2a2) // `FactorialOverflow()`.
                revert(0x1c, 0x04)
            }
            for {} x { x := sub(x, 1) } { result := mul(result, x) }
        }
    }

    /// @dev Returns the log2 of `x`.
    /// Equivalent to computing the index of the most significant bit (MSB) of `x`.
    /// Returns 0 if `x` is zero.
    function log2(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(r, shl(3, lt(0xff, shr(r, x))))
            // forgefmt: disable-next-item
            r := or(r, byte(and(0x1f, shr(shr(r, x), 0x8421084210842108cc6318c6db6d54be)),
                0x0706060506020504060203020504030106050205030304010505030400000000))
        }
    }

    /// @dev Returns the log2 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log2Up(uint256 x) internal pure returns (uint256 r) {
        r = log2(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(r, 1), x))
        }
    }

    /// @dev Returns the log10 of `x`.
    /// Returns 0 if `x` is zero.
    function log10(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            if iszero(lt(x, 100000000000000000000000000000000000000)) {
                x := div(x, 100000000000000000000000000000000000000)
                r := 38
            }
            if iszero(lt(x, 100000000000000000000)) {
                x := div(x, 100000000000000000000)
                r := add(r, 20)
            }
            if iszero(lt(x, 10000000000)) {
                x := div(x, 10000000000)
                r := add(r, 10)
            }
            if iszero(lt(x, 100000)) {
                x := div(x, 100000)
                r := add(r, 5)
            }
            r := add(r, add(gt(x, 9), add(gt(x, 99), add(gt(x, 999), gt(x, 9999)))))
        }
    }

    /// @dev Returns the log10 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log10Up(uint256 x) internal pure returns (uint256 r) {
        r = log10(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(exp(10, r), x))
        }
    }

    /// @dev Returns the log256 of `x`.
    /// Returns 0 if `x` is zero.
    function log256(uint256 x) internal pure returns (uint256 r) {
        /// @solidity memory-safe-assembly
        assembly {
            r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
            r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
            r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
            r := or(r, shl(4, lt(0xffff, shr(r, x))))
            r := or(shr(3, r), lt(0xff, shr(r, x)))
        }
    }

    /// @dev Returns the log256 of `x`, rounded up.
    /// Returns 0 if `x` is zero.
    function log256Up(uint256 x) internal pure returns (uint256 r) {
        r = log256(x);
        /// @solidity memory-safe-assembly
        assembly {
            r := add(r, lt(shl(shl(3, r), 1), x))
        }
    }

    /// @dev Returns the scientific notation format `mantissa * 10 ** exponent` of `x`.
    /// Useful for compressing prices (e.g. using 25 bit mantissa and 7 bit exponent).
    function sci(uint256 x) internal pure returns (uint256 mantissa, uint256 exponent) {
        /// @solidity memory-safe-assembly
        assembly {
            mantissa := x
            if mantissa {
                if iszero(mod(mantissa, 1000000000000000000000000000000000)) {
                    mantissa := div(mantissa, 1000000000000000000000000000000000)
                    exponent := 33
                }
                if iszero(mod(mantissa, 10000000000000000000)) {
                    mantissa := div(mantissa, 10000000000000000000)
                    exponent := add(exponent, 19)
                }
                if iszero(mod(mantissa, 1000000000000)) {
                    mantissa := div(mantissa, 1000000000000)
                    exponent := add(exponent, 12)
                }
                if iszero(mod(mantissa, 1000000)) {
                    mantissa := div(mantissa, 1000000)
                    exponent := add(exponent, 6)
                }
                if iszero(mod(mantissa, 10000)) {
                    mantissa := div(mantissa, 10000)
                    exponent := add(exponent, 4)
                }
                if iszero(mod(mantissa, 100)) {
                    mantissa := div(mantissa, 100)
                    exponent := add(exponent, 2)
                }
                if iszero(mod(mantissa, 10)) {
                    mantissa := div(mantissa, 10)
                    exponent := add(exponent, 1)
                }
            }
        }
    }

    /// @dev Convenience function for packing `x` into a smaller number using `sci`.
    /// The `mantissa` will be in bits [7..255] (the upper 249 bits).
    /// The `exponent` will be in bits [0..6] (the lower 7 bits).
    /// Use `SafeCastLib` to safely ensure that the `packed` number is small
    /// enough to fit in the desired unsigned integer type:
    /// ```
    ///     uint32 packed = SafeCastLib.toUint32(FixedPointMathLib.packSci(777 ether));
    /// ```
    function packSci(uint256 x) internal pure returns (uint256 packed) {
        (x, packed) = sci(x); // Reuse for `mantissa` and `exponent`.
        /// @solidity memory-safe-assembly
        assembly {
            if shr(249, x) {
                mstore(0x00, 0xce30380c) // `MantissaOverflow()`.
                revert(0x1c, 0x04)
            }
            packed := or(shl(7, x), packed)
        }
    }

    /// @dev Convenience function for unpacking a packed number from `packSci`.
    function unpackSci(uint256 packed) internal pure returns (uint256 unpacked) {
        unchecked {
            unpacked = (packed >> 7) * 10 ** (packed & 0x7f);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards zero.
    function avg(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = (x & y) + ((x ^ y) >> 1);
        }
    }

    /// @dev Returns the average of `x` and `y`. Rounds towards negative infinity.
    function avg(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = (x >> 1) + (y >> 1) + (x & y & 1);
        }
    }

    /// @dev Returns the absolute value of `x`.
    function abs(int256 x) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(sar(255, x), add(sar(255, x), x))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(mul(xor(sub(y, x), sub(x, y)), gt(x, y)), sub(y, x))
        }
    }

    /// @dev Returns the absolute distance between `x` and `y`.
    function dist(int256 x, int256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(mul(xor(sub(y, x), sub(x, y)), sgt(x, y)), sub(y, x))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), lt(y, x)))
        }
    }

    /// @dev Returns the minimum of `x` and `y`.
    function min(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), slt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), gt(y, x)))
        }
    }

    /// @dev Returns the maximum of `x` and `y`.
    function max(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, y), sgt(y, x)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(uint256 x, uint256 minValue, uint256 maxValue)
        internal
        pure
        returns (uint256 z)
    {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), gt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), lt(maxValue, z)))
        }
    }

    /// @dev Returns `x`, bounded to `minValue` and `maxValue`.
    function clamp(int256 x, int256 minValue, int256 maxValue) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := xor(x, mul(xor(x, minValue), sgt(minValue, x)))
            z := xor(z, mul(xor(z, maxValue), slt(maxValue, z)))
        }
    }

    /// @dev Returns greatest common divisor of `x` and `y`.
    function gcd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            for { z := x } y {} {
                let t := y
                y := mod(z, y)
                z := t
            }
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`,
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(uint256 a, uint256 b, uint256 t, uint256 begin, uint256 end)
        internal
        pure
        returns (uint256)
    {
        if (begin > end) {
            t = ~t;
            begin = ~begin;
            end = ~end;
        }
        if (t <= begin) return a;
        if (t >= end) return b;
        unchecked {
            if (b >= a) return a + fullMulDiv(b - a, t - begin, end - begin);
            return a - fullMulDiv(a - b, t - begin, end - begin);
        }
    }

    /// @dev Returns `a + (b - a) * (t - begin) / (end - begin)`.
    /// with `t` clamped between `begin` and `end` (inclusive).
    /// Agnostic to the order of (`a`, `b`) and (`end`, `begin`).
    /// If `begins == end`, returns `t <= begin ? a : b`.
    function lerp(int256 a, int256 b, int256 t, int256 begin, int256 end)
        internal
        pure
        returns (int256)
    {
        if (begin > end) {
            t = int256(~uint256(t));
            begin = int256(~uint256(begin));
            end = int256(~uint256(end));
        }
        if (t <= begin) return a;
        if (t >= end) return b;
        // forgefmt: disable-next-item
        unchecked {
            if (b >= a) return int256(uint256(a) + fullMulDiv(uint256(b) - uint256(a),
                uint256(t) - uint256(begin), uint256(end) - uint256(begin)));
            return int256(uint256(a) - fullMulDiv(uint256(a) - uint256(b),
                uint256(t) - uint256(begin), uint256(end) - uint256(begin)));
        }
    }

    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                   RAW NUMBER OPERATIONS                    */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x + y`, without checking for overflow.
    function rawAdd(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x + y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x - y`, without checking for underflow.
    function rawSub(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x - y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x * y`, without checking for overflow.
    function rawMul(int256 x, int256 y) internal pure returns (int256 z) {
        unchecked {
            z = x * y;
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawDiv(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := div(x, y)
        }
    }

    /// @dev Returns `x / y`, returning 0 if `y` is zero.
    function rawSDiv(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := sdiv(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawMod(uint256 x, uint256 y) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mod(x, y)
        }
    }

    /// @dev Returns `x % y`, returning 0 if `y` is zero.
    function rawSMod(int256 x, int256 y) internal pure returns (int256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := smod(x, y)
        }
    }

    /// @dev Returns `(x + y) % d`, return 0 if `d` if zero.
    function rawAddMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := addmod(x, y, d)
        }
    }

    /// @dev Returns `(x * y) % d`, return 0 if `d` if zero.
    function rawMulMod(uint256 x, uint256 y, uint256 d) internal pure returns (uint256 z) {
        /// @solidity memory-safe-assembly
        assembly {
            z := mulmod(x, y, d)
        }
    }
}