// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/**
 * @title Multicaller
 * @author vectorized.eth
 * @notice Contract that allows for efficient aggregation
 *         of multiple calls in a single transaction.
 */
contract Multicaller {
    // =============================================================
    //                            ERRORS
    // =============================================================
    /**
     * @dev The lengths of the input arrays are not the same.
     */
    error ArrayLengthsMismatch();
    // =============================================================
    //                    AGGREGATION OPERATIONS
    // =============================================================
    /**
     * @dev Aggregates multiple calls in a single transaction.
     * @param targets  An array of addresses to call.
     * @param data     An array of calldata to forward to the targets.
     * @param values   How much ETH to forward to each target.
     * @param refundTo The address to transfer any remaining ETH in the contract after the calls.
     *                 If `address(0)`, remaining ETH will NOT be refunded.
     *                 If `address(1)`, remaining ETH will be refunded to `msg.sender`.
     *                 If anything else, remaining ETH will be refunded to `refundTo`.
     * @return An array of the returndata from each call.
     */
    function aggregate(
        address[] calldata targets,
        bytes[] calldata data,
        uint256[] calldata values,
        address refundTo
    ) external payable returns (bytes[] memory) {
        assembly {
            if iszero(and(eq(targets.length, data.length), eq(data.length, values.length))) {
                // Store the function selector of `ArrayLengthsMismatch()`.
                mstore(returndatasize(), 0x3b800a46)
                // Revert with (offset, size).
                revert(0x1c, 0x04)
            }
            let resultsSize := 0x40
            if data.length {
                let results := 0x40
                // Left shift by 5 is equivalent to multiplying by 0x20.
                data.length := shl(5, data.length)
                // Copy the offsets from calldata into memory.
                calldatacopy(results, data.offset, data.length)
                // Offset into `results`.
                let resultsOffset := data.length
                // Pointer to the end of `results`.
                let end := add(results, data.length)
                // For deriving the calldata offsets from the `results` pointer.
                let valuesOffsetDiff := sub(values.offset, results)
                let targetsOffsetDiff := sub(targets.offset, results)
                for {} 1 {} {
                    // The offset of the current bytes in the calldata.
                    let o := add(data.offset, mload(results))
                    let memPtr := add(resultsOffset, 0x40)
                    // Copy the current bytes from calldata to the memory.
                    calldatacopy(
                        memPtr,
                        add(o, 0x20), // The offset of the current bytes' bytes.
                        calldataload(o) // The length of the current bytes.
                    )
                    if iszero(
                        call(
                            gas(), // Remaining gas.
                            calldataload(add(targetsOffsetDiff, results)), // Address to call.
                            calldataload(add(valuesOffsetDiff, results)), // ETH to send.
                            memPtr, // Start of input calldata in memory.
                            calldataload(o), // Size of input calldata.
                            0x00, // We will use returndatacopy instead.
                            0x00 // We will use returndatacopy instead.
                        )
                    ) {
                        // Bubble up the revert if the call reverts.
                        returndatacopy(0x00, 0x00, returndatasize())
                        revert(0x00, returndatasize())
                    }
                    // Append the current `resultsOffset` into `results`.
                    mstore(results, resultsOffset)
                    // Append the returndatasize, and the returndata.
                    mstore(memPtr, returndatasize())
                    returndatacopy(add(memPtr, 0x20), 0x00, returndatasize())
                    // Advance the `resultsOffset` by `returndatasize() + 0x20`,
                    // rounded up to the next multiple of 0x20.
                    resultsOffset := and(add(add(resultsOffset, returndatasize()), 0x3f), not(0x1f))
                    // Advance the `results` pointer.
                    results := add(results, 0x20)
                    if eq(results, end) { break }
                }
                resultsSize := add(resultsOffset, 0x40)
            }
            if refundTo {
                // Force transfers all the remaining ETH in the contract to `refundTo`,
                // with a gas stipend of 100000, which should be enough for most use cases.
                // If sending via a regular call fails, force sends the ETH by
                // creating a temporary contract which uses `SELFDESTRUCT` to force send the ETH.
                if selfbalance() {
                    // If `refundTo` is `address(1)`, replace it with the `msg.sender`.
                    refundTo := xor(refundTo, mul(eq(refundTo, 1), xor(refundTo, caller())))
                    // Transfer the ETH and check if it succeeded or not.
                    if iszero(
                        call(100000, refundTo, selfbalance(), codesize(), 0x00, codesize(), 0x00)
                    ) {
                        mstore(0x00, refundTo) // Store the address in scratch space.
                        mstore8(0x0b, 0x73) // Opcode `PUSH20`.
                        mstore8(0x20, 0xff) // Opcode `SELFDESTRUCT`.
                        // We can directly use `SELFDESTRUCT` in the contract creation.
                        // Compatible with `SENDALL`: https://eips.ethereum.org/EIPS/eip-4758
                        if iszero(create(selfbalance(), 0x0b, 0x16)) {
                            // Coerce gas estimation to provide enough gas for the `create` above.
                            revert(codesize(), codesize())
                        }
                    }
                }
            }
            mstore(0x00, 0x20) // Store the memory offset of the `results`.
            mstore(0x20, targets.length) // Store `targets.length` into `results`.
            // Direct return.
            return(0x00, resultsSize)
        }
    }
    /**
     * @dev For receiving ETH.
     *      Does nothing and returns nothing.
     *      Called instead of `fallback()` if the calldatasize is zero.
     */
    receive() external payable {}
    /**
     * @dev Decompresses the calldata and performs a delegatecall
     *      with the decompressed calldata to itself.
     *
     *      Accompanying JavaScript library to compress the calldata:
     *      https://github.com/vectorized/solady/blob/main/js/solady.js
     *      (See: `LibZip.cdCompress`)
     */
    fallback() external payable {
        assembly {
            // If the calldata starts with the bitwise negation of
            // `bytes4(keccak256("aggregate(address[],bytes[],uint256[],address)"))`.
            let s := calldataload(returndatasize())
            if eq(shr(224, s), 0x66e0daa0) {
                mstore(returndatasize(), not(s))
                let o := 4
                for { let i := o } lt(i, calldatasize()) {} {
                    let c := byte(returndatasize(), calldataload(i))
                    i := add(i, 1)
                    if iszero(c) {
                        let d := byte(returndatasize(), calldataload(i))
                        i := add(i, 1)
                        // Fill with either 0xff or 0x00.
                        mstore(o, not(returndatasize()))
                        if iszero(gt(d, 0x7f)) { codecopy(o, codesize(), add(d, 1)) }
                        o := add(o, add(and(d, 0x7f), 1))
                        continue
                    }
                    mstore8(o, c)
                    o := add(o, 1)
                }
                let success := delegatecall(gas(), address(), 0x00, o, 0x00, 0x00)
                returndatacopy(0x00, 0x00, returndatasize())
                if iszero(success) { revert(0x00, returndatasize()) }
                return(0x00, returndatasize())
            }
            revert(returndatasize(), returndatasize())
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Constants } from "../libraries/Constants.sol";
/// @title Proxy
/// @notice Proxy is a transparent proxy that passes through the call if the caller is the owner or
///         if the caller is address(0), meaning that the call originated from an off-chain
///         simulation.
contract Proxy {
    /// @notice An event that is emitted each time the implementation is changed. This event is part
    ///         of the EIP-1967 specification.
    /// @param implementation The address of the implementation contract
    event Upgraded(address indexed implementation);
    /// @notice An event that is emitted each time the owner is upgraded. This event is part of the
    ///         EIP-1967 specification.
    /// @param previousAdmin The previous owner of the contract
    /// @param newAdmin      The new owner of the contract
    event AdminChanged(address previousAdmin, address newAdmin);
    /// @notice A modifier that reverts if not called by the owner or by address(0) to allow
    ///         eth_call to interact with this proxy without needing to use low-level storage
    ///         inspection. We assume that nobody is able to trigger calls from address(0) during
    ///         normal EVM execution.
    modifier proxyCallIfNotAdmin() {
        if (msg.sender == _getAdmin() || msg.sender == address(0)) {
            _;
        } else {
            // This WILL halt the call frame on completion.
            _doProxyCall();
        }
    }
    /// @notice Sets the initial admin during contract deployment. Admin address is stored at the
    ///         EIP-1967 admin storage slot so that accidental storage collision with the
    ///         implementation is not possible.
    /// @param _admin Address of the initial contract admin. Admin as the ability to access the
    ///               transparent proxy interface.
    constructor(address _admin) {
        _changeAdmin(_admin);
    }
    // slither-disable-next-line locked-ether
    receive() external payable {
        // Proxy call by default.
        _doProxyCall();
    }
    // slither-disable-next-line locked-ether
    fallback() external payable {
        // Proxy call by default.
        _doProxyCall();
    }
    /// @notice Set the implementation contract address. The code at the given address will execute
    ///         when this contract is called.
    /// @param _implementation Address of the implementation contract.
    function upgradeTo(address _implementation) public virtual proxyCallIfNotAdmin {
        _setImplementation(_implementation);
    }
    /// @notice Set the implementation and call a function in a single transaction. Useful to ensure
    ///         atomic execution of initialization-based upgrades.
    /// @param _implementation Address of the implementation contract.
    /// @param _data           Calldata to delegatecall the new implementation with.
    function upgradeToAndCall(
        address _implementation,
        bytes calldata _data
    )
        public
        payable
        virtual
        proxyCallIfNotAdmin
        returns (bytes memory)
    {
        _setImplementation(_implementation);
        (bool success, bytes memory returndata) = _implementation.delegatecall(_data);
        require(success, "Proxy: delegatecall to new implementation contract failed");
        return returndata;
    }
    /// @notice Changes the owner of the proxy contract. Only callable by the owner.
    /// @param _admin New owner of the proxy contract.
    function changeAdmin(address _admin) public virtual proxyCallIfNotAdmin {
        _changeAdmin(_admin);
    }
    /// @notice Gets the owner of the proxy contract.
    /// @return Owner address.
    function admin() public virtual proxyCallIfNotAdmin returns (address) {
        return _getAdmin();
    }
    //// @notice Queries the implementation address.
    /// @return Implementation address.
    function implementation() public virtual proxyCallIfNotAdmin returns (address) {
        return _getImplementation();
    }
    /// @notice Sets the implementation address.
    /// @param _implementation New implementation address.
    function _setImplementation(address _implementation) internal {
        bytes32 proxyImplementation = Constants.PROXY_IMPLEMENTATION_ADDRESS;
        assembly {
            sstore(proxyImplementation, _implementation)
        }
        emit Upgraded(_implementation);
    }
    /// @notice Changes the owner of the proxy contract.
    /// @param _admin New owner of the proxy contract.
    function _changeAdmin(address _admin) internal {
        address previous = _getAdmin();
        bytes32 proxyOwner = Constants.PROXY_OWNER_ADDRESS;
        assembly {
            sstore(proxyOwner, _admin)
        }
        emit AdminChanged(previous, _admin);
    }
    /// @notice Performs the proxy call via a delegatecall.
    function _doProxyCall() internal {
        address impl = _getImplementation();
        require(impl != address(0), "Proxy: implementation not initialized");
        assembly {
            // Copy calldata into memory at 0x0....calldatasize.
            calldatacopy(0x0, 0x0, calldatasize())
            // Perform the delegatecall, make sure to pass all available gas.
            let success := delegatecall(gas(), impl, 0x0, calldatasize(), 0x0, 0x0)
            // Copy returndata into memory at 0x0....returndatasize. Note that this *will*
            // overwrite the calldata that we just copied into memory but that doesn't really
            // matter because we'll be returning in a second anyway.
            returndatacopy(0x0, 0x0, returndatasize())
            // Success == 0 means a revert. We'll revert too and pass the data up.
            if iszero(success) { revert(0x0, returndatasize()) }
            // Otherwise we'll just return and pass the data up.
            return(0x0, returndatasize())
        }
    }
    /// @notice Queries the implementation address.
    /// @return Implementation address.
    function _getImplementation() internal view returns (address) {
        address impl;
        bytes32 proxyImplementation = Constants.PROXY_IMPLEMENTATION_ADDRESS;
        assembly {
            impl := sload(proxyImplementation)
        }
        return impl;
    }
    /// @notice Queries the owner of the proxy contract.
    /// @return Owner address.
    function _getAdmin() internal view returns (address) {
        address owner;
        bytes32 proxyOwner = Constants.PROXY_OWNER_ADDRESS;
        assembly {
            owner := sload(proxyOwner)
        }
        return owner;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { ResourceMetering } from "../L1/ResourceMetering.sol";
/// @title Constants
/// @notice Constants is a library for storing constants. Simple! Don't put everything in here, just
///         the stuff used in multiple contracts. Constants that only apply to a single contract
///         should be defined in that contract instead.
library Constants {
    /// @notice Special address to be used as the tx origin for gas estimation calls in the
    ///         OptimismPortal and CrossDomainMessenger calls. You only need to use this address if
    ///         the minimum gas limit specified by the user is not actually enough to execute the
    ///         given message and you're attempting to estimate the actual necessary gas limit. We
    ///         use address(1) because it's the ecrecover precompile and therefore guaranteed to
    ///         never have any code on any EVM chain.
    address internal constant ESTIMATION_ADDRESS = address(1);
    /// @notice Value used for the L2 sender storage slot in both the OptimismPortal and the
    ///         CrossDomainMessenger contracts before an actual sender is set. This value is
    ///         non-zero to reduce the gas cost of message passing transactions.
    address internal constant DEFAULT_L2_SENDER = 0x000000000000000000000000000000000000dEaD;
    /// @notice The storage slot that holds the address of a proxy implementation.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)`
    bytes32 internal constant PROXY_IMPLEMENTATION_ADDRESS =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /// @notice The storage slot that holds the address of the owner.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)`
    bytes32 internal constant PROXY_OWNER_ADDRESS = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /// @notice Returns the default values for the ResourceConfig. These are the recommended values
    ///         for a production network.
    function DEFAULT_RESOURCE_CONFIG() internal pure returns (ResourceMetering.ResourceConfig memory) {
        ResourceMetering.ResourceConfig memory config = ResourceMetering.ResourceConfig({
            maxResourceLimit: 20_000_000,
            elasticityMultiplier: 10,
            baseFeeMaxChangeDenominator: 8,
            minimumBaseFee: 1 gwei,
            systemTxMaxGas: 1_000_000,
            maximumBaseFee: type(uint128).max
        });
        return config;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { Burn } from "../libraries/Burn.sol";
import { Arithmetic } from "../libraries/Arithmetic.sol";
/// @custom:upgradeable
/// @title ResourceMetering
/// @notice ResourceMetering implements an EIP-1559 style resource metering system where pricing
///         updates automatically based on current demand.
abstract contract ResourceMetering is Initializable {
    /// @notice Represents the various parameters that control the way in which resources are
    ///         metered. Corresponds to the EIP-1559 resource metering system.
    /// @custom:field prevBaseFee   Base fee from the previous block(s).
    /// @custom:field prevBoughtGas Amount of gas bought so far in the current block.
    /// @custom:field prevBlockNum  Last block number that the base fee was updated.
    struct ResourceParams {
        uint128 prevBaseFee;
        uint64 prevBoughtGas;
        uint64 prevBlockNum;
    }
    /// @notice Represents the configuration for the EIP-1559 based curve for the deposit gas
    ///         market. These values should be set with care as it is possible to set them in
    ///         a way that breaks the deposit gas market. The target resource limit is defined as
    ///         maxResourceLimit / elasticityMultiplier. This struct was designed to fit within a
    ///         single word. There is additional space for additions in the future.
    /// @custom:field maxResourceLimit             Represents the maximum amount of deposit gas that
    ///                                            can be purchased per block.
    /// @custom:field elasticityMultiplier         Determines the target resource limit along with
    ///                                            the resource limit.
    /// @custom:field baseFeeMaxChangeDenominator  Determines max change on fee per block.
    /// @custom:field minimumBaseFee               The min deposit base fee, it is clamped to this
    ///                                            value.
    /// @custom:field systemTxMaxGas               The amount of gas supplied to the system
    ///                                            transaction. This should be set to the same
    ///                                            number that the op-node sets as the gas limit
    ///                                            for the system transaction.
    /// @custom:field maximumBaseFee               The max deposit base fee, it is clamped to this
    ///                                            value.
    struct ResourceConfig {
        uint32 maxResourceLimit;
        uint8 elasticityMultiplier;
        uint8 baseFeeMaxChangeDenominator;
        uint32 minimumBaseFee;
        uint32 systemTxMaxGas;
        uint128 maximumBaseFee;
    }
    /// @notice EIP-1559 style gas parameters.
    ResourceParams public params;
    /// @notice Reserve extra slots (to a total of 50) in the storage layout for future upgrades.
    uint256[48] private __gap;
    /// @notice Meters access to a function based an amount of a requested resource.
    /// @param _amount Amount of the resource requested.
    modifier metered(uint64 _amount) {
        // Record initial gas amount so we can refund for it later.
        uint256 initialGas = gasleft();
        // Run the underlying function.
        _;
        // Run the metering function.
        _metered(_amount, initialGas);
    }
    /// @notice An internal function that holds all of the logic for metering a resource.
    /// @param _amount     Amount of the resource requested.
    /// @param _initialGas The amount of gas before any modifier execution.
    function _metered(uint64 _amount, uint256 _initialGas) internal {
        // Update block number and base fee if necessary.
        uint256 blockDiff = block.number - params.prevBlockNum;
        ResourceConfig memory config = _resourceConfig();
        int256 targetResourceLimit =
            int256(uint256(config.maxResourceLimit)) / int256(uint256(config.elasticityMultiplier));
        if (blockDiff > 0) {
            // Handle updating EIP-1559 style gas parameters. We use EIP-1559 to restrict the rate
            // at which deposits can be created and therefore limit the potential for deposits to
            // spam the L2 system. Fee scheme is very similar to EIP-1559 with minor changes.
            int256 gasUsedDelta = int256(uint256(params.prevBoughtGas)) - targetResourceLimit;
            int256 baseFeeDelta = (int256(uint256(params.prevBaseFee)) * gasUsedDelta)
                / (targetResourceLimit * int256(uint256(config.baseFeeMaxChangeDenominator)));
            // Update base fee by adding the base fee delta and clamp the resulting value between
            // min and max.
            int256 newBaseFee = Arithmetic.clamp({
                _value: int256(uint256(params.prevBaseFee)) + baseFeeDelta,
                _min: int256(uint256(config.minimumBaseFee)),
                _max: int256(uint256(config.maximumBaseFee))
            });
            // If we skipped more than one block, we also need to account for every empty block.
            // Empty block means there was no demand for deposits in that block, so we should
            // reflect this lack of demand in the fee.
            if (blockDiff > 1) {
                // Update the base fee by repeatedly applying the exponent 1-(1/change_denominator)
                // blockDiff - 1 times. Simulates multiple empty blocks. Clamp the resulting value
                // between min and max.
                newBaseFee = Arithmetic.clamp({
                    _value: Arithmetic.cdexp({
                        _coefficient: newBaseFee,
                        _denominator: int256(uint256(config.baseFeeMaxChangeDenominator)),
                        _exponent: int256(blockDiff - 1)
                    }),
                    _min: int256(uint256(config.minimumBaseFee)),
                    _max: int256(uint256(config.maximumBaseFee))
                });
            }
            // Update new base fee, reset bought gas, and update block number.
            params.prevBaseFee = uint128(uint256(newBaseFee));
            params.prevBoughtGas = 0;
            params.prevBlockNum = uint64(block.number);
        }
        // Make sure we can actually buy the resource amount requested by the user.
        params.prevBoughtGas += _amount;
        require(
            int256(uint256(params.prevBoughtGas)) <= int256(uint256(config.maxResourceLimit)),
            "ResourceMetering: cannot buy more gas than available gas limit"
        );
        // Determine the amount of ETH to be paid.
        uint256 resourceCost = uint256(_amount) * uint256(params.prevBaseFee);
        // We currently charge for this ETH amount as an L1 gas burn, so we convert the ETH amount
        // into gas by dividing by the L1 base fee. We assume a minimum base fee of 1 gwei to avoid
        // division by zero for L1s that don't support 1559 or to avoid excessive gas burns during
        // periods of extremely low L1 demand. One-day average gas fee hasn't dipped below 1 gwei
        // during any 1 day period in the last 5 years, so should be fine.
        uint256 gasCost = resourceCost / Math.max(block.basefee, 1 gwei);
        // Give the user a refund based on the amount of gas they used to do all of the work up to
        // this point. Since we're at the end of the modifier, this should be pretty accurate. Acts
        // effectively like a dynamic stipend (with a minimum value).
        uint256 usedGas = _initialGas - gasleft();
        if (gasCost > usedGas) {
            Burn.gas(gasCost - usedGas);
        }
    }
    /// @notice Virtual function that returns the resource config.
    ///         Contracts that inherit this contract must implement this function.
    /// @return ResourceConfig
    function _resourceConfig() internal virtual returns (ResourceConfig memory);
    /// @notice Sets initial resource parameter values.
    ///         This function must either be called by the initializer function of an upgradeable
    ///         child contract.
    // solhint-disable-next-line func-name-mixedcase
    function __ResourceMetering_init() internal onlyInitializing {
        params = ResourceParams({ prevBaseFee: 1 gwei, prevBoughtGas: 0, prevBlockNum: uint64(block.number) });
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/Address.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!Address.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }
    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }
    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);
            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////
            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }
            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)
                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)
                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }
            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;
            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;
            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256
            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }
    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }
    /**
     * @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`.
        // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`.
        // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`.
        // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a
        // good first aproximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1;
        uint256 x = a;
        if (x >> 128 > 0) {
            x >>= 128;
            result <<= 64;
        }
        if (x >> 64 > 0) {
            x >>= 64;
            result <<= 32;
        }
        if (x >> 32 > 0) {
            x >>= 32;
            result <<= 16;
        }
        if (x >> 16 > 0) {
            x >>= 16;
            result <<= 8;
        }
        if (x >> 8 > 0) {
            x >>= 8;
            result <<= 4;
        }
        if (x >> 4 > 0) {
            x >>= 4;
            result <<= 2;
        }
        if (x >> 2 > 0) {
            result <<= 1;
        }
        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }
    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        uint256 result = sqrt(a);
        if (rounding == Rounding.Up && result * result < a) {
            result += 1;
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @title Burn
/// @notice Utilities for burning stuff.
library Burn {
    /// @notice Burns a given amount of ETH.
    /// @param _amount Amount of ETH to burn.
    function eth(uint256 _amount) internal {
        new Burner{ value: _amount }();
    }
    /// @notice Burns a given amount of gas.
    /// @param _amount Amount of gas to burn.
    function gas(uint256 _amount) internal view {
        uint256 i = 0;
        uint256 initialGas = gasleft();
        while (initialGas - gasleft() < _amount) {
            ++i;
        }
    }
}
/// @title Burner
/// @notice Burner self-destructs on creation and sends all ETH to itself, removing all ETH given to
///         the contract from the circulating supply. Self-destructing is the only way to remove ETH
///         from the circulating supply.
contract Burner {
    constructor() payable {
        selfdestruct(payable(address(this)));
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { SignedMath } from "@openzeppelin/contracts/utils/math/SignedMath.sol";
import { FixedPointMathLib } from "@rari-capital/solmate/src/utils/FixedPointMathLib.sol";
/// @title Arithmetic
/// @notice Even more math than before.
library Arithmetic {
    /// @notice Clamps a value between a minimum and maximum.
    /// @param _value The value to clamp.
    /// @param _min   The minimum value.
    /// @param _max   The maximum value.
    /// @return The clamped value.
    function clamp(int256 _value, int256 _min, int256 _max) internal pure returns (int256) {
        return SignedMath.min(SignedMath.max(_value, _min), _max);
    }
    /// @notice (c)oefficient (d)enominator (exp)onentiation function.
    ///         Returns the result of: c * (1 - 1/d)^exp.
    /// @param _coefficient Coefficient of the function.
    /// @param _denominator Fractional denominator.
    /// @param _exponent    Power function exponent.
    /// @return Result of c * (1 - 1/d)^exp.
    function cdexp(int256 _coefficient, int256 _denominator, int256 _exponent) internal pure returns (int256) {
        return (_coefficient * (FixedPointMathLib.powWad(1e18 - (1e18 / _denominator), _exponent * 1e18))) / 1e18;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library 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
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev 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) {
        require(isContract(target), "Address: delegate call to non-contract");
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.
    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }
    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
        return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0.
    }
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return 0;
            // When the result is > (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 (x >= 135305999368893231589) revert("EXP_OVERFLOW");
            // 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;
            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));
        }
    }
    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            require(x > 0, "UNDEFINED");
            // 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.
            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            int256 k = int256(log2(uint256(x))) - 96;
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);
            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);
            // 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.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }
            // r 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
            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }
    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // Divide z by the denominator.
            z := div(z, denominator)
        }
    }
    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // First, divide z - 1 by the denominator and add 1.
            // We allow z - 1 to underflow if z is 0, because we multiply the
            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
        }
    }
    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }
                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)
                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }
                    // Store x squared.
                    let xx := mul(x, x)
                    // Round to the nearest number.
                    let xxRound := add(xx, half)
                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }
                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)
                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)
                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }
                        // Round to the nearest number.
                        let zxRound := add(zx, half)
                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }
                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }
    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.
            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.
            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, 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(y, 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }
    function log2(uint256 x) internal pure returns (uint256 r) {
        require(x > 0, "UNDEFINED");
        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))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { SafeCall } from "src/libraries/SafeCall.sol";
import { DisputeGameFactory, IDisputeGame } from "src/dispute/DisputeGameFactory.sol";
import { SystemConfig } from "src/L1/SystemConfig.sol";
import { SuperchainConfig } from "src/L1/SuperchainConfig.sol";
import { Constants } from "src/libraries/Constants.sol";
import { Types } from "src/libraries/Types.sol";
import { Hashing } from "src/libraries/Hashing.sol";
import { SecureMerkleTrie } from "src/libraries/trie/SecureMerkleTrie.sol";
import { AddressAliasHelper } from "src/vendor/AddressAliasHelper.sol";
import { ResourceMetering } from "src/L1/ResourceMetering.sol";
import { ISemver } from "src/universal/ISemver.sol";
import { Constants } from "src/libraries/Constants.sol";
import "src/libraries/PortalErrors.sol";
import "src/dispute/lib/Types.sol";
/// @custom:proxied
/// @title OptimismPortal2
/// @notice The OptimismPortal is a low-level contract responsible for passing messages between L1
///         and L2. Messages sent directly to the OptimismPortal have no form of replayability.
///         Users are encouraged to use the L1CrossDomainMessenger for a higher-level interface.
contract OptimismPortal2 is Initializable, ResourceMetering, ISemver {
    /// @notice Represents a proven withdrawal.
    /// @custom:field disputeGameProxy The address of the dispute game proxy that the withdrawal was proven against.
    /// @custom:field timestamp        Timestamp at whcih the withdrawal was proven.
    struct ProvenWithdrawal {
        IDisputeGame disputeGameProxy;
        uint64 timestamp;
    }
    /// @notice The delay between when a withdrawal transaction is proven and when it may be finalized.
    uint256 internal immutable PROOF_MATURITY_DELAY_SECONDS;
    /// @notice The delay between when a dispute game is resolved and when a withdrawal proven against it may be
    ///         finalized.
    uint256 internal immutable DISPUTE_GAME_FINALITY_DELAY_SECONDS;
    /// @notice Version of the deposit event.
    uint256 internal constant DEPOSIT_VERSION = 0;
    /// @notice The L2 gas limit set when eth is deposited using the receive() function.
    uint64 internal constant RECEIVE_DEFAULT_GAS_LIMIT = 100_000;
    /// @notice Address of the L2 account which initiated a withdrawal in this transaction.
    ///         If the of this variable is the default L2 sender address, then we are NOT inside of
    ///         a call to finalizeWithdrawalTransaction.
    address public l2Sender;
    /// @notice A list of withdrawal hashes which have been successfully finalized.
    mapping(bytes32 => bool) public finalizedWithdrawals;
    /// @custom:legacy
    /// @custom:spacer provenWithdrawals
    /// @notice Spacer taking up the legacy `provenWithdrawals` mapping slot.
    bytes32 private spacer_52_0_32;
    /// @custom:legacy
    /// @custom:spacer paused
    /// @notice Spacer for backwards compatibility.
    bool private spacer_53_0_1;
    /// @notice Contract of the Superchain Config.
    SuperchainConfig public superchainConfig;
    /// @custom:legacy
    /// @custom:spacer l2Oracle
    /// @notice Spacer taking up the legacy `l2Oracle` address slot.
    address private spacer_54_0_20;
    /// @notice Contract of the SystemConfig.
    /// @custom:network-specific
    SystemConfig public systemConfig;
    /// @notice Address of the DisputeGameFactory.
    /// @custom:network-specific
    DisputeGameFactory public disputeGameFactory;
    /// @notice A mapping of withdrawal hashes to proof submitters to `ProvenWithdrawal` data.
    mapping(bytes32 => mapping(address => ProvenWithdrawal)) public provenWithdrawals;
    /// @notice A mapping of dispute game addresses to whether or not they are blacklisted.
    mapping(IDisputeGame => bool) public disputeGameBlacklist;
    /// @notice The game type that the OptimismPortal consults for output proposals.
    GameType public respectedGameType;
    /// @notice The timestamp at which the respected game type was last updated.
    uint64 public respectedGameTypeUpdatedAt;
    /// @notice Mapping of withdrawal hashes to addresses that have submitted a proof for the withdrawal.
    mapping(bytes32 => address[]) public proofSubmitters;
    /// @custom:spacer _balance (custom gas token)
    /// @notice Spacer for forwards compatibility.
    bytes32 private spacer_61_0_32;
    /// @notice Emitted when a transaction is deposited from L1 to L2.
    ///         The parameters of this event are read by the rollup node and used to derive deposit
    ///         transactions on L2.
    /// @param from       Address that triggered the deposit transaction.
    /// @param to         Address that the deposit transaction is directed to.
    /// @param version    Version of this deposit transaction event.
    /// @param opaqueData ABI encoded deposit data to be parsed off-chain.
    event TransactionDeposited(address indexed from, address indexed to, uint256 indexed version, bytes opaqueData);
    /// @notice Emitted when a withdrawal transaction is proven.
    /// @param withdrawalHash Hash of the withdrawal transaction.
    /// @param from           Address that triggered the withdrawal transaction.
    /// @param to             Address that the withdrawal transaction is directed to.
    event WithdrawalProven(bytes32 indexed withdrawalHash, address indexed from, address indexed to);
    /// @notice Emitted when a withdrawal transaction is proven. Exists as a separate event to allow for backwards
    ///         compatibility for tooling that observes the `WithdrawalProven` event.
    /// @param withdrawalHash Hash of the withdrawal transaction.
    /// @param proofSubmitter Address of the proof submitter.
    event WithdrawalProvenExtension1(bytes32 indexed withdrawalHash, address indexed proofSubmitter);
    /// @notice Emitted when a withdrawal transaction is finalized.
    /// @param withdrawalHash Hash of the withdrawal transaction.
    /// @param success        Whether the withdrawal transaction was successful.
    event WithdrawalFinalized(bytes32 indexed withdrawalHash, bool success);
    /// @notice Emitted when a dispute game is blacklisted by the Guardian.
    /// @param disputeGame Address of the dispute game that was blacklisted.
    event DisputeGameBlacklisted(IDisputeGame indexed disputeGame);
    /// @notice Emitted when the Guardian changes the respected game type in the portal.
    /// @param newGameType The new respected game type.
    /// @param updatedAt   The timestamp at which the respected game type was updated.
    event RespectedGameTypeSet(GameType indexed newGameType, Timestamp indexed updatedAt);
    /// @notice Reverts when paused.
    modifier whenNotPaused() {
        if (paused()) revert CallPaused();
        _;
    }
    /// @notice Semantic version.
    /// @custom:semver 3.10.0
    string public constant version = "3.10.0";
    /// @notice Constructs the OptimismPortal contract.
    constructor(uint256 _proofMaturityDelaySeconds, uint256 _disputeGameFinalityDelaySeconds) {
        PROOF_MATURITY_DELAY_SECONDS = _proofMaturityDelaySeconds;
        DISPUTE_GAME_FINALITY_DELAY_SECONDS = _disputeGameFinalityDelaySeconds;
        initialize({
            _disputeGameFactory: DisputeGameFactory(address(0)),
            _systemConfig: SystemConfig(address(0)),
            _superchainConfig: SuperchainConfig(address(0)),
            _initialRespectedGameType: GameType.wrap(0)
        });
    }
    /// @notice Initializer.
    /// @param _disputeGameFactory Contract of the DisputeGameFactory.
    /// @param _systemConfig Contract of the SystemConfig.
    /// @param _superchainConfig Contract of the SuperchainConfig.
    function initialize(
        DisputeGameFactory _disputeGameFactory,
        SystemConfig _systemConfig,
        SuperchainConfig _superchainConfig,
        GameType _initialRespectedGameType
    )
        public
        initializer
    {
        disputeGameFactory = _disputeGameFactory;
        systemConfig = _systemConfig;
        superchainConfig = _superchainConfig;
        // Set the `l2Sender` slot, only if it is currently empty. This signals the first initialization of the
        // contract.
        if (l2Sender == address(0)) {
            l2Sender = Constants.DEFAULT_L2_SENDER;
            // Set the `respectedGameTypeUpdatedAt` timestamp, to ignore all games of the respected type prior
            // to this operation.
            respectedGameTypeUpdatedAt = uint64(block.timestamp);
            // Set the initial respected game type
            respectedGameType = _initialRespectedGameType;
        }
        __ResourceMetering_init();
    }
    /// @notice Getter function for the address of the guardian.
    ///         Public getter is legacy and will be removed in the future. Use `SuperchainConfig.guardian()` instead.
    /// @return Address of the guardian.
    /// @custom:legacy
    function guardian() public view returns (address) {
        return superchainConfig.guardian();
    }
    /// @notice Getter for the current paused status.
    function paused() public view returns (bool) {
        return superchainConfig.paused();
    }
    /// @notice Getter for the proof maturity delay.
    function proofMaturityDelaySeconds() public view returns (uint256) {
        return PROOF_MATURITY_DELAY_SECONDS;
    }
    /// @notice Getter for the dispute game finality delay.
    function disputeGameFinalityDelaySeconds() public view returns (uint256) {
        return DISPUTE_GAME_FINALITY_DELAY_SECONDS;
    }
    /// @notice Computes the minimum gas limit for a deposit.
    ///         The minimum gas limit linearly increases based on the size of the calldata.
    ///         This is to prevent users from creating L2 resource usage without paying for it.
    ///         This function can be used when interacting with the portal to ensure forwards
    ///         compatibility.
    /// @param _byteCount Number of bytes in the calldata.
    /// @return The minimum gas limit for a deposit.
    function minimumGasLimit(uint64 _byteCount) public pure returns (uint64) {
        return _byteCount * 16 + 21000;
    }
    /// @notice Accepts value so that users can send ETH directly to this contract and have the
    ///         funds be deposited to their address on L2. This is intended as a convenience
    ///         function for EOAs. Contracts should call the depositTransaction() function directly
    ///         otherwise any deposited funds will be lost due to address aliasing.
    receive() external payable {
        depositTransaction(msg.sender, msg.value, RECEIVE_DEFAULT_GAS_LIMIT, false, bytes(""));
    }
    /// @notice Accepts ETH value without triggering a deposit to L2.
    ///         This function mainly exists for the sake of the migration between the legacy
    ///         Optimism system and Bedrock.
    function donateETH() external payable {
        // Intentionally empty.
    }
    /// @notice Getter for the resource config.
    ///         Used internally by the ResourceMetering contract.
    ///         The SystemConfig is the source of truth for the resource config.
    /// @return ResourceMetering ResourceConfig
    function _resourceConfig() internal view override returns (ResourceMetering.ResourceConfig memory) {
        return systemConfig.resourceConfig();
    }
    /// @notice Proves a withdrawal transaction.
    /// @param _tx               Withdrawal transaction to finalize.
    /// @param _disputeGameIndex Index of the dispute game to prove the withdrawal against.
    /// @param _outputRootProof  Inclusion proof of the L2ToL1MessagePasser contract's storage root.
    /// @param _withdrawalProof  Inclusion proof of the withdrawal in L2ToL1MessagePasser contract.
    function proveWithdrawalTransaction(
        Types.WithdrawalTransaction memory _tx,
        uint256 _disputeGameIndex,
        Types.OutputRootProof calldata _outputRootProof,
        bytes[] calldata _withdrawalProof
    )
        external
        whenNotPaused
    {
        // Prevent users from creating a deposit transaction where this address is the message
        // sender on L2. Because this is checked here, we do not need to check again in
        // `finalizeWithdrawalTransaction`.
        require(_tx.target != address(this), "OptimismPortal: you cannot send messages to the portal contract");
        // Fetch the dispute game proxy from the `DisputeGameFactory` contract.
        (GameType gameType,, IDisputeGame gameProxy) = disputeGameFactory.gameAtIndex(_disputeGameIndex);
        Claim outputRoot = gameProxy.rootClaim();
        // The game type of the dispute game must be the respected game type.
        require(gameType.raw() == respectedGameType.raw(), "OptimismPortal: invalid game type");
        // Verify that the output root can be generated with the elements in the proof.
        require(
            outputRoot.raw() == Hashing.hashOutputRootProof(_outputRootProof),
            "OptimismPortal: invalid output root proof"
        );
        // Load the ProvenWithdrawal into memory, using the withdrawal hash as a unique identifier.
        bytes32 withdrawalHash = Hashing.hashWithdrawal(_tx);
        // We do not allow for proving withdrawals against dispute games that have resolved against the favor
        // of the root claim.
        require(
            gameProxy.status() != GameStatus.CHALLENGER_WINS,
            "OptimismPortal: cannot prove against invalid dispute games"
        );
        // Compute the storage slot of the withdrawal hash in the L2ToL1MessagePasser contract.
        // Refer to the Solidity documentation for more information on how storage layouts are
        // computed for mappings.
        bytes32 storageKey = keccak256(
            abi.encode(
                withdrawalHash,
                uint256(0) // The withdrawals mapping is at the first slot in the layout.
            )
        );
        // Verify that the hash of this withdrawal was stored in the L2toL1MessagePasser contract
        // on L2. If this is true, under the assumption that the SecureMerkleTrie does not have
        // bugs, then we know that this withdrawal was actually triggered on L2 and can therefore
        // be relayed on L1.
        require(
            SecureMerkleTrie.verifyInclusionProof({
                _key: abi.encode(storageKey),
                _value: hex"01",
                _proof: _withdrawalProof,
                _root: _outputRootProof.messagePasserStorageRoot
            }),
            "OptimismPortal: invalid withdrawal inclusion proof"
        );
        // Designate the withdrawalHash as proven by storing the `disputeGameProxy` & `timestamp` in the
        // `provenWithdrawals` mapping. A `withdrawalHash` can only be proven once unless the dispute game it proved
        // against resolves against the favor of the root claim.
        provenWithdrawals[withdrawalHash][msg.sender] =
            ProvenWithdrawal({ disputeGameProxy: gameProxy, timestamp: uint64(block.timestamp) });
        // Emit a `WithdrawalProven` event.
        emit WithdrawalProven(withdrawalHash, _tx.sender, _tx.target);
        // Emit a `WithdrawalProvenExtension1` event.
        emit WithdrawalProvenExtension1(withdrawalHash, msg.sender);
        // Add the proof submitter to the list of proof submitters for this withdrawal hash.
        proofSubmitters[withdrawalHash].push(msg.sender);
    }
    /// @notice Finalizes a withdrawal transaction.
    /// @param _tx Withdrawal transaction to finalize.
    function finalizeWithdrawalTransaction(Types.WithdrawalTransaction memory _tx) external whenNotPaused {
        finalizeWithdrawalTransactionExternalProof(_tx, msg.sender);
    }
    /// @notice Finalizes a withdrawal transaction, using an external proof submitter.
    /// @param _tx Withdrawal transaction to finalize.
    /// @param _proofSubmitter Address of the proof submitter.
    function finalizeWithdrawalTransactionExternalProof(
        Types.WithdrawalTransaction memory _tx,
        address _proofSubmitter
    )
        public
        whenNotPaused
    {
        // Make sure that the l2Sender has not yet been set. The l2Sender is set to a value other
        // than the default value when a withdrawal transaction is being finalized. This check is
        // a defacto reentrancy guard.
        require(
            l2Sender == Constants.DEFAULT_L2_SENDER, "OptimismPortal: can only trigger one withdrawal per transaction"
        );
        // Compute the withdrawal hash.
        bytes32 withdrawalHash = Hashing.hashWithdrawal(_tx);
        // Check that the withdrawal can be finalized.
        checkWithdrawal(withdrawalHash, _proofSubmitter);
        // Mark the withdrawal as finalized so it can't be replayed.
        finalizedWithdrawals[withdrawalHash] = true;
        // Set the l2Sender so contracts know who triggered this withdrawal on L2.
        l2Sender = _tx.sender;
        // Trigger the call to the target contract. We use a custom low level method
        // SafeCall.callWithMinGas to ensure two key properties
        //   1. Target contracts cannot force this call to run out of gas by returning a very large
        //      amount of data (and this is OK because we don't care about the returndata here).
        //   2. The amount of gas provided to the execution context of the target is at least the
        //      gas limit specified by the user. If there is not enough gas in the current context
        //      to accomplish this, `callWithMinGas` will revert.
        bool success = SafeCall.callWithMinGas(_tx.target, _tx.gasLimit, _tx.value, _tx.data);
        // Reset the l2Sender back to the default value.
        l2Sender = Constants.DEFAULT_L2_SENDER;
        // All withdrawals are immediately finalized. Replayability can
        // be achieved through contracts built on top of this contract
        emit WithdrawalFinalized(withdrawalHash, success);
        // Reverting here is useful for determining the exact gas cost to successfully execute the
        // sub call to the target contract if the minimum gas limit specified by the user would not
        // be sufficient to execute the sub call.
        if (!success && tx.origin == Constants.ESTIMATION_ADDRESS) {
            revert GasEstimation();
        }
    }
    /// @notice Accepts deposits of ETH and data, and emits a TransactionDeposited event for use in
    ///         deriving deposit transactions. Note that if a deposit is made by a contract, its
    ///         address will be aliased when retrieved using `tx.origin` or `msg.sender`. Consider
    ///         using the CrossDomainMessenger contracts for a simpler developer experience.
    /// @param _to         Target address on L2.
    /// @param _value      ETH value to send to the recipient.
    /// @param _gasLimit   Amount of L2 gas to purchase by burning gas on L1.
    /// @param _isCreation Whether or not the transaction is a contract creation.
    /// @param _data       Data to trigger the recipient with.
    function depositTransaction(
        address _to,
        uint256 _value,
        uint64 _gasLimit,
        bool _isCreation,
        bytes memory _data
    )
        public
        payable
        metered(_gasLimit)
    {
        // Just to be safe, make sure that people specify address(0) as the target when doing
        // contract creations.
        if (_isCreation && _to != address(0)) revert BadTarget();
        // Prevent depositing transactions that have too small of a gas limit. Users should pay
        // more for more resource usage.
        if (_gasLimit < minimumGasLimit(uint64(_data.length))) revert SmallGasLimit();
        // Prevent the creation of deposit transactions that have too much calldata. This gives an
        // upper limit on the size of unsafe blocks over the p2p network. 120kb is chosen to ensure
        // that the transaction can fit into the p2p network policy of 128kb even though deposit
        // transactions are not gossipped over the p2p network.
        if (_data.length > 120_000) revert LargeCalldata();
        // Transform the from-address to its alias if the caller is a contract.
        address from = msg.sender;
        if (msg.sender != tx.origin) {
            from = AddressAliasHelper.applyL1ToL2Alias(msg.sender);
        }
        // Compute the opaque data that will be emitted as part of the TransactionDeposited event.
        // We use opaque data so that we can update the TransactionDeposited event in the future
        // without breaking the current interface.
        bytes memory opaqueData = abi.encodePacked(msg.value, _value, _gasLimit, _isCreation, _data);
        // Emit a TransactionDeposited event so that the rollup node can derive a deposit
        // transaction for this deposit.
        emit TransactionDeposited(from, _to, DEPOSIT_VERSION, opaqueData);
    }
    /// @notice Blacklists a dispute game. Should only be used in the event that a dispute game resolves incorrectly.
    /// @param _disputeGame Dispute game to blacklist.
    function blacklistDisputeGame(IDisputeGame _disputeGame) external {
        if (msg.sender != guardian()) revert Unauthorized();
        disputeGameBlacklist[_disputeGame] = true;
        emit DisputeGameBlacklisted(_disputeGame);
    }
    /// @notice Sets the respected game type. Changing this value can alter the security properties of the system,
    ///         depending on the new game's behavior.
    /// @param _gameType The game type to consult for output proposals.
    function setRespectedGameType(GameType _gameType) external {
        if (msg.sender != guardian()) revert Unauthorized();
        respectedGameType = _gameType;
        respectedGameTypeUpdatedAt = uint64(block.timestamp);
        emit RespectedGameTypeSet(_gameType, Timestamp.wrap(respectedGameTypeUpdatedAt));
    }
    /// @notice Checks if a withdrawal can be finalized. This function will revert if the withdrawal cannot be
    ///         finalized, and otherwise has no side-effects.
    /// @param _withdrawalHash Hash of the withdrawal to check.
    /// @param _proofSubmitter The submitter of the proof for the withdrawal hash
    function checkWithdrawal(bytes32 _withdrawalHash, address _proofSubmitter) public view {
        ProvenWithdrawal memory provenWithdrawal = provenWithdrawals[_withdrawalHash][_proofSubmitter];
        IDisputeGame disputeGameProxy = provenWithdrawal.disputeGameProxy;
        // The dispute game must not be blacklisted.
        require(!disputeGameBlacklist[disputeGameProxy], "OptimismPortal: dispute game has been blacklisted");
        // A withdrawal can only be finalized if it has been proven. We know that a withdrawal has
        // been proven at least once when its timestamp is non-zero. Unproven withdrawals will have
        // a timestamp of zero.
        require(
            provenWithdrawal.timestamp != 0,
            "OptimismPortal: withdrawal has not been proven by proof submitter address yet"
        );
        uint64 createdAt = disputeGameProxy.createdAt().raw();
        // As a sanity check, we make sure that the proven withdrawal's timestamp is greater than
        // starting timestamp inside the Dispute Game. Not strictly necessary but extra layer of
        // safety against weird bugs in the proving step.
        require(
            provenWithdrawal.timestamp > createdAt,
            "OptimismPortal: withdrawal timestamp less than dispute game creation timestamp"
        );
        // A proven withdrawal must wait at least `PROOF_MATURITY_DELAY_SECONDS` before finalizing.
        require(
            block.timestamp - provenWithdrawal.timestamp > PROOF_MATURITY_DELAY_SECONDS,
            "OptimismPortal: proven withdrawal has not matured yet"
        );
        // A proven withdrawal must wait until the dispute game it was proven against has been
        // resolved in favor of the root claim (the output proposal). This is to prevent users
        // from finalizing withdrawals proven against non-finalized output roots.
        require(
            disputeGameProxy.status() == GameStatus.DEFENDER_WINS,
            "OptimismPortal: output proposal has not been validated"
        );
        // The game type of the dispute game must be the respected game type. This was also checked in
        // `proveWithdrawalTransaction`, but we check it again in case the respected game type has changed since
        // the withdrawal was proven.
        require(disputeGameProxy.gameType().raw() == respectedGameType.raw(), "OptimismPortal: invalid game type");
        // The game must have been created after `respectedGameTypeUpdatedAt`. This is to prevent users from creating
        // invalid disputes against a deployed game type while the off-chain challenge agents are not watching.
        require(
            createdAt >= respectedGameTypeUpdatedAt,
            "OptimismPortal: dispute game created before respected game type was updated"
        );
        // Before a withdrawal can be finalized, the dispute game it was proven against must have been
        // resolved for at least `DISPUTE_GAME_FINALITY_DELAY_SECONDS`. This is to allow for manual
        // intervention in the event that a dispute game is resolved incorrectly.
        require(
            block.timestamp - disputeGameProxy.resolvedAt().raw() > DISPUTE_GAME_FINALITY_DELAY_SECONDS,
            "OptimismPortal: output proposal in air-gap"
        );
        // Check that this withdrawal has not already been finalized, this is replay protection.
        require(!finalizedWithdrawals[_withdrawalHash], "OptimismPortal: withdrawal has already been finalized");
    }
    /// @notice External getter for the number of proof submitters for a withdrawal hash.
    /// @param _withdrawalHash Hash of the withdrawal.
    /// @return The number of proof submitters for the withdrawal hash.
    function numProofSubmitters(bytes32 _withdrawalHash) external view returns (uint256) {
        return proofSubmitters[_withdrawalHash].length;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/Address.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!Address.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @title SafeCall
/// @notice Perform low level safe calls
library SafeCall {
    /// @notice Performs a low level call without copying any returndata.
    /// @dev Passes no calldata to the call context.
    /// @param _target   Address to call
    /// @param _gas      Amount of gas to pass to the call
    /// @param _value    Amount of value to pass to the call
    function send(address _target, uint256 _gas, uint256 _value) internal returns (bool) {
        bool _success;
        assembly {
            _success :=
                call(
                    _gas, // gas
                    _target, // recipient
                    _value, // ether value
                    0, // inloc
                    0, // inlen
                    0, // outloc
                    0 // outlen
                )
        }
        return _success;
    }
    /// @notice Perform a low level call without copying any returndata
    /// @param _target   Address to call
    /// @param _gas      Amount of gas to pass to the call
    /// @param _value    Amount of value to pass to the call
    /// @param _calldata Calldata to pass to the call
    function call(address _target, uint256 _gas, uint256 _value, bytes memory _calldata) internal returns (bool) {
        bool _success;
        assembly {
            _success :=
                call(
                    _gas, // gas
                    _target, // recipient
                    _value, // ether value
                    add(_calldata, 32), // inloc
                    mload(_calldata), // inlen
                    0, // outloc
                    0 // outlen
                )
        }
        return _success;
    }
    /// @notice Helper function to determine if there is sufficient gas remaining within the context
    ///         to guarantee that the minimum gas requirement for a call will be met as well as
    ///         optionally reserving a specified amount of gas for after the call has concluded.
    /// @param _minGas      The minimum amount of gas that may be passed to the target context.
    /// @param _reservedGas Optional amount of gas to reserve for the caller after the execution
    ///                     of the target context.
    /// @return `true` if there is enough gas remaining to safely supply `_minGas` to the target
    ///         context as well as reserve `_reservedGas` for the caller after the execution of
    ///         the target context.
    /// @dev !!!!! FOOTGUN ALERT !!!!!
    ///      1.) The 40_000 base buffer is to account for the worst case of the dynamic cost of the
    ///          `CALL` opcode's `address_access_cost`, `positive_value_cost`, and
    ///          `value_to_empty_account_cost` factors with an added buffer of 5,700 gas. It is
    ///          still possible to self-rekt by initiating a withdrawal with a minimum gas limit
    ///          that does not account for the `memory_expansion_cost` & `code_execution_cost`
    ///          factors of the dynamic cost of the `CALL` opcode.
    ///      2.) This function should *directly* precede the external call if possible. There is an
    ///          added buffer to account for gas consumed between this check and the call, but it
    ///          is only 5,700 gas.
    ///      3.) Because EIP-150 ensures that a maximum of 63/64ths of the remaining gas in the call
    ///          frame may be passed to a subcontext, we need to ensure that the gas will not be
    ///          truncated.
    ///      4.) Use wisely. This function is not a silver bullet.
    function hasMinGas(uint256 _minGas, uint256 _reservedGas) internal view returns (bool) {
        bool _hasMinGas;
        assembly {
            // Equation: gas × 63 ≥ minGas × 64 + 63(40_000 + reservedGas)
            _hasMinGas := iszero(lt(mul(gas(), 63), add(mul(_minGas, 64), mul(add(40000, _reservedGas), 63))))
        }
        return _hasMinGas;
    }
    /// @notice Perform a low level call without copying any returndata. This function
    ///         will revert if the call cannot be performed with the specified minimum
    ///         gas.
    /// @param _target   Address to call
    /// @param _minGas   The minimum amount of gas that may be passed to the call
    /// @param _value    Amount of value to pass to the call
    /// @param _calldata Calldata to pass to the call
    function callWithMinGas(
        address _target,
        uint256 _minGas,
        uint256 _value,
        bytes memory _calldata
    )
        internal
        returns (bool)
    {
        bool _success;
        bool _hasMinGas = hasMinGas(_minGas, 0);
        assembly {
            // Assertion: gasleft() >= (_minGas * 64) / 63 + 40_000
            if iszero(_hasMinGas) {
                // Store the "Error(string)" selector in scratch space.
                mstore(0, 0x08c379a0)
                // Store the pointer to the string length in scratch space.
                mstore(32, 32)
                // Store the string.
                //
                // SAFETY:
                // - We pad the beginning of the string with two zero bytes as well as the
                // length (24) to ensure that we override the free memory pointer at offset
                // 0x40. This is necessary because the free memory pointer is likely to
                // be greater than 1 byte when this function is called, but it is incredibly
                // unlikely that it will be greater than 3 bytes. As for the data within
                // 0x60, it is ensured that it is 0 due to 0x60 being the zero offset.
                // - It's fine to clobber the free memory pointer, we're reverting.
                mstore(88, 0x0000185361666543616c6c3a204e6f7420656e6f75676820676173)
                // Revert with 'Error("SafeCall: Not enough gas")'
                revert(28, 100)
            }
            // The call will be supplied at least ((_minGas * 64) / 63) gas due to the
            // above assertion. This ensures that, in all circumstances (except for when the
            // `_minGas` does not account for the `memory_expansion_cost` and `code_execution_cost`
            // factors of the dynamic cost of the `CALL` opcode), the call will receive at least
            // the minimum amount of gas specified.
            _success :=
                call(
                    gas(), // gas
                    _target, // recipient
                    _value, // ether value
                    add(_calldata, 32), // inloc
                    mload(_calldata), // inlen
                    0x00, // outloc
                    0x00 // outlen
                )
        }
        return _success;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { LibClone } from "@solady/utils/LibClone.sol";
import { OwnableUpgradeable } from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import { ISemver } from "src/universal/ISemver.sol";
import { IDisputeGame } from "src/dispute/interfaces/IDisputeGame.sol";
import { IDisputeGameFactory } from "src/dispute/interfaces/IDisputeGameFactory.sol";
import "src/dispute/lib/Types.sol";
import "src/dispute/lib/Errors.sol";
/// @title DisputeGameFactory
/// @notice A factory contract for creating `IDisputeGame` contracts. All created dispute games are stored in both a
///         mapping and an append only array. The timestamp of the creation time of the dispute game is packed tightly
///         into the storage slot with the address of the dispute game to make offchain discoverability of playable
///         dispute games easier.
contract DisputeGameFactory is OwnableUpgradeable, IDisputeGameFactory, ISemver {
    /// @dev Allows for the creation of clone proxies with immutable arguments.
    using LibClone for address;
    /// @notice Semantic version.
    /// @custom:semver 1.0.0
    string public constant version = "1.0.0";
    /// @inheritdoc IDisputeGameFactory
    mapping(GameType => IDisputeGame) public gameImpls;
    /// @inheritdoc IDisputeGameFactory
    mapping(GameType => uint256) public initBonds;
    /// @notice Mapping of a hash of `gameType || rootClaim || extraData` to the deployed `IDisputeGame` clone (where
    //          `||` denotes concatenation).
    mapping(Hash => GameId) internal _disputeGames;
    /// @notice An append-only array of disputeGames that have been created. Used by offchain game solvers to
    ///         efficiently track dispute games.
    GameId[] internal _disputeGameList;
    /// @notice Constructs a new DisputeGameFactory contract.
    constructor() OwnableUpgradeable() {
        initialize(address(0));
    }
    /// @notice Initializes the contract.
    /// @param _owner The owner of the contract.
    function initialize(address _owner) public initializer {
        __Ownable_init();
        _transferOwnership(_owner);
    }
    /// @inheritdoc IDisputeGameFactory
    function gameCount() external view returns (uint256 gameCount_) {
        gameCount_ = _disputeGameList.length;
    }
    /// @inheritdoc IDisputeGameFactory
    function games(
        GameType _gameType,
        Claim _rootClaim,
        bytes calldata _extraData
    )
        external
        view
        returns (IDisputeGame proxy_, Timestamp timestamp_)
    {
        Hash uuid = getGameUUID(_gameType, _rootClaim, _extraData);
        (, Timestamp timestamp, address proxy) = _disputeGames[uuid].unpack();
        (proxy_, timestamp_) = (IDisputeGame(proxy), timestamp);
    }
    /// @inheritdoc IDisputeGameFactory
    function gameAtIndex(uint256 _index)
        external
        view
        returns (GameType gameType_, Timestamp timestamp_, IDisputeGame proxy_)
    {
        (GameType gameType, Timestamp timestamp, address proxy) = _disputeGameList[_index].unpack();
        (gameType_, timestamp_, proxy_) = (gameType, timestamp, IDisputeGame(proxy));
    }
    /// @inheritdoc IDisputeGameFactory
    function create(
        GameType _gameType,
        Claim _rootClaim,
        bytes calldata _extraData
    )
        external
        payable
        returns (IDisputeGame proxy_)
    {
        // Grab the implementation contract for the given `GameType`.
        IDisputeGame impl = gameImpls[_gameType];
        // If there is no implementation to clone for the given `GameType`, revert.
        if (address(impl) == address(0)) revert NoImplementation(_gameType);
        // If the required initialization bond is not met, revert.
        if (msg.value != initBonds[_gameType]) revert IncorrectBondAmount();
        // Get the hash of the parent block.
        bytes32 parentHash = blockhash(block.number - 1);
        // Clone the implementation contract and initialize it with the given parameters.
        //
        // CWIA Calldata Layout:
        // ┌──────────────┬────────────────────────────────────┐
        // │    Bytes     │            Description             │
        // ├──────────────┼────────────────────────────────────┤
        // │ [0, 20)      │ Game creator address               │
        // │ [20, 52)     │ Root claim                         │
        // │ [52, 84)     │ Parent block hash at creation time │
        // │ [84, 84 + n) │ Extra data (opaque)                │
        // └──────────────┴────────────────────────────────────┘
        proxy_ = IDisputeGame(address(impl).clone(abi.encodePacked(msg.sender, _rootClaim, parentHash, _extraData)));
        proxy_.initialize{ value: msg.value }();
        // Compute the unique identifier for the dispute game.
        Hash uuid = getGameUUID(_gameType, _rootClaim, _extraData);
        // If a dispute game with the same UUID already exists, revert.
        if (GameId.unwrap(_disputeGames[uuid]) != bytes32(0)) revert GameAlreadyExists(uuid);
        // Pack the game ID.
        GameId id = LibGameId.pack(_gameType, Timestamp.wrap(uint64(block.timestamp)), address(proxy_));
        // Store the dispute game id in the mapping & emit the `DisputeGameCreated` event.
        _disputeGames[uuid] = id;
        _disputeGameList.push(id);
        emit DisputeGameCreated(address(proxy_), _gameType, _rootClaim);
    }
    /// @inheritdoc IDisputeGameFactory
    function getGameUUID(
        GameType _gameType,
        Claim _rootClaim,
        bytes calldata _extraData
    )
        public
        pure
        returns (Hash uuid_)
    {
        uuid_ = Hash.wrap(keccak256(abi.encode(_gameType, _rootClaim, _extraData)));
    }
    /// @inheritdoc IDisputeGameFactory
    function findLatestGames(
        GameType _gameType,
        uint256 _start,
        uint256 _n
    )
        external
        view
        returns (GameSearchResult[] memory games_)
    {
        // If the `_start` index is greater than or equal to the game array length or `_n == 0`, return an empty array.
        if (_start >= _disputeGameList.length || _n == 0) return games_;
        // Allocate enough memory for the full array, but start the array's length at `0`. We may not use all of the
        // memory allocated, but we don't know ahead of time the final size of the array.
        assembly {
            games_ := mload(0x40)
            mstore(0x40, add(games_, add(0x20, shl(0x05, _n))))
        }
        // Perform a reverse linear search for the `_n` most recent games of type `_gameType`.
        for (uint256 i = _start; i >= 0 && i <= _start;) {
            GameId id = _disputeGameList[i];
            (GameType gameType, Timestamp timestamp, address proxy) = id.unpack();
            if (gameType.raw() == _gameType.raw()) {
                // Increase the size of the `games_` array by 1.
                // SAFETY: We can safely lazily allocate memory here because we pre-allocated enough memory for the max
                //         possible size of the array.
                assembly {
                    mstore(games_, add(mload(games_), 0x01))
                }
                bytes memory extraData = IDisputeGame(proxy).extraData();
                Claim rootClaim = IDisputeGame(proxy).rootClaim();
                games_[games_.length - 1] = GameSearchResult({
                    index: i,
                    metadata: id,
                    timestamp: timestamp,
                    rootClaim: rootClaim,
                    extraData: extraData
                });
                if (games_.length >= _n) break;
            }
            unchecked {
                i--;
            }
        }
    }
    /// @inheritdoc IDisputeGameFactory
    function setImplementation(GameType _gameType, IDisputeGame _impl) external onlyOwner {
        gameImpls[_gameType] = _impl;
        emit ImplementationSet(address(_impl), _gameType);
    }
    /// @inheritdoc IDisputeGameFactory
    function setInitBond(GameType _gameType, uint256 _initBond) external onlyOwner {
        initBonds[_gameType] = _initBond;
        emit InitBondUpdated(_gameType, _initBond);
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { OwnableUpgradeable } from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import { ISemver } from "src/universal/ISemver.sol";
import { ResourceMetering } from "src/L1/ResourceMetering.sol";
import { Storage } from "src/libraries/Storage.sol";
import { Constants } from "src/libraries/Constants.sol";
/// @title SystemConfig
/// @notice The SystemConfig contract is used to manage configuration of an Optimism network.
///         All configuration is stored on L1 and picked up by L2 as part of the derviation of
///         the L2 chain.
contract SystemConfig is OwnableUpgradeable, ISemver {
    /// @notice Enum representing different types of updates.
    /// @custom:value BATCHER              Represents an update to the batcher hash.
    /// @custom:value GAS_CONFIG           Represents an update to txn fee config on L2.
    /// @custom:value GAS_LIMIT            Represents an update to gas limit on L2.
    /// @custom:value UNSAFE_BLOCK_SIGNER  Represents an update to the signer key for unsafe
    ///                                    block distrubution.
    enum UpdateType {
        BATCHER,
        GAS_CONFIG,
        GAS_LIMIT,
        UNSAFE_BLOCK_SIGNER
    }
    /// @notice Struct representing the addresses of L1 system contracts. These should be the
    ///         proxies and are network specific.
    struct Addresses {
        address l1CrossDomainMessenger;
        address l1ERC721Bridge;
        address l1StandardBridge;
        address disputeGameFactory;
        address optimismPortal;
        address optimismMintableERC20Factory;
    }
    /// @notice Version identifier, used for upgrades.
    uint256 public constant VERSION = 0;
    /// @notice Storage slot that the unsafe block signer is stored at.
    ///         Storing it at this deterministic storage slot allows for decoupling the storage
    ///         layout from the way that `solc` lays out storage. The `op-node` uses a storage
    ///         proof to fetch this value.
    /// @dev    NOTE: this value will be migrated to another storage slot in a future version.
    ///         User input should not be placed in storage in this contract until this migration
    ///         happens. It is unlikely that keccak second preimage resistance will be broken,
    ///         but it is better to be safe than sorry.
    bytes32 public constant UNSAFE_BLOCK_SIGNER_SLOT = keccak256("systemconfig.unsafeblocksigner");
    /// @notice Storage slot that the L1CrossDomainMessenger address is stored at.
    bytes32 public constant L1_CROSS_DOMAIN_MESSENGER_SLOT =
        bytes32(uint256(keccak256("systemconfig.l1crossdomainmessenger")) - 1);
    /// @notice Storage slot that the L1ERC721Bridge address is stored at.
    bytes32 public constant L1_ERC_721_BRIDGE_SLOT = bytes32(uint256(keccak256("systemconfig.l1erc721bridge")) - 1);
    /// @notice Storage slot that the L1StandardBridge address is stored at.
    bytes32 public constant L1_STANDARD_BRIDGE_SLOT = bytes32(uint256(keccak256("systemconfig.l1standardbridge")) - 1);
    /// @notice Storage slot that the OptimismPortal address is stored at.
    bytes32 public constant OPTIMISM_PORTAL_SLOT = bytes32(uint256(keccak256("systemconfig.optimismportal")) - 1);
    /// @notice Storage slot that the OptimismMintableERC20Factory address is stored at.
    bytes32 public constant OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT =
        bytes32(uint256(keccak256("systemconfig.optimismmintableerc20factory")) - 1);
    /// @notice Storage slot that the batch inbox address is stored at.
    bytes32 public constant BATCH_INBOX_SLOT = bytes32(uint256(keccak256("systemconfig.batchinbox")) - 1);
    /// @notice Storage slot for block at which the op-node can start searching for logs from.
    bytes32 public constant START_BLOCK_SLOT = bytes32(uint256(keccak256("systemconfig.startBlock")) - 1);
    /// @notice Storage slot for the DisputeGameFactory address.
    bytes32 public constant DISPUTE_GAME_FACTORY_SLOT =
        bytes32(uint256(keccak256("systemconfig.disputegamefactory")) - 1);
    /// @notice The maximum gas limit that can be set for L2 blocks. This limit is used to enforce that the blocks
    ///         on L2 are not too large to process and prove. Over time, this value can be increased as various
    ///         optimizations and improvements are made to the system at large.
    uint64 internal constant MAX_GAS_LIMIT = 200_000_000;
    /// @notice Fixed L2 gas overhead. Used as part of the L2 fee calculation.
    uint256 public overhead;
    /// @notice Dynamic L2 gas overhead. Used as part of the L2 fee calculation.
    uint256 public scalar;
    /// @notice Identifier for the batcher.
    ///         For version 1 of this configuration, this is represented as an address left-padded
    ///         with zeros to 32 bytes.
    bytes32 public batcherHash;
    /// @notice L2 block gas limit.
    uint64 public gasLimit;
    /// @notice The configuration for the deposit fee market.
    ///         Used by the OptimismPortal to meter the cost of buying L2 gas on L1.
    ///         Set as internal with a getter so that the struct is returned instead of a tuple.
    ResourceMetering.ResourceConfig internal _resourceConfig;
    /// @notice Emitted when configuration is updated.
    /// @param version    SystemConfig version.
    /// @param updateType Type of update.
    /// @param data       Encoded update data.
    event ConfigUpdate(uint256 indexed version, UpdateType indexed updateType, bytes data);
    /// @notice Semantic version.
    /// @custom:semver 2.2.0
    string public constant version = "2.2.0";
    /// @notice Constructs the SystemConfig contract. Cannot set
    ///         the owner to `address(0)` due to the Ownable contract's
    ///         implementation, so set it to `address(0xdEaD)`
    /// @dev    START_BLOCK_SLOT is set to type(uint256).max here so that it will be a dead value
    ///         in the singleton and is skipped by initialize when setting the start block.
    constructor() {
        Storage.setUint(START_BLOCK_SLOT, type(uint256).max);
        initialize({
            _owner: address(0xdEaD),
            _overhead: 0,
            _scalar: 0,
            _batcherHash: bytes32(0),
            _gasLimit: 1,
            _unsafeBlockSigner: address(0),
            _config: ResourceMetering.ResourceConfig({
                maxResourceLimit: 1,
                elasticityMultiplier: 1,
                baseFeeMaxChangeDenominator: 2,
                minimumBaseFee: 0,
                systemTxMaxGas: 0,
                maximumBaseFee: 0
            }),
            _batchInbox: address(0),
            _addresses: SystemConfig.Addresses({
                l1CrossDomainMessenger: address(0),
                l1ERC721Bridge: address(0),
                l1StandardBridge: address(0),
                disputeGameFactory: address(0),
                optimismPortal: address(0),
                optimismMintableERC20Factory: address(0)
            })
        });
    }
    /// @notice Initializer.
    ///         The resource config must be set before the require check.
    /// @param _owner             Initial owner of the contract.
    /// @param _overhead          Initial overhead value.
    /// @param _scalar            Initial scalar value.
    /// @param _batcherHash       Initial batcher hash.
    /// @param _gasLimit          Initial gas limit.
    /// @param _unsafeBlockSigner Initial unsafe block signer address.
    /// @param _config            Initial ResourceConfig.
    /// @param _batchInbox        Batch inbox address. An identifier for the op-node to find
    ///                           canonical data.
    /// @param _addresses         Set of L1 contract addresses. These should be the proxies.
    function initialize(
        address _owner,
        uint256 _overhead,
        uint256 _scalar,
        bytes32 _batcherHash,
        uint64 _gasLimit,
        address _unsafeBlockSigner,
        ResourceMetering.ResourceConfig memory _config,
        address _batchInbox,
        SystemConfig.Addresses memory _addresses
    )
        public
        initializer
    {
        __Ownable_init();
        transferOwnership(_owner);
        // These are set in ascending order of their UpdateTypes.
        _setBatcherHash(_batcherHash);
        _setGasConfig({ _overhead: _overhead, _scalar: _scalar });
        _setGasLimit(_gasLimit);
        Storage.setAddress(UNSAFE_BLOCK_SIGNER_SLOT, _unsafeBlockSigner);
        Storage.setAddress(BATCH_INBOX_SLOT, _batchInbox);
        Storage.setAddress(L1_CROSS_DOMAIN_MESSENGER_SLOT, _addresses.l1CrossDomainMessenger);
        Storage.setAddress(L1_ERC_721_BRIDGE_SLOT, _addresses.l1ERC721Bridge);
        Storage.setAddress(L1_STANDARD_BRIDGE_SLOT, _addresses.l1StandardBridge);
        Storage.setAddress(DISPUTE_GAME_FACTORY_SLOT, _addresses.disputeGameFactory);
        Storage.setAddress(OPTIMISM_PORTAL_SLOT, _addresses.optimismPortal);
        Storage.setAddress(OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT, _addresses.optimismMintableERC20Factory);
        _setStartBlock();
        _setResourceConfig(_config);
        require(_gasLimit >= minimumGasLimit(), "SystemConfig: gas limit too low");
    }
    /// @notice Returns the minimum L2 gas limit that can be safely set for the system to
    ///         operate. The L2 gas limit must be larger than or equal to the amount of
    ///         gas that is allocated for deposits per block plus the amount of gas that
    ///         is allocated for the system transaction.
    ///         This function is used to determine if changes to parameters are safe.
    /// @return uint64 Minimum gas limit.
    function minimumGasLimit() public view returns (uint64) {
        return uint64(_resourceConfig.maxResourceLimit) + uint64(_resourceConfig.systemTxMaxGas);
    }
    /// @notice Returns the maximum L2 gas limit that can be safely set for the system to
    ///         operate. This bound is used to prevent the gas limit from being set too high
    ///         and causing the system to be unable to process and/or prove L2 blocks.
    /// @return uint64 Maximum gas limit.
    function maximumGasLimit() public pure returns (uint64) {
        return MAX_GAS_LIMIT;
    }
    /// @notice High level getter for the unsafe block signer address.
    ///         Unsafe blocks can be propagated across the p2p network if they are signed by the
    ///         key corresponding to this address.
    /// @return addr_ Address of the unsafe block signer.
    function unsafeBlockSigner() public view returns (address addr_) {
        addr_ = Storage.getAddress(UNSAFE_BLOCK_SIGNER_SLOT);
    }
    /// @notice Getter for the L1CrossDomainMessenger address.
    function l1CrossDomainMessenger() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_CROSS_DOMAIN_MESSENGER_SLOT);
    }
    /// @notice Getter for the L1ERC721Bridge address.
    function l1ERC721Bridge() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_ERC_721_BRIDGE_SLOT);
    }
    /// @notice Getter for the L1StandardBridge address.
    function l1StandardBridge() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_STANDARD_BRIDGE_SLOT);
    }
    /// @notice Getter for the DisputeGameFactory address.
    function disputeGameFactory() external view returns (address addr_) {
        addr_ = Storage.getAddress(DISPUTE_GAME_FACTORY_SLOT);
    }
    /// @notice Getter for the OptimismPortal address.
    function optimismPortal() external view returns (address addr_) {
        addr_ = Storage.getAddress(OPTIMISM_PORTAL_SLOT);
    }
    /// @notice Getter for the OptimismMintableERC20Factory address.
    function optimismMintableERC20Factory() external view returns (address addr_) {
        addr_ = Storage.getAddress(OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT);
    }
    /// @notice Getter for the BatchInbox address.
    function batchInbox() external view returns (address addr_) {
        addr_ = Storage.getAddress(BATCH_INBOX_SLOT);
    }
    /// @notice Getter for the StartBlock number.
    function startBlock() external view returns (uint256 startBlock_) {
        startBlock_ = Storage.getUint(START_BLOCK_SLOT);
    }
    /// @notice Updates the unsafe block signer address. Can only be called by the owner.
    /// @param _unsafeBlockSigner New unsafe block signer address.
    function setUnsafeBlockSigner(address _unsafeBlockSigner) external onlyOwner {
        _setUnsafeBlockSigner(_unsafeBlockSigner);
    }
    /// @notice Updates the unsafe block signer address.
    /// @param _unsafeBlockSigner New unsafe block signer address.
    function _setUnsafeBlockSigner(address _unsafeBlockSigner) internal {
        Storage.setAddress(UNSAFE_BLOCK_SIGNER_SLOT, _unsafeBlockSigner);
        bytes memory data = abi.encode(_unsafeBlockSigner);
        emit ConfigUpdate(VERSION, UpdateType.UNSAFE_BLOCK_SIGNER, data);
    }
    /// @notice Updates the batcher hash. Can only be called by the owner.
    /// @param _batcherHash New batcher hash.
    function setBatcherHash(bytes32 _batcherHash) external onlyOwner {
        _setBatcherHash(_batcherHash);
    }
    /// @notice Internal function for updating the batcher hash.
    /// @param _batcherHash New batcher hash.
    function _setBatcherHash(bytes32 _batcherHash) internal {
        batcherHash = _batcherHash;
        bytes memory data = abi.encode(_batcherHash);
        emit ConfigUpdate(VERSION, UpdateType.BATCHER, data);
    }
    /// @notice Updates gas config. Can only be called by the owner.
    /// @param _overhead New overhead value.
    /// @param _scalar   New scalar value.
    function setGasConfig(uint256 _overhead, uint256 _scalar) external onlyOwner {
        _setGasConfig(_overhead, _scalar);
    }
    /// @notice Internal function for updating the gas config.
    /// @param _overhead New overhead value.
    /// @param _scalar   New scalar value.
    function _setGasConfig(uint256 _overhead, uint256 _scalar) internal {
        overhead = _overhead;
        scalar = _scalar;
        bytes memory data = abi.encode(_overhead, _scalar);
        emit ConfigUpdate(VERSION, UpdateType.GAS_CONFIG, data);
    }
    /// @notice Updates the L2 gas limit. Can only be called by the owner.
    /// @param _gasLimit New gas limit.
    function setGasLimit(uint64 _gasLimit) external onlyOwner {
        _setGasLimit(_gasLimit);
    }
    /// @notice Internal function for updating the L2 gas limit.
    /// @param _gasLimit New gas limit.
    function _setGasLimit(uint64 _gasLimit) internal {
        require(_gasLimit >= minimumGasLimit(), "SystemConfig: gas limit too low");
        require(_gasLimit <= maximumGasLimit(), "SystemConfig: gas limit too high");
        gasLimit = _gasLimit;
        bytes memory data = abi.encode(_gasLimit);
        emit ConfigUpdate(VERSION, UpdateType.GAS_LIMIT, data);
    }
    /// @notice Sets the start block in a backwards compatible way. Proxies
    ///         that were initialized before the startBlock existed in storage
    ///         can have their start block set by a user provided override.
    ///         A start block of 0 indicates that there is no override and the
    ///         start block will be set by `block.number`.
    /// @dev    This logic is used to patch legacy deployments with new storage values.
    ///         Use the override if it is provided as a non zero value and the value
    ///         has not already been set in storage. Use `block.number` if the value
    ///         has already been set in storage
    function _setStartBlock() internal {
        if (Storage.getUint(START_BLOCK_SLOT) == 0) {
            Storage.setUint(START_BLOCK_SLOT, block.number);
        }
    }
    /// @notice A getter for the resource config.
    ///         Ensures that the struct is returned instead of a tuple.
    /// @return ResourceConfig
    function resourceConfig() external view returns (ResourceMetering.ResourceConfig memory) {
        return _resourceConfig;
    }
    /// @notice An internal setter for the resource config.
    ///         Ensures that the config is sane before storing it by checking for invariants.
    ///         In the future, this method may emit an event that the `op-node` picks up
    ///         for when the resource config is changed.
    /// @param _config The new resource config.
    function _setResourceConfig(ResourceMetering.ResourceConfig memory _config) internal {
        // Min base fee must be less than or equal to max base fee.
        require(
            _config.minimumBaseFee <= _config.maximumBaseFee, "SystemConfig: min base fee must be less than max base"
        );
        // Base fee change denominator must be greater than 1.
        require(_config.baseFeeMaxChangeDenominator > 1, "SystemConfig: denominator must be larger than 1");
        // Max resource limit plus system tx gas must be less than or equal to the L2 gas limit.
        // The gas limit must be increased before these values can be increased.
        require(_config.maxResourceLimit + _config.systemTxMaxGas <= gasLimit, "SystemConfig: gas limit too low");
        // Elasticity multiplier must be greater than 0.
        require(_config.elasticityMultiplier > 0, "SystemConfig: elasticity multiplier cannot be 0");
        // No precision loss when computing target resource limit.
        require(
            ((_config.maxResourceLimit / _config.elasticityMultiplier) * _config.elasticityMultiplier)
                == _config.maxResourceLimit,
            "SystemConfig: precision loss with target resource limit"
        );
        _resourceConfig = _config;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { ISemver } from "src/universal/ISemver.sol";
import { Storage } from "src/libraries/Storage.sol";
/// @custom:audit none This contracts is not yet audited.
/// @title SuperchainConfig
/// @notice The SuperchainConfig contract is used to manage configuration of global superchain values.
contract SuperchainConfig is Initializable, ISemver {
    /// @notice Enum representing different types of updates.
    /// @custom:value GUARDIAN            Represents an update to the guardian.
    enum UpdateType {
        GUARDIAN
    }
    /// @notice Whether or not the Superchain is paused.
    bytes32 public constant PAUSED_SLOT = bytes32(uint256(keccak256("superchainConfig.paused")) - 1);
    /// @notice The address of the guardian, which can pause withdrawals from the System.
    ///         It can only be modified by an upgrade.
    bytes32 public constant GUARDIAN_SLOT = bytes32(uint256(keccak256("superchainConfig.guardian")) - 1);
    /// @notice Emitted when the pause is triggered.
    /// @param identifier A string helping to identify provenance of the pause transaction.
    event Paused(string identifier);
    /// @notice Emitted when the pause is lifted.
    event Unpaused();
    /// @notice Emitted when configuration is updated.
    /// @param updateType Type of update.
    /// @param data       Encoded update data.
    event ConfigUpdate(UpdateType indexed updateType, bytes data);
    /// @notice Semantic version.
    /// @custom:semver 1.1.0
    string public constant version = "1.1.0";
    /// @notice Constructs the SuperchainConfig contract.
    constructor() {
        initialize({ _guardian: address(0), _paused: false });
    }
    /// @notice Initializer.
    /// @param _guardian    Address of the guardian, can pause the OptimismPortal.
    /// @param _paused      Initial paused status.
    function initialize(address _guardian, bool _paused) public initializer {
        _setGuardian(_guardian);
        if (_paused) {
            _pause("Initializer paused");
        }
    }
    /// @notice Getter for the guardian address.
    function guardian() public view returns (address guardian_) {
        guardian_ = Storage.getAddress(GUARDIAN_SLOT);
    }
    /// @notice Getter for the current paused status.
    function paused() public view returns (bool paused_) {
        paused_ = Storage.getBool(PAUSED_SLOT);
    }
    /// @notice Pauses withdrawals.
    /// @param _identifier (Optional) A string to identify provenance of the pause transaction.
    function pause(string memory _identifier) external {
        require(msg.sender == guardian(), "SuperchainConfig: only guardian can pause");
        _pause(_identifier);
    }
    /// @notice Pauses withdrawals.
    /// @param _identifier (Optional) A string to identify provenance of the pause transaction.
    function _pause(string memory _identifier) internal {
        Storage.setBool(PAUSED_SLOT, true);
        emit Paused(_identifier);
    }
    /// @notice Unpauses withdrawals.
    function unpause() external {
        require(msg.sender == guardian(), "SuperchainConfig: only guardian can unpause");
        Storage.setBool(PAUSED_SLOT, false);
        emit Unpaused();
    }
    /// @notice Sets the guardian address. This is only callable during initialization, so an upgrade
    ///         will be required to change the guardian.
    /// @param _guardian The new guardian address.
    function _setGuardian(address _guardian) internal {
        Storage.setAddress(GUARDIAN_SLOT, _guardian);
        emit ConfigUpdate(UpdateType.GUARDIAN, abi.encode(_guardian));
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { ResourceMetering } from "src/L1/ResourceMetering.sol";
/// @title Constants
/// @notice Constants is a library for storing constants. Simple! Don't put everything in here, just
///         the stuff used in multiple contracts. Constants that only apply to a single contract
///         should be defined in that contract instead.
library Constants {
    /// @notice Special address to be used as the tx origin for gas estimation calls in the
    ///         OptimismPortal and CrossDomainMessenger calls. You only need to use this address if
    ///         the minimum gas limit specified by the user is not actually enough to execute the
    ///         given message and you're attempting to estimate the actual necessary gas limit. We
    ///         use address(1) because it's the ecrecover precompile and therefore guaranteed to
    ///         never have any code on any EVM chain.
    address internal constant ESTIMATION_ADDRESS = address(1);
    /// @notice Value used for the L2 sender storage slot in both the OptimismPortal and the
    ///         CrossDomainMessenger contracts before an actual sender is set. This value is
    ///         non-zero to reduce the gas cost of message passing transactions.
    address internal constant DEFAULT_L2_SENDER = 0x000000000000000000000000000000000000dEaD;
    /// @notice The storage slot that holds the address of a proxy implementation.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)`
    bytes32 internal constant PROXY_IMPLEMENTATION_ADDRESS =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /// @notice The storage slot that holds the address of the owner.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)`
    bytes32 internal constant PROXY_OWNER_ADDRESS = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /// @notice Returns the default values for the ResourceConfig. These are the recommended values
    ///         for a production network.
    function DEFAULT_RESOURCE_CONFIG() internal pure returns (ResourceMetering.ResourceConfig memory) {
        ResourceMetering.ResourceConfig memory config = ResourceMetering.ResourceConfig({
            maxResourceLimit: 20_000_000,
            elasticityMultiplier: 10,
            baseFeeMaxChangeDenominator: 8,
            minimumBaseFee: 1 gwei,
            systemTxMaxGas: 1_000_000,
            maximumBaseFee: type(uint128).max
        });
        return config;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title Types
/// @notice Contains various types used throughout the Optimism contract system.
library Types {
    /// @notice OutputProposal represents a commitment to the L2 state. The timestamp is the L1
    ///         timestamp that the output root is posted. This timestamp is used to verify that the
    ///         finalization period has passed since the output root was submitted.
    /// @custom:field outputRoot    Hash of the L2 output.
    /// @custom:field timestamp     Timestamp of the L1 block that the output root was submitted in.
    /// @custom:field l2BlockNumber L2 block number that the output corresponds to.
    struct OutputProposal {
        bytes32 outputRoot;
        uint128 timestamp;
        uint128 l2BlockNumber;
    }
    /// @notice Struct representing the elements that are hashed together to generate an output root
    ///         which itself represents a snapshot of the L2 state.
    /// @custom:field version                  Version of the output root.
    /// @custom:field stateRoot                Root of the state trie at the block of this output.
    /// @custom:field messagePasserStorageRoot Root of the message passer storage trie.
    /// @custom:field latestBlockhash          Hash of the block this output was generated from.
    struct OutputRootProof {
        bytes32 version;
        bytes32 stateRoot;
        bytes32 messagePasserStorageRoot;
        bytes32 latestBlockhash;
    }
    /// @notice Struct representing a deposit transaction (L1 => L2 transaction) created by an end
    ///         user (as opposed to a system deposit transaction generated by the system).
    /// @custom:field from        Address of the sender of the transaction.
    /// @custom:field to          Address of the recipient of the transaction.
    /// @custom:field isCreation  True if the transaction is a contract creation.
    /// @custom:field value       Value to send to the recipient.
    /// @custom:field mint        Amount of ETH to mint.
    /// @custom:field gasLimit    Gas limit of the transaction.
    /// @custom:field data        Data of the transaction.
    /// @custom:field l1BlockHash Hash of the block the transaction was submitted in.
    /// @custom:field logIndex    Index of the log in the block the transaction was submitted in.
    struct UserDepositTransaction {
        address from;
        address to;
        bool isCreation;
        uint256 value;
        uint256 mint;
        uint64 gasLimit;
        bytes data;
        bytes32 l1BlockHash;
        uint256 logIndex;
    }
    /// @notice Struct representing a withdrawal transaction.
    /// @custom:field nonce    Nonce of the withdrawal transaction
    /// @custom:field sender   Address of the sender of the transaction.
    /// @custom:field target   Address of the recipient of the transaction.
    /// @custom:field value    Value to send to the recipient.
    /// @custom:field gasLimit Gas limit of the transaction.
    /// @custom:field data     Data of the transaction.
    struct WithdrawalTransaction {
        uint256 nonce;
        address sender;
        address target;
        uint256 value;
        uint256 gasLimit;
        bytes data;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { Types } from "src/libraries/Types.sol";
import { Encoding } from "src/libraries/Encoding.sol";
/// @title Hashing
/// @notice Hashing handles Optimism's various different hashing schemes.
library Hashing {
    /// @notice Computes the hash of the RLP encoded L2 transaction that would be generated when a
    ///         given deposit is sent to the L2 system. Useful for searching for a deposit in the L2
    ///         system.
    /// @param _tx User deposit transaction to hash.
    /// @return Hash of the RLP encoded L2 deposit transaction.
    function hashDepositTransaction(Types.UserDepositTransaction memory _tx) internal pure returns (bytes32) {
        return keccak256(Encoding.encodeDepositTransaction(_tx));
    }
    /// @notice Computes the deposit transaction's "source hash", a value that guarantees the hash
    ///         of the L2 transaction that corresponds to a deposit is unique and is
    ///         deterministically generated from L1 transaction data.
    /// @param _l1BlockHash Hash of the L1 block where the deposit was included.
    /// @param _logIndex    The index of the log that created the deposit transaction.
    /// @return Hash of the deposit transaction's "source hash".
    function hashDepositSource(bytes32 _l1BlockHash, uint256 _logIndex) internal pure returns (bytes32) {
        bytes32 depositId = keccak256(abi.encode(_l1BlockHash, _logIndex));
        return keccak256(abi.encode(bytes32(0), depositId));
    }
    /// @notice Hashes the cross domain message based on the version that is encoded into the
    ///         message nonce.
    /// @param _nonce    Message nonce with version encoded into the first two bytes.
    /// @param _sender   Address of the sender of the message.
    /// @param _target   Address of the target of the message.
    /// @param _value    ETH value to send to the target.
    /// @param _gasLimit Gas limit to use for the message.
    /// @param _data     Data to send with the message.
    /// @return Hashed cross domain message.
    function hashCrossDomainMessage(
        uint256 _nonce,
        address _sender,
        address _target,
        uint256 _value,
        uint256 _gasLimit,
        bytes memory _data
    )
        internal
        pure
        returns (bytes32)
    {
        (, uint16 version) = Encoding.decodeVersionedNonce(_nonce);
        if (version == 0) {
            return hashCrossDomainMessageV0(_target, _sender, _data, _nonce);
        } else if (version == 1) {
            return hashCrossDomainMessageV1(_nonce, _sender, _target, _value, _gasLimit, _data);
        } else {
            revert("Hashing: unknown cross domain message version");
        }
    }
    /// @notice Hashes a cross domain message based on the V0 (legacy) encoding.
    /// @param _target Address of the target of the message.
    /// @param _sender Address of the sender of the message.
    /// @param _data   Data to send with the message.
    /// @param _nonce  Message nonce.
    /// @return Hashed cross domain message.
    function hashCrossDomainMessageV0(
        address _target,
        address _sender,
        bytes memory _data,
        uint256 _nonce
    )
        internal
        pure
        returns (bytes32)
    {
        return keccak256(Encoding.encodeCrossDomainMessageV0(_target, _sender, _data, _nonce));
    }
    /// @notice Hashes a cross domain message based on the V1 (current) encoding.
    /// @param _nonce    Message nonce.
    /// @param _sender   Address of the sender of the message.
    /// @param _target   Address of the target of the message.
    /// @param _value    ETH value to send to the target.
    /// @param _gasLimit Gas limit to use for the message.
    /// @param _data     Data to send with the message.
    /// @return Hashed cross domain message.
    function hashCrossDomainMessageV1(
        uint256 _nonce,
        address _sender,
        address _target,
        uint256 _value,
        uint256 _gasLimit,
        bytes memory _data
    )
        internal
        pure
        returns (bytes32)
    {
        return keccak256(Encoding.encodeCrossDomainMessageV1(_nonce, _sender, _target, _value, _gasLimit, _data));
    }
    /// @notice Derives the withdrawal hash according to the encoding in the L2 Withdrawer contract
    /// @param _tx Withdrawal transaction to hash.
    /// @return Hashed withdrawal transaction.
    function hashWithdrawal(Types.WithdrawalTransaction memory _tx) internal pure returns (bytes32) {
        return keccak256(abi.encode(_tx.nonce, _tx.sender, _tx.target, _tx.value, _tx.gasLimit, _tx.data));
    }
    /// @notice Hashes the various elements of an output root proof into an output root hash which
    ///         can be used to check if the proof is valid.
    /// @param _outputRootProof Output root proof which should hash to an output root.
    /// @return Hashed output root proof.
    function hashOutputRootProof(Types.OutputRootProof memory _outputRootProof) internal pure returns (bytes32) {
        return keccak256(
            abi.encode(
                _outputRootProof.version,
                _outputRootProof.stateRoot,
                _outputRootProof.messagePasserStorageRoot,
                _outputRootProof.latestBlockhash
            )
        );
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { MerkleTrie } from "./MerkleTrie.sol";
/// @title SecureMerkleTrie
/// @notice SecureMerkleTrie is a thin wrapper around the MerkleTrie library that hashes the input
///         keys. Ethereum's state trie hashes input keys before storing them.
library SecureMerkleTrie {
    /// @notice Verifies a proof that a given key/value pair is present in the Merkle trie.
    /// @param _key   Key of the node to search for, as a hex string.
    /// @param _value Value of the node to search for, as a hex string.
    /// @param _proof Merkle trie inclusion proof for the desired node. Unlike traditional Merkle
    ///               trees, this proof is executed top-down and consists of a list of RLP-encoded
    ///               nodes that make a path down to the target node.
    /// @param _root  Known root of the Merkle trie. Used to verify that the included proof is
    ///               correctly constructed.
    /// @return valid_ Whether or not the proof is valid.
    function verifyInclusionProof(
        bytes memory _key,
        bytes memory _value,
        bytes[] memory _proof,
        bytes32 _root
    )
        internal
        pure
        returns (bool valid_)
    {
        bytes memory key = _getSecureKey(_key);
        valid_ = MerkleTrie.verifyInclusionProof(key, _value, _proof, _root);
    }
    /// @notice Retrieves the value associated with a given key.
    /// @param _key   Key to search for, as hex bytes.
    /// @param _proof Merkle trie inclusion proof for the key.
    /// @param _root  Known root of the Merkle trie.
    /// @return value_ Value of the key if it exists.
    function get(bytes memory _key, bytes[] memory _proof, bytes32 _root) internal pure returns (bytes memory value_) {
        bytes memory key = _getSecureKey(_key);
        value_ = MerkleTrie.get(key, _proof, _root);
    }
    /// @notice Computes the hashed version of the input key.
    /// @param _key Key to hash.
    /// @return hash_ Hashed version of the key.
    function _getSecureKey(bytes memory _key) private pure returns (bytes memory hash_) {
        hash_ = abi.encodePacked(keccak256(_key));
    }
}
// SPDX-License-Identifier: Apache-2.0
/*
 * Copyright 2019-2021, Offchain Labs, Inc.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *    http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
pragma solidity ^0.8.0;
library AddressAliasHelper {
    uint160 constant offset = uint160(0x1111000000000000000000000000000000001111);
    /// @notice Utility function that converts the address in the L1 that submitted a tx to
    /// the inbox to the msg.sender viewed in the L2
    /// @param l1Address the address in the L1 that triggered the tx to L2
    /// @return l2Address L2 address as viewed in msg.sender
    function applyL1ToL2Alias(address l1Address) internal pure returns (address l2Address) {
        unchecked {
            l2Address = address(uint160(l1Address) + offset);
        }
    }
    /// @notice Utility function that converts the msg.sender viewed in the L2 to the
    /// address in the L1 that submitted a tx to the inbox
    /// @param l2Address L2 address as viewed in msg.sender
    /// @return l1Address the address in the L1 that triggered the tx to L2
    function undoL1ToL2Alias(address l2Address) internal pure returns (address l1Address) {
        unchecked {
            l1Address = address(uint160(l2Address) - offset);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { Burn } from "src/libraries/Burn.sol";
import { Arithmetic } from "src/libraries/Arithmetic.sol";
/// @custom:upgradeable
/// @title ResourceMetering
/// @notice ResourceMetering implements an EIP-1559 style resource metering system where pricing
///         updates automatically based on current demand.
abstract contract ResourceMetering is Initializable {
    /// @notice Error returned when too much gas resource is consumed.
    error OutOfGas();
    /// @notice Represents the various parameters that control the way in which resources are
    ///         metered. Corresponds to the EIP-1559 resource metering system.
    /// @custom:field prevBaseFee   Base fee from the previous block(s).
    /// @custom:field prevBoughtGas Amount of gas bought so far in the current block.
    /// @custom:field prevBlockNum  Last block number that the base fee was updated.
    struct ResourceParams {
        uint128 prevBaseFee;
        uint64 prevBoughtGas;
        uint64 prevBlockNum;
    }
    /// @notice Represents the configuration for the EIP-1559 based curve for the deposit gas
    ///         market. These values should be set with care as it is possible to set them in
    ///         a way that breaks the deposit gas market. The target resource limit is defined as
    ///         maxResourceLimit / elasticityMultiplier. This struct was designed to fit within a
    ///         single word. There is additional space for additions in the future.
    /// @custom:field maxResourceLimit             Represents the maximum amount of deposit gas that
    ///                                            can be purchased per block.
    /// @custom:field elasticityMultiplier         Determines the target resource limit along with
    ///                                            the resource limit.
    /// @custom:field baseFeeMaxChangeDenominator  Determines max change on fee per block.
    /// @custom:field minimumBaseFee               The min deposit base fee, it is clamped to this
    ///                                            value.
    /// @custom:field systemTxMaxGas               The amount of gas supplied to the system
    ///                                            transaction. This should be set to the same
    ///                                            number that the op-node sets as the gas limit
    ///                                            for the system transaction.
    /// @custom:field maximumBaseFee               The max deposit base fee, it is clamped to this
    ///                                            value.
    struct ResourceConfig {
        uint32 maxResourceLimit;
        uint8 elasticityMultiplier;
        uint8 baseFeeMaxChangeDenominator;
        uint32 minimumBaseFee;
        uint32 systemTxMaxGas;
        uint128 maximumBaseFee;
    }
    /// @notice EIP-1559 style gas parameters.
    ResourceParams public params;
    /// @notice Reserve extra slots (to a total of 50) in the storage layout for future upgrades.
    uint256[48] private __gap;
    /// @notice Meters access to a function based an amount of a requested resource.
    /// @param _amount Amount of the resource requested.
    modifier metered(uint64 _amount) {
        // Record initial gas amount so we can refund for it later.
        uint256 initialGas = gasleft();
        // Run the underlying function.
        _;
        // Run the metering function.
        _metered(_amount, initialGas);
    }
    /// @notice An internal function that holds all of the logic for metering a resource.
    /// @param _amount     Amount of the resource requested.
    /// @param _initialGas The amount of gas before any modifier execution.
    function _metered(uint64 _amount, uint256 _initialGas) internal {
        // Update block number and base fee if necessary.
        uint256 blockDiff = block.number - params.prevBlockNum;
        ResourceConfig memory config = _resourceConfig();
        int256 targetResourceLimit =
            int256(uint256(config.maxResourceLimit)) / int256(uint256(config.elasticityMultiplier));
        if (blockDiff > 0) {
            // Handle updating EIP-1559 style gas parameters. We use EIP-1559 to restrict the rate
            // at which deposits can be created and therefore limit the potential for deposits to
            // spam the L2 system. Fee scheme is very similar to EIP-1559 with minor changes.
            int256 gasUsedDelta = int256(uint256(params.prevBoughtGas)) - targetResourceLimit;
            int256 baseFeeDelta = (int256(uint256(params.prevBaseFee)) * gasUsedDelta)
                / (targetResourceLimit * int256(uint256(config.baseFeeMaxChangeDenominator)));
            // Update base fee by adding the base fee delta and clamp the resulting value between
            // min and max.
            int256 newBaseFee = Arithmetic.clamp({
                _value: int256(uint256(params.prevBaseFee)) + baseFeeDelta,
                _min: int256(uint256(config.minimumBaseFee)),
                _max: int256(uint256(config.maximumBaseFee))
            });
            // If we skipped more than one block, we also need to account for every empty block.
            // Empty block means there was no demand for deposits in that block, so we should
            // reflect this lack of demand in the fee.
            if (blockDiff > 1) {
                // Update the base fee by repeatedly applying the exponent 1-(1/change_denominator)
                // blockDiff - 1 times. Simulates multiple empty blocks. Clamp the resulting value
                // between min and max.
                newBaseFee = Arithmetic.clamp({
                    _value: Arithmetic.cdexp({
                        _coefficient: newBaseFee,
                        _denominator: int256(uint256(config.baseFeeMaxChangeDenominator)),
                        _exponent: int256(blockDiff - 1)
                    }),
                    _min: int256(uint256(config.minimumBaseFee)),
                    _max: int256(uint256(config.maximumBaseFee))
                });
            }
            // Update new base fee, reset bought gas, and update block number.
            params.prevBaseFee = uint128(uint256(newBaseFee));
            params.prevBoughtGas = 0;
            params.prevBlockNum = uint64(block.number);
        }
        // Make sure we can actually buy the resource amount requested by the user.
        params.prevBoughtGas += _amount;
        if (int256(uint256(params.prevBoughtGas)) > int256(uint256(config.maxResourceLimit))) {
            revert OutOfGas();
        }
        // Determine the amount of ETH to be paid.
        uint256 resourceCost = uint256(_amount) * uint256(params.prevBaseFee);
        // We currently charge for this ETH amount as an L1 gas burn, so we convert the ETH amount
        // into gas by dividing by the L1 base fee. We assume a minimum base fee of 1 gwei to avoid
        // division by zero for L1s that don't support 1559 or to avoid excessive gas burns during
        // periods of extremely low L1 demand. One-day average gas fee hasn't dipped below 1 gwei
        // during any 1 day period in the last 5 years, so should be fine.
        uint256 gasCost = resourceCost / Math.max(block.basefee, 1 gwei);
        // Give the user a refund based on the amount of gas they used to do all of the work up to
        // this point. Since we're at the end of the modifier, this should be pretty accurate. Acts
        // effectively like a dynamic stipend (with a minimum value).
        uint256 usedGas = _initialGas - gasleft();
        if (gasCost > usedGas) {
            Burn.gas(gasCost - usedGas);
        }
    }
    /// @notice Virtual function that returns the resource config.
    ///         Contracts that inherit this contract must implement this function.
    /// @return ResourceConfig
    function _resourceConfig() internal virtual returns (ResourceConfig memory);
    /// @notice Sets initial resource parameter values.
    ///         This function must either be called by the initializer function of an upgradeable
    ///         child contract.
    function __ResourceMetering_init() internal onlyInitializing {
        if (params.prevBlockNum == 0) {
            params = ResourceParams({ prevBaseFee: 1 gwei, prevBoughtGas: 0, prevBlockNum: uint64(block.number) });
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title ISemver
/// @notice ISemver is a simple contract for ensuring that contracts are
///         versioned using semantic versioning.
interface ISemver {
    /// @notice Getter for the semantic version of the contract. This is not
    ///         meant to be used onchain but instead meant to be used by offchain
    ///         tooling.
    /// @return Semver contract version as a string.
    function version() external view returns (string memory);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @notice Error for when a deposit or withdrawal is to a bad target.
error BadTarget();
/// @notice Error for when a deposit has too much calldata.
error LargeCalldata();
/// @notice Error for when a deposit has too small of a gas limit.
error SmallGasLimit();
/// @notice Error for when a withdrawal transfer fails.
error TransferFailed();
/// @notice Error for when a method is called that only works when using a custom gas token.
error OnlyCustomGasToken();
/// @notice Error for when a method cannot be called with non zero CALLVALUE.
error NoValue();
/// @notice Error for an unauthorized CALLER.
error Unauthorized();
/// @notice Error for when a method cannot be called when paused. This could be renamed
///         to `Paused` in the future, but it collides with the `Paused` event.
error CallPaused();
/// @notice Error for special gas estimation.
error GasEstimation();
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.15;
import "src/dispute/lib/LibUDT.sol";
/// @notice The current status of the dispute game.
enum GameStatus {
    // The game is currently in progress, and has not been resolved.
    IN_PROGRESS,
    // The game has concluded, and the `rootClaim` was challenged successfully.
    CHALLENGER_WINS,
    // The game has concluded, and the `rootClaim` could not be contested.
    DEFENDER_WINS
}
/// @notice Represents an L2 output root and the L2 block number at which it was generated.
/// @custom:field root The output root.
/// @custom:field l2BlockNumber The L2 block number at which the output root was generated.
struct OutputRoot {
    Hash root;
    uint256 l2BlockNumber;
}
/// @title GameTypes
/// @notice A library that defines the IDs of games that can be played.
library GameTypes {
    /// @dev A dispute game type the uses the cannon vm.
    GameType internal constant CANNON = GameType.wrap(0);
    /// @dev A permissioned dispute game type the uses the cannon vm.
    GameType internal constant PERMISSIONED_CANNON = GameType.wrap(1);
    /// @notice A dispute game type the uses the asterisc VM
    GameType internal constant ASTERISC = GameType.wrap(2);
    /// @notice A dispute game type that uses an alphabet vm.
    ///         Not intended for production use.
    GameType internal constant ALPHABET = GameType.wrap(255);
}
/// @title VMStatuses
/// @notice Named type aliases for the various valid VM status bytes.
library VMStatuses {
    /// @notice The VM has executed successfully and the outcome is valid.
    VMStatus internal constant VALID = VMStatus.wrap(0);
    /// @notice The VM has executed successfully and the outcome is invalid.
    VMStatus internal constant INVALID = VMStatus.wrap(1);
    /// @notice The VM has paniced.
    VMStatus internal constant PANIC = VMStatus.wrap(2);
    /// @notice The VM execution is still in progress.
    VMStatus internal constant UNFINISHED = VMStatus.wrap(3);
}
/// @title LocalPreimageKey
/// @notice Named type aliases for local `PreimageOracle` key identifiers.
library LocalPreimageKey {
    /// @notice The identifier for the L1 head hash.
    uint256 internal constant L1_HEAD_HASH = 0x01;
    /// @notice The identifier for the starting output root.
    uint256 internal constant STARTING_OUTPUT_ROOT = 0x02;
    /// @notice The identifier for the disputed output root.
    uint256 internal constant DISPUTED_OUTPUT_ROOT = 0x03;
    /// @notice The identifier for the disputed L2 block number.
    uint256 internal constant DISPUTED_L2_BLOCK_NUMBER = 0x04;
    /// @notice The identifier for the chain ID.
    uint256 internal constant CHAIN_ID = 0x05;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library 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
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev 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) {
        require(isContract(target), "Address: delegate call to non-contract");
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.4;
/// @notice Minimal proxy library.
/// @author Solady (https://github.com/vectorized/solady/blob/main/src/utils/LibClone.sol)
/// @author Minimal proxy by 0age (https://github.com/0age)
/// @author Clones with immutable args by wighawag, zefram.eth, Saw-mon & Natalie
/// (https://github.com/Saw-mon-and-Natalie/clones-with-immutable-args)
/// @author Minimal ERC1967 proxy by jtriley-eth (https://github.com/jtriley-eth/minimum-viable-proxy)
///
/// @dev Minimal proxy:
/// Although the sw0nt pattern saves 5 gas over the erc-1167 pattern during runtime,
/// it is not supported out-of-the-box on Etherscan. Hence, we choose to use the 0age pattern,
/// which saves 4 gas over the erc-1167 pattern during runtime, and has the smallest bytecode.
///
/// @dev Minimal proxy (PUSH0 variant):
/// This is a new minimal proxy that uses the PUSH0 opcode introduced during Shanghai.
/// It is optimized first for minimal runtime gas, then for minimal bytecode.
/// The PUSH0 clone functions are intentionally postfixed with a jarring "_PUSH0" as
/// many EVM chains may not support the PUSH0 opcode in the early months after Shanghai.
/// Please use with caution.
///
/// @dev Clones with immutable args (CWIA):
/// The implementation of CWIA here implements a `receive()` method that emits the
/// `ReceiveETH(uint256)` event. This skips the `DELEGATECALL` when there is no calldata,
/// enabling us to accept hard gas-capped `sends` & `transfers` for maximum backwards
/// composability. The minimal proxy implementation does not offer this feature.
///
/// @dev Minimal ERC1967 proxy:
/// An minimal ERC1967 proxy, intended to be upgraded with UUPS.
/// This is NOT the same as ERC1967Factory's transparent proxy, which includes admin logic.
library LibClone {
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                       CUSTOM ERRORS                        */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Unable to deploy the clone.
    error DeploymentFailed();
    /// @dev The salt must start with either the zero address or `by`.
    error SaltDoesNotStartWith();
    /// @dev The ETH transfer has failed.
    error ETHTransferFailed();
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                  MINIMAL PROXY OPERATIONS                  */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Deploys a clone of `implementation`.
    function clone(address implementation) internal returns (address instance) {
        instance = clone(0, implementation);
    }
    /// @dev Deploys a clone of `implementation`.
    function clone(uint256 value, address implementation) internal returns (address instance) {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * --------------------------------------------------------------------------+
             * CREATION (9 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                       |
             * --------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize     | r         |                              |
             * 3d         | RETURNDATASIZE    | 0 r       |                              |
             * 81         | DUP2              | r 0 r     |                              |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                              |
             * 3d         | RETURNDATASIZE    | 0 o r 0 r |                              |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code   |
             * f3         | RETURN            |           | [0..runSize): runtime code   |
             * --------------------------------------------------------------------------|
             * RUNTIME (44 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode  | Mnemonic       | Stack                  | Memory                |
             * --------------------------------------------------------------------------|
             *                                                                           |
             * ::: keep some values in stack ::::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | 0                      |                       |
             * 3d      | RETURNDATASIZE | 0 0                    |                       |
             * 3d      | RETURNDATASIZE | 0 0 0                  |                       |
             * 3d      | RETURNDATASIZE | 0 0 0 0                |                       |
             *                                                                           |
             * ::: copy calldata to memory ::::::::::::::::::::::::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0 0 0            |                       |
             * 3d      | RETURNDATASIZE | 0 cds 0 0 0 0          |                       |
             * 3d      | RETURNDATASIZE | 0 0 cds 0 0 0 0        |                       |
             * 37      | CALLDATACOPY   | 0 0 0 0                | [0..cds): calldata    |
             *                                                                           |
             * ::: delegate call to the implementation contract :::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0 0 0            | [0..cds): calldata    |
             * 3d      | RETURNDATASIZE | 0 cds 0 0 0 0          | [0..cds): calldata    |
             * 73 addr | PUSH20 addr    | addr 0 cds 0 0 0 0     | [0..cds): calldata    |
             * 5a      | GAS            | gas addr 0 cds 0 0 0 0 | [0..cds): calldata    |
             * f4      | DELEGATECALL   | success 0 0            | [0..cds): calldata    |
             *                                                                           |
             * ::: copy return data to memory :::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds success 0 0        | [0..cds): calldata    |
             * 3d      | RETURNDATASIZE | rds rds success 0 0    | [0..cds): calldata    |
             * 93      | SWAP4          | 0 rds success 0 rds    | [0..cds): calldata    |
             * 80      | DUP1           | 0 0 rds success 0 rds  | [0..cds): calldata    |
             * 3e      | RETURNDATACOPY | success 0 rds          | [0..rds): returndata  |
             *                                                                           |
             * 60 0x2a | PUSH1 0x2a     | 0x2a success 0 rds     | [0..rds): returndata  |
             * 57      | JUMPI          | 0 rds                  | [0..rds): returndata  |
             *                                                                           |
             * ::: revert :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * fd      | REVERT         |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: return :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b      | JUMPDEST       | 0 rds                  | [0..rds): returndata  |
             * f3      | RETURN         |                        | [0..rds): returndata  |
             * --------------------------------------------------------------------------+
             */
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            instance := create(value, 0x0c, 0x35)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Deploys a deterministic clone of `implementation` with `salt`.
    function cloneDeterministic(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic(0, implementation, salt);
    }
    /// @dev Deploys a deterministic clone of `implementation` with `salt`.
    function cloneDeterministic(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            instance := create2(value, 0x0c, 0x35, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Returns the initialization code hash of the clone of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x21, 0x5af43d3d93803e602a57fd5bf3)
            mstore(0x14, implementation)
            mstore(0x00, 0x602c3d8160093d39f33d3d3d3d363d3d37363d73)
            hash := keccak256(0x0c, 0x35)
            mstore(0x21, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Returns the address of the deterministic clone of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(address implementation, bytes32 salt, address deployer)
        internal
        pure
        returns (address predicted)
    {
        bytes32 hash = initCodeHash(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*          MINIMAL PROXY OPERATIONS (PUSH0 VARIANT)          */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Deploys a PUSH0 clone of `implementation`.
    function clone_PUSH0(address implementation) internal returns (address instance) {
        instance = clone_PUSH0(0, implementation);
    }
    /// @dev Deploys a PUSH0 clone of `implementation`.
    function clone_PUSH0(uint256 value, address implementation)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * --------------------------------------------------------------------------+
             * CREATION (9 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                       |
             * --------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize     | r         |                              |
             * 5f         | PUSH0             | 0 r       |                              |
             * 81         | DUP2              | r 0 r     |                              |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                              |
             * 5f         | PUSH0             | 0 o r 0 r |                              |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code   |
             * f3         | RETURN            |           | [0..runSize): runtime code   |
             * --------------------------------------------------------------------------|
             * RUNTIME (45 bytes)                                                        |
             * --------------------------------------------------------------------------|
             * Opcode  | Mnemonic       | Stack                  | Memory                |
             * --------------------------------------------------------------------------|
             *                                                                           |
             * ::: keep some values in stack ::::::::::::::::::::::::::::::::::::::::::: |
             * 5f      | PUSH0          | 0                      |                       |
             * 5f      | PUSH0          | 0 0                    |                       |
             *                                                                           |
             * ::: copy calldata to memory ::::::::::::::::::::::::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0                |                       |
             * 5f      | PUSH0          | 0 cds 0 0              |                       |
             * 5f      | PUSH0          | 0 0 cds 0 0            |                       |
             * 37      | CALLDATACOPY   | 0 0                    | [0..cds): calldata    |
             *                                                                           |
             * ::: delegate call to the implementation contract :::::::::::::::::::::::: |
             * 36      | CALLDATASIZE   | cds 0 0                | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 cds 0 0              | [0..cds): calldata    |
             * 73 addr | PUSH20 addr    | addr 0 cds 0 0         | [0..cds): calldata    |
             * 5a      | GAS            | gas addr 0 cds 0 0     | [0..cds): calldata    |
             * f4      | DELEGATECALL   | success                | [0..cds): calldata    |
             *                                                                           |
             * ::: copy return data to memory :::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds success            | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 rds success          | [0..cds): calldata    |
             * 5f      | PUSH0          | 0 0 rds success        | [0..cds): calldata    |
             * 3e      | RETURNDATACOPY | success                | [0..rds): returndata  |
             *                                                                           |
             * 60 0x29 | PUSH1 0x29     | 0x29 success           | [0..rds): returndata  |
             * 57      | JUMPI          |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: revert :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d      | RETURNDATASIZE | rds                    | [0..rds): returndata  |
             * 5f      | PUSH0          | 0 rds                  | [0..rds): returndata  |
             * fd      | REVERT         |                        | [0..rds): returndata  |
             *                                                                           |
             * ::: return :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b      | JUMPDEST       |                        | [0..rds): returndata  |
             * 3d      | RETURNDATASIZE | rds                    | [0..rds): returndata  |
             * 5f      | PUSH0          | 0 rds                  | [0..rds): returndata  |
             * f3      | RETURN         |                        | [0..rds): returndata  |
             * --------------------------------------------------------------------------+
             */
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            instance := create(value, 0x0e, 0x36)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Deploys a deterministic PUSH0 clone of `implementation` with `salt`.
    function cloneDeterministic_PUSH0(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic_PUSH0(0, implementation, salt);
    }
    /// @dev Deploys a deterministic PUSH0 clone of `implementation` with `salt`.
    function cloneDeterministic_PUSH0(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            instance := create2(value, 0x0e, 0x36, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Returns the initialization code hash of the PUSH0 clone of `implementation`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash_PUSH0(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x24, 0x5af43d5f5f3e6029573d5ffd5b3d5ff3) // 16
            mstore(0x14, implementation) // 20
            mstore(0x00, 0x602d5f8160095f39f35f5f365f5f37365f73) // 9 + 9
            hash := keccak256(0x0e, 0x36)
            mstore(0x24, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Returns the address of the deterministic PUSH0 clone of `implementation`,
    /// with `salt` by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress_PUSH0(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHash_PUSH0(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*           CLONES WITH IMMUTABLE ARGS OPERATIONS            */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    // Note: This implementation of CWIA differs from the original implementation.
    // If the calldata is empty, it will emit a `ReceiveETH(uint256)` event and skip the `DELEGATECALL`.
    /// @dev Deploys a clone of `implementation` with immutable arguments encoded in `data`.
    function clone(address implementation, bytes memory data) internal returns (address instance) {
        instance = clone(0, implementation, data);
    }
    /// @dev Deploys a clone of `implementation` with immutable arguments encoded in `data`.
    function clone(uint256 value, address implementation, bytes memory data)
        internal
        returns (address instance)
    {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)
            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)
            // The `creationSize` is `extraLength + 108`
            // The `runSize` is `creationSize - 10`.
            /**
             * ---------------------------------------------------------------------------------------------------+
             * CREATION (10 bytes)                                                                                |
             * ---------------------------------------------------------------------------------------------------|
             * Opcode     | Mnemonic          | Stack     | Memory                                                |
             * ---------------------------------------------------------------------------------------------------|
             * 61 runSize | PUSH2 runSize     | r         |                                                       |
             * 3d         | RETURNDATASIZE    | 0 r       |                                                       |
             * 81         | DUP2              | r 0 r     |                                                       |
             * 60 offset  | PUSH1 offset      | o r 0 r   |                                                       |
             * 3d         | RETURNDATASIZE    | 0 o r 0 r |                                                       |
             * 39         | CODECOPY          | 0 r       | [0..runSize): runtime code                            |
             * f3         | RETURN            |           | [0..runSize): runtime code                            |
             * ---------------------------------------------------------------------------------------------------|
             * RUNTIME (98 bytes + extraLength)                                                                   |
             * ---------------------------------------------------------------------------------------------------|
             * Opcode   | Mnemonic       | Stack                    | Memory                                      |
             * ---------------------------------------------------------------------------------------------------|
             *                                                                                                    |
             * ::: if no calldata, emit event & return w/o `DELEGATECALL` ::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds                      |                                             |
             * 60 0x2c  | PUSH1 0x2c     | 0x2c cds                 |                                             |
             * 57       | JUMPI          |                          |                                             |
             * 34       | CALLVALUE      | cv                       |                                             |
             * 3d       | RETURNDATASIZE | 0 cv                     |                                             |
             * 52       | MSTORE         |                          | [0..0x20): callvalue                        |
             * 7f sig   | PUSH32 0x9e..  | sig                      | [0..0x20): callvalue                        |
             * 59       | MSIZE          | 0x20 sig                 | [0..0x20): callvalue                        |
             * 3d       | RETURNDATASIZE | 0 0x20 sig               | [0..0x20): callvalue                        |
             * a1       | LOG1           |                          | [0..0x20): callvalue                        |
             * 00       | STOP           |                          | [0..0x20): callvalue                        |
             * 5b       | JUMPDEST       |                          |                                             |
             *                                                                                                    |
             * ::: copy calldata to memory :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds                      |                                             |
             * 3d       | RETURNDATASIZE | 0 cds                    |                                             |
             * 3d       | RETURNDATASIZE | 0 0 cds                  |                                             |
             * 37       | CALLDATACOPY   |                          | [0..cds): calldata                          |
             *                                                                                                    |
             * ::: keep some values in stack :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d       | RETURNDATASIZE | 0                        | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0                      | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0 0                    | [0..cds): calldata                          |
             * 3d       | RETURNDATASIZE | 0 0 0 0                  | [0..cds): calldata                          |
             * 61 extra | PUSH2 extra    | e 0 0 0 0                | [0..cds): calldata                          |
             *                                                                                                    |
             * ::: copy extra data to memory :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 80       | DUP1           | e e 0 0 0 0              | [0..cds): calldata                          |
             * 60 0x62  | PUSH1 0x62     | 0x62 e e 0 0 0 0         | [0..cds): calldata                          |
             * 36       | CALLDATASIZE   | cds 0x62 e e 0 0 0 0     | [0..cds): calldata                          |
             * 39       | CODECOPY       | e 0 0 0 0                | [0..cds): calldata, [cds..cds+e): extraData |
             *                                                                                                    |
             * ::: delegate call to the implementation contract ::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36       | CALLDATASIZE   | cds e 0 0 0 0            | [0..cds): calldata, [cds..cds+e): extraData |
             * 01       | ADD            | cds+e 0 0 0 0            | [0..cds): calldata, [cds..cds+e): extraData |
             * 3d       | RETURNDATASIZE | 0 cds+e 0 0 0 0          | [0..cds): calldata, [cds..cds+e): extraData |
             * 73 addr  | PUSH20 addr    | addr 0 cds+e 0 0 0 0     | [0..cds): calldata, [cds..cds+e): extraData |
             * 5a       | GAS            | gas addr 0 cds+e 0 0 0 0 | [0..cds): calldata, [cds..cds+e): extraData |
             * f4       | DELEGATECALL   | success 0 0              | [0..cds): calldata, [cds..cds+e): extraData |
             *                                                                                                    |
             * ::: copy return data to memory ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d       | RETURNDATASIZE | rds success 0 0          | [0..cds): calldata, [cds..cds+e): extraData |
             * 3d       | RETURNDATASIZE | rds rds success 0 0      | [0..cds): calldata, [cds..cds+e): extraData |
             * 93       | SWAP4          | 0 rds success 0 rds      | [0..cds): calldata, [cds..cds+e): extraData |
             * 80       | DUP1           | 0 0 rds success 0 rds    | [0..cds): calldata, [cds..cds+e): extraData |
             * 3e       | RETURNDATACOPY | success 0 rds            | [0..rds): returndata                        |
             *                                                                                                    |
             * 60 0x60  | PUSH1 0x60     | 0x60 success 0 rds       | [0..rds): returndata                        |
             * 57       | JUMPI          | 0 rds                    | [0..rds): returndata                        |
             *                                                                                                    |
             * ::: revert ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * fd       | REVERT         |                          | [0..rds): returndata                        |
             *                                                                                                    |
             * ::: return ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b       | JUMPDEST       | 0 rds                    | [0..rds): returndata                        |
             * f3       | RETURN         |                          | [0..rds): returndata                        |
             * ---------------------------------------------------------------------------------------------------+
             */
            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                // Do a out-of-gas revert if `extraLength` is too big. 0xffff - 0x62 + 0x01 = 0xff9e.
                // The actual EVM limit may be smaller and may change over time.
                sub(data, add(0x59, lt(extraLength, 0xff9e))),
                or(shl(0x78, add(extraLength, 0x62)), 0xfd6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))
            instance := create(value, sub(data, 0x4c), add(extraLength, 0x6c))
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }
    /// @dev Deploys a deterministic clone of `implementation`
    /// with immutable arguments encoded in `data` and `salt`.
    function cloneDeterministic(address implementation, bytes memory data, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = cloneDeterministic(0, implementation, data, salt);
    }
    /// @dev Deploys a deterministic clone of `implementation`
    /// with immutable arguments encoded in `data` and `salt`.
    function cloneDeterministic(
        uint256 value,
        address implementation,
        bytes memory data,
        bytes32 salt
    ) internal returns (address instance) {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)
            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)
            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                // Do a out-of-gas revert if `extraLength` is too big. 0xffff - 0x62 + 0x01 = 0xff9e.
                // The actual EVM limit may be smaller and may change over time.
                sub(data, add(0x59, lt(extraLength, 0xff9e))),
                or(shl(0x78, add(extraLength, 0x62)), 0xfd6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))
            instance := create2(value, sub(data, 0x4c), add(extraLength, 0x6c), salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }
    /// @dev Returns the initialization code hash of the clone of `implementation`
    /// using immutable arguments encoded in `data`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHash(address implementation, bytes memory data)
        internal
        pure
        returns (bytes32 hash)
    {
        assembly {
            // Compute the boundaries of the data and cache the memory slots around it.
            let mBefore3 := mload(sub(data, 0x60))
            let mBefore2 := mload(sub(data, 0x40))
            let mBefore1 := mload(sub(data, 0x20))
            let dataLength := mload(data)
            let dataEnd := add(add(data, 0x20), dataLength)
            let mAfter1 := mload(dataEnd)
            // Do a out-of-gas revert if `dataLength` is too big. 0xffff - 0x02 - 0x62 = 0xff9b.
            // The actual EVM limit may be smaller and may change over time.
            returndatacopy(returndatasize(), returndatasize(), gt(dataLength, 0xff9b))
            // +2 bytes for telling how much data there is appended to the call.
            let extraLength := add(dataLength, 2)
            mstore(data, 0x5af43d3d93803e606057fd5bf3) // Write the bytecode before the data.
            mstore(sub(data, 0x0d), implementation) // Write the address of the implementation.
            // Write the rest of the bytecode.
            mstore(
                sub(data, 0x21),
                or(shl(0x48, extraLength), 0x593da1005b363d3d373d3d3d3d610000806062363936013d73)
            )
            // `keccak256("ReceiveETH(uint256)")`
            mstore(
                sub(data, 0x3a), 0x9e4ac34f21c619cefc926c8bd93b54bf5a39c7ab2127a895af1cc0691d7e3dff
            )
            mstore(
                sub(data, 0x5a),
                or(shl(0x78, add(extraLength, 0x62)), 0x6100003d81600a3d39f336602c57343d527f)
            )
            mstore(dataEnd, shl(0xf0, extraLength))
            hash := keccak256(sub(data, 0x4c), add(extraLength, 0x6c))
            // Restore the overwritten memory surrounding `data`.
            mstore(dataEnd, mAfter1)
            mstore(data, dataLength)
            mstore(sub(data, 0x20), mBefore1)
            mstore(sub(data, 0x40), mBefore2)
            mstore(sub(data, 0x60), mBefore3)
        }
    }
    /// @dev Returns the address of the deterministic clone of
    /// `implementation` using immutable arguments encoded in `data`, with `salt`, by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(
        address implementation,
        bytes memory data,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHash(implementation, data);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*              MINIMAL ERC1967 PROXY OPERATIONS              */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    // Note: The ERC1967 proxy here is intended to be upgraded with UUPS.
    // This is NOT the same as ERC1967Factory's transparent proxy, which includes admin logic.
    /// @dev Deploys a minimal ERC1967 proxy with `implementation`.
    function deployERC1967(address implementation) internal returns (address instance) {
        instance = deployERC1967(0, implementation);
    }
    /// @dev Deploys a minimal ERC1967 proxy with `implementation`.
    function deployERC1967(uint256 value, address implementation)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            /**
             * ---------------------------------------------------------------------------------+
             * CREATION (34 bytes)                                                              |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             * 60 runSize | PUSH1 runSize  | r                |                                 |
             * 3d         | RETURNDATASIZE | 0 r              |                                 |
             * 81         | DUP2           | r 0 r            |                                 |
             * 60 offset  | PUSH1 offset   | o r 0 r          |                                 |
             * 3d         | RETURNDATASIZE | 0 o r 0 r        |                                 |
             * 39         | CODECOPY       | 0 r              | [0..runSize): runtime code      |
             * 73 impl    | PUSH20 impl    | impl 0 r         | [0..runSize): runtime code      |
             * 60 slotPos | PUSH1 slotPos  | slotPos impl 0 r | [0..runSize): runtime code      |
             * 51         | MLOAD          | slot impl 0 r    | [0..runSize): runtime code      |
             * 55         | SSTORE         | 0 r              | [0..runSize): runtime code      |
             * f3         | RETURN         |                  | [0..runSize): runtime code      |
             * ---------------------------------------------------------------------------------|
             * RUNTIME (62 bytes)                                                               |
             * ---------------------------------------------------------------------------------|
             * Opcode     | Mnemonic       | Stack            | Memory                          |
             * ---------------------------------------------------------------------------------|
             *                                                                                  |
             * ::: copy calldata to memory :::::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 36         | CALLDATASIZE   | cds              |                                 |
             * 3d         | RETURNDATASIZE | 0 cds            |                                 |
             * 3d         | RETURNDATASIZE | 0 0 cds          |                                 |
             * 37         | CALLDATACOPY   |                  | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: delegatecall to implementation ::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | 0                |                                 |
             * 3d         | RETURNDATASIZE | 0 0              |                                 |
             * 36         | CALLDATASIZE   | cds 0 0          | [0..calldatasize): calldata     |
             * 3d         | RETURNDATASIZE | 0 cds 0 0        | [0..calldatasize): calldata     |
             * 7f slot    | PUSH32 slot    | s 0 cds 0 0      | [0..calldatasize): calldata     |
             * 54         | SLOAD          | i 0 cds 0 0      | [0..calldatasize): calldata     |
             * 5a         | GAS            | g i 0 cds 0 0    | [0..calldatasize): calldata     |
             * f4         | DELEGATECALL   | succ             | [0..calldatasize): calldata     |
             *                                                                                  |
             * ::: copy returndata to memory :::::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds succ         | [0..calldatasize): calldata     |
             * 60 0x00    | PUSH1 0x00     | 0 rds succ       | [0..calldatasize): calldata     |
             * 80         | DUP1           | 0 0 rds succ     | [0..calldatasize): calldata     |
             * 3e         | RETURNDATACOPY | succ             | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: branch on delegatecall status :::::::::::::::::::::::::::::::::::::::::::::: |
             * 60 0x38    | PUSH1 0x38     | dest succ        | [0..returndatasize): returndata |
             * 57         | JUMPI          |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall failed, revert :::::::::::::::::::::::::::::::::::::::::::::::: |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * fd         | REVERT         |                  | [0..returndatasize): returndata |
             *                                                                                  |
             * ::: delegatecall succeeded, return ::::::::::::::::::::::::::::::::::::::::::::: |
             * 5b         | JUMPDEST       |                  | [0..returndatasize): returndata |
             * 3d         | RETURNDATASIZE | rds              | [0..returndatasize): returndata |
             * 60 0x00    | PUSH1 0x00     | 0 rds            | [0..returndatasize): returndata |
             * f3         | RETURN         |                  | [0..returndatasize): returndata |
             * ---------------------------------------------------------------------------------+
             */
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            instance := create(value, 0x21, 0x5f)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }
    /// @dev Deploys a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    function deployDeterministicERC1967(address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        instance = deployDeterministicERC1967(0, implementation, salt);
    }
    /// @dev Deploys a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    function deployDeterministicERC1967(uint256 value, address implementation, bytes32 salt)
        internal
        returns (address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            instance := create2(value, 0x21, 0x5f, salt)
            if iszero(instance) {
                mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                revert(0x1c, 0x04)
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }
    /// @dev Creates a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967(address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        return createDeterministicERC1967(0, implementation, salt);
    }
    /// @dev Creates a deterministic minimal ERC1967 proxy with `implementation` and `salt`.
    /// Note: This method is intended for use in ERC4337 factories,
    /// which are expected to NOT revert if the proxy is already deployed.
    function createDeterministicERC1967(uint256 value, address implementation, bytes32 salt)
        internal
        returns (bool alreadyDeployed, address instance)
    {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            // Compute and store the bytecode hash.
            mstore(add(m, 0x35), keccak256(0x21, 0x5f))
            mstore(m, shl(88, address()))
            mstore8(m, 0xff) // Write the prefix.
            mstore(add(m, 0x15), salt)
            instance := keccak256(m, 0x55)
            for {} 1 {} {
                if iszero(extcodesize(instance)) {
                    instance := create2(value, 0x21, 0x5f, salt)
                    if iszero(instance) {
                        mstore(0x00, 0x30116425) // `DeploymentFailed()`.
                        revert(0x1c, 0x04)
                    }
                    break
                }
                alreadyDeployed := 1
                if iszero(value) { break }
                if iszero(call(gas(), instance, value, codesize(), 0x00, codesize(), 0x00)) {
                    mstore(0x00, 0xb12d13eb) // `ETHTransferFailed()`.
                    revert(0x1c, 0x04)
                }
                break
            }
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }
    /// @dev Returns the initialization code hash of the clone of `implementation`
    /// using immutable arguments encoded in `data`.
    /// Used for mining vanity addresses with create2crunch.
    function initCodeHashERC1967(address implementation) internal pure returns (bytes32 hash) {
        /// @solidity memory-safe-assembly
        assembly {
            let m := mload(0x40) // Cache the free memory pointer.
            mstore(0x60, 0xcc3735a920a3ca505d382bbc545af43d6000803e6038573d6000fd5b3d6000f3)
            mstore(0x40, 0x5155f3363d3d373d3d363d7f360894a13ba1a3210667c828492db98dca3e2076)
            mstore(0x20, 0x6009)
            mstore(0x1e, implementation)
            mstore(0x0a, 0x603d3d8160223d3973)
            hash := keccak256(0x21, 0x5f)
            mstore(0x40, m) // Restore the free memory pointer.
            mstore(0x60, 0) // Restore the zero slot.
        }
    }
    /// @dev Returns the address of the deterministic clone of
    /// `implementation` using immutable arguments encoded in `data`, with `salt`, by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddressERC1967(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        bytes32 hash = initCodeHashERC1967(implementation);
        predicted = predictDeterministicAddress(hash, salt, deployer);
    }
    /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/
    /*                      OTHER OPERATIONS                      */
    /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/
    /// @dev Returns the address when a contract with initialization code hash,
    /// `hash`, is deployed with `salt`, by `deployer`.
    /// Note: The returned result has dirty upper 96 bits. Please clean if used in assembly.
    function predictDeterministicAddress(bytes32 hash, bytes32 salt, address deployer)
        internal
        pure
        returns (address predicted)
    {
        /// @solidity memory-safe-assembly
        assembly {
            // Compute and store the bytecode hash.
            mstore8(0x00, 0xff) // Write the prefix.
            mstore(0x35, hash)
            mstore(0x01, shl(96, deployer))
            mstore(0x15, salt)
            predicted := keccak256(0x00, 0x55)
            mstore(0x35, 0) // Restore the overwritten part of the free memory pointer.
        }
    }
    /// @dev Requires that `salt` starts with either the zero address or `by`.
    function checkStartsWith(bytes32 salt, address by) internal pure {
        /// @solidity memory-safe-assembly
        assembly {
            // If the salt does not start with the zero address or `by`.
            if iszero(or(iszero(shr(96, salt)), eq(shr(96, shl(96, by)), shr(96, salt)))) {
                mstore(0x00, 0x0c4549ef) // `SaltDoesNotStartWith()`.
                revert(0x1c, 0x04)
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)
pragma solidity ^0.8.0;
import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";
/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;
    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }
    function __Ownable_init_unchained() internal onlyInitializing {
        _transferOwnership(_msgSender());
    }
    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }
    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }
    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }
    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { IInitializable } from "src/dispute/interfaces/IInitializable.sol";
import "src/dispute/lib/Types.sol";
/// @title IDisputeGame
/// @notice The generic interface for a DisputeGame contract.
interface IDisputeGame is IInitializable {
    /// @notice Emitted when the game is resolved.
    /// @param status The status of the game after resolution.
    event Resolved(GameStatus indexed status);
    /// @notice Returns the timestamp that the DisputeGame contract was created at.
    /// @return createdAt_ The timestamp that the DisputeGame contract was created at.
    function createdAt() external view returns (Timestamp createdAt_);
    /// @notice Returns the timestamp that the DisputeGame contract was resolved at.
    /// @return resolvedAt_ The timestamp that the DisputeGame contract was resolved at.
    function resolvedAt() external view returns (Timestamp resolvedAt_);
    /// @notice Returns the current status of the game.
    /// @return status_ The current status of the game.
    function status() external view returns (GameStatus status_);
    /// @notice Getter for the game type.
    /// @dev The reference impl should be entirely different depending on the type (fault, validity)
    ///      i.e. The game type should indicate the security model.
    /// @return gameType_ The type of proof system being used.
    function gameType() external view returns (GameType gameType_);
    /// @notice Getter for the creator of the dispute game.
    /// @dev `clones-with-immutable-args` argument #1
    /// @return creator_ The creator of the dispute game.
    function gameCreator() external pure returns (address creator_);
    /// @notice Getter for the root claim.
    /// @dev `clones-with-immutable-args` argument #2
    /// @return rootClaim_ The root claim of the DisputeGame.
    function rootClaim() external pure returns (Claim rootClaim_);
    /// @notice Getter for the parent hash of the L1 block when the dispute game was created.
    /// @dev `clones-with-immutable-args` argument #3
    /// @return l1Head_ The parent hash of the L1 block when the dispute game was created.
    function l1Head() external pure returns (Hash l1Head_);
    /// @notice Getter for the extra data.
    /// @dev `clones-with-immutable-args` argument #4
    /// @return extraData_ Any extra data supplied to the dispute game contract by the creator.
    function extraData() external pure returns (bytes memory extraData_);
    /// @notice If all necessary information has been gathered, this function should mark the game
    ///         status as either `CHALLENGER_WINS` or `DEFENDER_WINS` and return the status of
    ///         the resolved game. It is at this stage that the bonds should be awarded to the
    ///         necessary parties.
    /// @dev May only be called if the `status` is `IN_PROGRESS`.
    /// @return status_ The status of the game after resolution.
    function resolve() external returns (GameStatus status_);
    /// @notice A compliant implementation of this interface should return the components of the
    ///         game UUID's preimage provided in the cwia payload. The preimage of the UUID is
    ///         constructed as `keccak256(gameType . rootClaim . extraData)` where `.` denotes
    ///         concatenation.
    /// @return gameType_ The type of proof system being used.
    /// @return rootClaim_ The root claim of the DisputeGame.
    /// @return extraData_ Any extra data supplied to the dispute game contract by the creator.
    function gameData() external view returns (GameType gameType_, Claim rootClaim_, bytes memory extraData_);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { IDisputeGame } from "./IDisputeGame.sol";
import "src/dispute/lib/Types.sol";
/// @title IDisputeGameFactory
/// @notice The interface for a DisputeGameFactory contract.
interface IDisputeGameFactory {
    /// @notice Emitted when a new dispute game is created
    /// @param disputeProxy The address of the dispute game proxy
    /// @param gameType The type of the dispute game proxy's implementation
    /// @param rootClaim The root claim of the dispute game
    event DisputeGameCreated(address indexed disputeProxy, GameType indexed gameType, Claim indexed rootClaim);
    /// @notice Emitted when a new game implementation added to the factory
    /// @param impl The implementation contract for the given `GameType`.
    /// @param gameType The type of the DisputeGame.
    event ImplementationSet(address indexed impl, GameType indexed gameType);
    /// @notice Emitted when a game type's initialization bond is updated
    /// @param gameType The type of the DisputeGame.
    /// @param newBond The new bond (in wei) for initializing the game type.
    event InitBondUpdated(GameType indexed gameType, uint256 indexed newBond);
    /// @notice Information about a dispute game found in a `findLatestGames` search.
    struct GameSearchResult {
        uint256 index;
        GameId metadata;
        Timestamp timestamp;
        Claim rootClaim;
        bytes extraData;
    }
    /// @notice The total number of dispute games created by this factory.
    /// @return gameCount_ The total number of dispute games created by this factory.
    function gameCount() external view returns (uint256 gameCount_);
    /// @notice `games` queries an internal mapping that maps the hash of
    ///         `gameType ++ rootClaim ++ extraData` to the deployed `DisputeGame` clone.
    /// @dev `++` equates to concatenation.
    /// @param _gameType The type of the DisputeGame - used to decide the proxy implementation
    /// @param _rootClaim The root claim of the DisputeGame.
    /// @param _extraData Any extra data that should be provided to the created dispute game.
    /// @return proxy_ The clone of the `DisputeGame` created with the given parameters.
    ///         Returns `address(0)` if nonexistent.
    /// @return timestamp_ The timestamp of the creation of the dispute game.
    function games(
        GameType _gameType,
        Claim _rootClaim,
        bytes calldata _extraData
    )
        external
        view
        returns (IDisputeGame proxy_, Timestamp timestamp_);
    /// @notice `gameAtIndex` returns the dispute game contract address and its creation timestamp
    ///          at the given index. Each created dispute game increments the underlying index.
    /// @param _index The index of the dispute game.
    /// @return gameType_ The type of the DisputeGame - used to decide the proxy implementation.
    /// @return timestamp_ The timestamp of the creation of the dispute game.
    /// @return proxy_ The clone of the `DisputeGame` created with the given parameters.
    ///         Returns `address(0)` if nonexistent.
    function gameAtIndex(uint256 _index)
        external
        view
        returns (GameType gameType_, Timestamp timestamp_, IDisputeGame proxy_);
    /// @notice `gameImpls` is a mapping that maps `GameType`s to their respective
    ///         `IDisputeGame` implementations.
    /// @param _gameType The type of the dispute game.
    /// @return impl_ The address of the implementation of the game type.
    ///         Will be cloned on creation of a new dispute game with the given `gameType`.
    function gameImpls(GameType _gameType) external view returns (IDisputeGame impl_);
    /// @notice Returns the required bonds for initializing a dispute game of the given type.
    /// @param _gameType The type of the dispute game.
    /// @return bond_ The required bond for initializing a dispute game of the given type.
    function initBonds(GameType _gameType) external view returns (uint256 bond_);
    /// @notice Creates a new DisputeGame proxy contract.
    /// @param _gameType The type of the DisputeGame - used to decide the proxy implementation.
    /// @param _rootClaim The root claim of the DisputeGame.
    /// @param _extraData Any extra data that should be provided to the created dispute game.
    /// @return proxy_ The address of the created DisputeGame proxy.
    function create(
        GameType _gameType,
        Claim _rootClaim,
        bytes calldata _extraData
    )
        external
        payable
        returns (IDisputeGame proxy_);
    /// @notice Sets the implementation contract for a specific `GameType`.
    /// @dev May only be called by the `owner`.
    /// @param _gameType The type of the DisputeGame.
    /// @param _impl The implementation contract for the given `GameType`.
    function setImplementation(GameType _gameType, IDisputeGame _impl) external;
    /// @notice Sets the bond (in wei) for initializing a game type.
    /// @dev May only be called by the `owner`.
    /// @param _gameType The type of the DisputeGame.
    /// @param _initBond The bond (in wei) for initializing a game type.
    function setInitBond(GameType _gameType, uint256 _initBond) external;
    /// @notice Returns a unique identifier for the given dispute game parameters.
    /// @dev Hashes the concatenation of `gameType . rootClaim . extraData`
    ///      without expanding memory.
    /// @param _gameType The type of the DisputeGame.
    /// @param _rootClaim The root claim of the DisputeGame.
    /// @param _extraData Any extra data that should be provided to the created dispute game.
    /// @return uuid_ The unique identifier for the given dispute game parameters.
    function getGameUUID(
        GameType _gameType,
        Claim _rootClaim,
        bytes memory _extraData
    )
        external
        pure
        returns (Hash uuid_);
    /// @notice Finds the `_n` most recent `GameId`'s of type `_gameType` starting at `_start`. If there are less than
    ///         `_n` games of type `_gameType` starting at `_start`, then the returned array will be shorter than `_n`.
    /// @param _gameType The type of game to find.
    /// @param _start The index to start the reverse search from.
    /// @param _n The number of games to find.
    function findLatestGames(
        GameType _gameType,
        uint256 _start,
        uint256 _n
    )
        external
        view
        returns (GameSearchResult[] memory games_);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.15;
import "src/dispute/lib/LibUDT.sol";
////////////////////////////////////////////////////////////////
//                `DisputeGameFactory` Errors                 //
////////////////////////////////////////////////////////////////
/// @notice Thrown when a dispute game is attempted to be created with an unsupported game type.
/// @param gameType The unsupported game type.
error NoImplementation(GameType gameType);
/// @notice Thrown when a dispute game that already exists is attempted to be created.
/// @param uuid The UUID of the dispute game that already exists.
error GameAlreadyExists(Hash uuid);
/// @notice Thrown when the root claim has an unexpected VM status.
///         Some games can only start with a root-claim with a specific status.
/// @param rootClaim is the claim that was unexpected.
error UnexpectedRootClaim(Claim rootClaim);
////////////////////////////////////////////////////////////////
//                 `FaultDisputeGame` Errors                  //
////////////////////////////////////////////////////////////////
/// @notice Thrown when a dispute game has already been initialized.
error AlreadyInitialized();
/// @notice Thrown when a supplied bond is not equal to the required bond amount to cover the cost of the interaction.
error IncorrectBondAmount();
/// @notice Thrown when a credit claim is attempted for a value of 0.
error NoCreditToClaim();
/// @notice Thrown when the transfer of credit to a recipient account reverts.
error BondTransferFailed();
/// @notice Thrown when the `extraData` passed to the CWIA proxy is of improper length, or contains invalid information.
error BadExtraData();
/// @notice Thrown when a defense against the root claim is attempted.
error CannotDefendRootClaim();
/// @notice Thrown when a claim is attempting to be made that already exists.
error ClaimAlreadyExists();
/// @notice Thrown when a disputed claim does not match its index in the game.
error InvalidDisputedClaimIndex();
/// @notice Thrown when an action that requires the game to be `IN_PROGRESS` is invoked when
///         the game is not in progress.
error GameNotInProgress();
/// @notice Thrown when a move is attempted to be made after the clock has timed out.
error ClockTimeExceeded();
/// @notice Thrown when the game is attempted to be resolved too early.
error ClockNotExpired();
/// @notice Thrown when a move is attempted to be made at or greater than the max depth of the game.
error GameDepthExceeded();
/// @notice Thrown when a step is attempted above the maximum game depth.
error InvalidParent();
/// @notice Thrown when an invalid prestate is supplied to `step`.
error InvalidPrestate();
/// @notice Thrown when a step is made that computes the expected post state correctly.
error ValidStep();
/// @notice Thrown when a game is attempted to be initialized with an L1 head that does
///         not contain the disputed output root.
error L1HeadTooOld();
/// @notice Thrown when an invalid local identifier is passed to the `addLocalData` function.
error InvalidLocalIdent();
/// @notice Thrown when resolving claims out of order.
error OutOfOrderResolution();
/// @notice Thrown when resolving a claim that has already been resolved.
error ClaimAlreadyResolved();
/// @notice Thrown when a parent output root is attempted to be found on a claim that is in
///         the output root portion of the tree.
error ClaimAboveSplit();
/// @notice Thrown on deployment if the split depth is greater than or equal to the max
///         depth of the game.
error InvalidSplitDepth();
/// @notice Thrown on deployment if the max clock duration is less than or equal to the clock extension.
error InvalidClockExtension();
/// @notice Thrown on deployment if the max depth is greater than `LibPosition.`
error MaxDepthTooLarge();
/// @notice Thrown when trying to step against a claim for a second time, after it has already been countered with
///         an instruction step.
error DuplicateStep();
/// @notice Thrown when an anchor root is not found for a given game type.
error AnchorRootNotFound();
/// @notice Thrown when an output root proof is invalid.
error InvalidOutputRootProof();
/// @notice Thrown when header RLP is invalid with respect to the block hash in an output root proof.
error InvalidHeaderRLP();
/// @notice Thrown when there is a match between the block number in the output root proof and the block number
///         claimed in the dispute game.
error BlockNumberMatches();
/// @notice Thrown when the L2 block number claim has already been challenged.
error L2BlockNumberChallenged();
////////////////////////////////////////////////////////////////
//              `PermissionedDisputeGame` Errors              //
////////////////////////////////////////////////////////////////
/// @notice Thrown when an unauthorized address attempts to interact with the game.
error BadAuth();
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title Storage
/// @notice Storage handles reading and writing to arbitary storage locations
library Storage {
    /// @notice Returns an address stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getAddress(bytes32 _slot) internal view returns (address addr_) {
        assembly {
            addr_ := sload(_slot)
        }
    }
    /// @notice Stores an address in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _address The protocol version to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting addresses
    ///      in arbitrary storage slots.
    function setAddress(bytes32 _slot, address _address) internal {
        assembly {
            sstore(_slot, _address)
        }
    }
    /// @notice Returns a uint256 stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getUint(bytes32 _slot) internal view returns (uint256 value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
    /// @notice Stores a value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _value The protocol version to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setUint(bytes32 _slot, uint256 _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Returns a bytes32 stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getBytes32(bytes32 _slot) internal view returns (bytes32 value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
    /// @notice Stores a bytes32 value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _value The bytes32 value to store.
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setBytes32(bytes32 _slot, bytes32 _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Stores a bool value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the bool in.
    /// @param _value The bool value to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setBool(bytes32 _slot, bool _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Returns a bool stored in an arbitrary storage slot.
    /// @param _slot The storage slot to retrieve the bool from.
    function getBool(bytes32 _slot) internal view returns (bool value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { Types } from "src/libraries/Types.sol";
import { Hashing } from "src/libraries/Hashing.sol";
import { RLPWriter } from "src/libraries/rlp/RLPWriter.sol";
/// @title Encoding
/// @notice Encoding handles Optimism's various different encoding schemes.
library Encoding {
    /// @notice RLP encodes the L2 transaction that would be generated when a given deposit is sent
    ///         to the L2 system. Useful for searching for a deposit in the L2 system. The
    ///         transaction is prefixed with 0x7e to identify its EIP-2718 type.
    /// @param _tx User deposit transaction to encode.
    /// @return RLP encoded L2 deposit transaction.
    function encodeDepositTransaction(Types.UserDepositTransaction memory _tx) internal pure returns (bytes memory) {
        bytes32 source = Hashing.hashDepositSource(_tx.l1BlockHash, _tx.logIndex);
        bytes[] memory raw = new bytes[](8);
        raw[0] = RLPWriter.writeBytes(abi.encodePacked(source));
        raw[1] = RLPWriter.writeAddress(_tx.from);
        raw[2] = _tx.isCreation ? RLPWriter.writeBytes("") : RLPWriter.writeAddress(_tx.to);
        raw[3] = RLPWriter.writeUint(_tx.mint);
        raw[4] = RLPWriter.writeUint(_tx.value);
        raw[5] = RLPWriter.writeUint(uint256(_tx.gasLimit));
        raw[6] = RLPWriter.writeBool(false);
        raw[7] = RLPWriter.writeBytes(_tx.data);
        return abi.encodePacked(uint8(0x7e), RLPWriter.writeList(raw));
    }
    /// @notice Encodes the cross domain message based on the version that is encoded into the
    ///         message nonce.
    /// @param _nonce    Message nonce with version encoded into the first two bytes.
    /// @param _sender   Address of the sender of the message.
    /// @param _target   Address of the target of the message.
    /// @param _value    ETH value to send to the target.
    /// @param _gasLimit Gas limit to use for the message.
    /// @param _data     Data to send with the message.
    /// @return Encoded cross domain message.
    function encodeCrossDomainMessage(
        uint256 _nonce,
        address _sender,
        address _target,
        uint256 _value,
        uint256 _gasLimit,
        bytes memory _data
    )
        internal
        pure
        returns (bytes memory)
    {
        (, uint16 version) = decodeVersionedNonce(_nonce);
        if (version == 0) {
            return encodeCrossDomainMessageV0(_target, _sender, _data, _nonce);
        } else if (version == 1) {
            return encodeCrossDomainMessageV1(_nonce, _sender, _target, _value, _gasLimit, _data);
        } else {
            revert("Encoding: unknown cross domain message version");
        }
    }
    /// @notice Encodes a cross domain message based on the V0 (legacy) encoding.
    /// @param _target Address of the target of the message.
    /// @param _sender Address of the sender of the message.
    /// @param _data   Data to send with the message.
    /// @param _nonce  Message nonce.
    /// @return Encoded cross domain message.
    function encodeCrossDomainMessageV0(
        address _target,
        address _sender,
        bytes memory _data,
        uint256 _nonce
    )
        internal
        pure
        returns (bytes memory)
    {
        return abi.encodeWithSignature("relayMessage(address,address,bytes,uint256)", _target, _sender, _data, _nonce);
    }
    /// @notice Encodes a cross domain message based on the V1 (current) encoding.
    /// @param _nonce    Message nonce.
    /// @param _sender   Address of the sender of the message.
    /// @param _target   Address of the target of the message.
    /// @param _value    ETH value to send to the target.
    /// @param _gasLimit Gas limit to use for the message.
    /// @param _data     Data to send with the message.
    /// @return Encoded cross domain message.
    function encodeCrossDomainMessageV1(
        uint256 _nonce,
        address _sender,
        address _target,
        uint256 _value,
        uint256 _gasLimit,
        bytes memory _data
    )
        internal
        pure
        returns (bytes memory)
    {
        return abi.encodeWithSignature(
            "relayMessage(uint256,address,address,uint256,uint256,bytes)",
            _nonce,
            _sender,
            _target,
            _value,
            _gasLimit,
            _data
        );
    }
    /// @notice Adds a version number into the first two bytes of a message nonce.
    /// @param _nonce   Message nonce to encode into.
    /// @param _version Version number to encode into the message nonce.
    /// @return Message nonce with version encoded into the first two bytes.
    function encodeVersionedNonce(uint240 _nonce, uint16 _version) internal pure returns (uint256) {
        uint256 nonce;
        assembly {
            nonce := or(shl(240, _version), _nonce)
        }
        return nonce;
    }
    /// @notice Pulls the version out of a version-encoded nonce.
    /// @param _nonce Message nonce with version encoded into the first two bytes.
    /// @return Nonce without encoded version.
    /// @return Version of the message.
    function decodeVersionedNonce(uint256 _nonce) internal pure returns (uint240, uint16) {
        uint240 nonce;
        uint16 version;
        assembly {
            nonce := and(_nonce, 0x0000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff)
            version := shr(240, _nonce)
        }
        return (nonce, version);
    }
    /// @notice Returns an appropriately encoded call to L1Block.setL1BlockValuesEcotone
    /// @param baseFeeScalar       L1 base fee Scalar
    /// @param blobBaseFeeScalar   L1 blob base fee Scalar
    /// @param sequenceNumber      Number of L2 blocks since epoch start.
    /// @param timestamp           L1 timestamp.
    /// @param number              L1 blocknumber.
    /// @param baseFee             L1 base fee.
    /// @param blobBaseFee         L1 blob base fee.
    /// @param hash                L1 blockhash.
    /// @param batcherHash         Versioned hash to authenticate batcher by.
    function encodeSetL1BlockValuesEcotone(
        uint32 baseFeeScalar,
        uint32 blobBaseFeeScalar,
        uint64 sequenceNumber,
        uint64 timestamp,
        uint64 number,
        uint256 baseFee,
        uint256 blobBaseFee,
        bytes32 hash,
        bytes32 batcherHash
    )
        internal
        pure
        returns (bytes memory)
    {
        bytes4 functionSignature = bytes4(keccak256("setL1BlockValuesEcotone()"));
        return abi.encodePacked(
            functionSignature,
            baseFeeScalar,
            blobBaseFeeScalar,
            sequenceNumber,
            timestamp,
            number,
            baseFee,
            blobBaseFee,
            hash,
            batcherHash
        );
    }
    /// @notice Returns an appropriately encoded call to L1Block.setL1BlockValuesInterop
    /// @param _baseFeeScalar       L1 base fee Scalar
    /// @param _blobBaseFeeScalar   L1 blob base fee Scalar
    /// @param _sequenceNumber      Number of L2 blocks since epoch start.
    /// @param _timestamp           L1 timestamp.
    /// @param _number              L1 blocknumber.
    /// @param _baseFee             L1 base fee.
    /// @param _blobBaseFee         L1 blob base fee.
    /// @param _hash                L1 blockhash.
    /// @param _batcherHash         Versioned hash to authenticate batcher by.
    /// @param _dependencySet       Array of the chain IDs in the interop dependency set.
    function encodeSetL1BlockValuesInterop(
        uint32 _baseFeeScalar,
        uint32 _blobBaseFeeScalar,
        uint64 _sequenceNumber,
        uint64 _timestamp,
        uint64 _number,
        uint256 _baseFee,
        uint256 _blobBaseFee,
        bytes32 _hash,
        bytes32 _batcherHash,
        uint256[] memory _dependencySet
    )
        internal
        pure
        returns (bytes memory)
    {
        require(_dependencySet.length <= type(uint8).max, "Encoding: dependency set length is too large");
        // Check that the batcher hash is just the address with 0 padding to the left for version 0.
        require(uint160(uint256(_batcherHash)) == uint256(_batcherHash), "Encoding: invalid batcher hash");
        bytes4 functionSignature = bytes4(keccak256("setL1BlockValuesInterop()"));
        return abi.encodePacked(
            functionSignature,
            _baseFeeScalar,
            _blobBaseFeeScalar,
            _sequenceNumber,
            _timestamp,
            _number,
            _baseFee,
            _blobBaseFee,
            _hash,
            _batcherHash,
            uint8(_dependencySet.length),
            _dependencySet
        );
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { Bytes } from "../Bytes.sol";
import { RLPReader } from "../rlp/RLPReader.sol";
/// @title MerkleTrie
/// @notice MerkleTrie is a small library for verifying standard Ethereum Merkle-Patricia trie
///         inclusion proofs. By default, this library assumes a hexary trie. One can change the
///         trie radix constant to support other trie radixes.
library MerkleTrie {
    /// @notice Struct representing a node in the trie.
    /// @custom:field encoded The RLP-encoded node.
    /// @custom:field decoded The RLP-decoded node.
    struct TrieNode {
        bytes encoded;
        RLPReader.RLPItem[] decoded;
    }
    /// @notice Determines the number of elements per branch node.
    uint256 internal constant TREE_RADIX = 16;
    /// @notice Branch nodes have TREE_RADIX elements and one value element.
    uint256 internal constant BRANCH_NODE_LENGTH = TREE_RADIX + 1;
    /// @notice Leaf nodes and extension nodes have two elements, a `path` and a `value`.
    uint256 internal constant LEAF_OR_EXTENSION_NODE_LENGTH = 2;
    /// @notice Prefix for even-nibbled extension node paths.
    uint8 internal constant PREFIX_EXTENSION_EVEN = 0;
    /// @notice Prefix for odd-nibbled extension node paths.
    uint8 internal constant PREFIX_EXTENSION_ODD = 1;
    /// @notice Prefix for even-nibbled leaf node paths.
    uint8 internal constant PREFIX_LEAF_EVEN = 2;
    /// @notice Prefix for odd-nibbled leaf node paths.
    uint8 internal constant PREFIX_LEAF_ODD = 3;
    /// @notice Verifies a proof that a given key/value pair is present in the trie.
    /// @param _key   Key of the node to search for, as a hex string.
    /// @param _value Value of the node to search for, as a hex string.
    /// @param _proof Merkle trie inclusion proof for the desired node. Unlike traditional Merkle
    ///               trees, this proof is executed top-down and consists of a list of RLP-encoded
    ///               nodes that make a path down to the target node.
    /// @param _root  Known root of the Merkle trie. Used to verify that the included proof is
    ///               correctly constructed.
    /// @return valid_ Whether or not the proof is valid.
    function verifyInclusionProof(
        bytes memory _key,
        bytes memory _value,
        bytes[] memory _proof,
        bytes32 _root
    )
        internal
        pure
        returns (bool valid_)
    {
        valid_ = Bytes.equal(_value, get(_key, _proof, _root));
    }
    /// @notice Retrieves the value associated with a given key.
    /// @param _key   Key to search for, as hex bytes.
    /// @param _proof Merkle trie inclusion proof for the key.
    /// @param _root  Known root of the Merkle trie.
    /// @return value_ Value of the key if it exists.
    function get(bytes memory _key, bytes[] memory _proof, bytes32 _root) internal pure returns (bytes memory value_) {
        require(_key.length > 0, "MerkleTrie: empty key");
        TrieNode[] memory proof = _parseProof(_proof);
        bytes memory key = Bytes.toNibbles(_key);
        bytes memory currentNodeID = abi.encodePacked(_root);
        uint256 currentKeyIndex = 0;
        // Proof is top-down, so we start at the first element (root).
        for (uint256 i = 0; i < proof.length; i++) {
            TrieNode memory currentNode = proof[i];
            // Key index should never exceed total key length or we'll be out of bounds.
            require(currentKeyIndex <= key.length, "MerkleTrie: key index exceeds total key length");
            if (currentKeyIndex == 0) {
                // First proof element is always the root node.
                require(
                    Bytes.equal(abi.encodePacked(keccak256(currentNode.encoded)), currentNodeID),
                    "MerkleTrie: invalid root hash"
                );
            } else if (currentNode.encoded.length >= 32) {
                // Nodes 32 bytes or larger are hashed inside branch nodes.
                require(
                    Bytes.equal(abi.encodePacked(keccak256(currentNode.encoded)), currentNodeID),
                    "MerkleTrie: invalid large internal hash"
                );
            } else {
                // Nodes smaller than 32 bytes aren't hashed.
                require(Bytes.equal(currentNode.encoded, currentNodeID), "MerkleTrie: invalid internal node hash");
            }
            if (currentNode.decoded.length == BRANCH_NODE_LENGTH) {
                if (currentKeyIndex == key.length) {
                    // Value is the last element of the decoded list (for branch nodes). There's
                    // some ambiguity in the Merkle trie specification because bytes(0) is a
                    // valid value to place into the trie, but for branch nodes bytes(0) can exist
                    // even when the value wasn't explicitly placed there. Geth treats a value of
                    // bytes(0) as "key does not exist" and so we do the same.
                    value_ = RLPReader.readBytes(currentNode.decoded[TREE_RADIX]);
                    require(value_.length > 0, "MerkleTrie: value length must be greater than zero (branch)");
                    // Extra proof elements are not allowed.
                    require(i == proof.length - 1, "MerkleTrie: value node must be last node in proof (branch)");
                    return value_;
                } else {
                    // We're not at the end of the key yet.
                    // Figure out what the next node ID should be and continue.
                    uint8 branchKey = uint8(key[currentKeyIndex]);
                    RLPReader.RLPItem memory nextNode = currentNode.decoded[branchKey];
                    currentNodeID = _getNodeID(nextNode);
                    currentKeyIndex += 1;
                }
            } else if (currentNode.decoded.length == LEAF_OR_EXTENSION_NODE_LENGTH) {
                bytes memory path = _getNodePath(currentNode);
                uint8 prefix = uint8(path[0]);
                uint8 offset = 2 - (prefix % 2);
                bytes memory pathRemainder = Bytes.slice(path, offset);
                bytes memory keyRemainder = Bytes.slice(key, currentKeyIndex);
                uint256 sharedNibbleLength = _getSharedNibbleLength(pathRemainder, keyRemainder);
                // Whether this is a leaf node or an extension node, the path remainder MUST be a
                // prefix of the key remainder (or be equal to the key remainder) or the proof is
                // considered invalid.
                require(
                    pathRemainder.length == sharedNibbleLength,
                    "MerkleTrie: path remainder must share all nibbles with key"
                );
                if (prefix == PREFIX_LEAF_EVEN || prefix == PREFIX_LEAF_ODD) {
                    // Prefix of 2 or 3 means this is a leaf node. For the leaf node to be valid,
                    // the key remainder must be exactly equal to the path remainder. We already
                    // did the necessary byte comparison, so it's more efficient here to check that
                    // the key remainder length equals the shared nibble length, which implies
                    // equality with the path remainder (since we already did the same check with
                    // the path remainder and the shared nibble length).
                    require(
                        keyRemainder.length == sharedNibbleLength,
                        "MerkleTrie: key remainder must be identical to path remainder"
                    );
                    // Our Merkle Trie is designed specifically for the purposes of the Ethereum
                    // state trie. Empty values are not allowed in the state trie, so we can safely
                    // say that if the value is empty, the key should not exist and the proof is
                    // invalid.
                    value_ = RLPReader.readBytes(currentNode.decoded[1]);
                    require(value_.length > 0, "MerkleTrie: value length must be greater than zero (leaf)");
                    // Extra proof elements are not allowed.
                    require(i == proof.length - 1, "MerkleTrie: value node must be last node in proof (leaf)");
                    return value_;
                } else if (prefix == PREFIX_EXTENSION_EVEN || prefix == PREFIX_EXTENSION_ODD) {
                    // Prefix of 0 or 1 means this is an extension node. We move onto the next node
                    // in the proof and increment the key index by the length of the path remainder
                    // which is equal to the shared nibble length.
                    currentNodeID = _getNodeID(currentNode.decoded[1]);
                    currentKeyIndex += sharedNibbleLength;
                } else {
                    revert("MerkleTrie: received a node with an unknown prefix");
                }
            } else {
                revert("MerkleTrie: received an unparseable node");
            }
        }
        revert("MerkleTrie: ran out of proof elements");
    }
    /// @notice Parses an array of proof elements into a new array that contains both the original
    ///         encoded element and the RLP-decoded element.
    /// @param _proof Array of proof elements to parse.
    /// @return proof_ Proof parsed into easily accessible structs.
    function _parseProof(bytes[] memory _proof) private pure returns (TrieNode[] memory proof_) {
        uint256 length = _proof.length;
        proof_ = new TrieNode[](length);
        for (uint256 i = 0; i < length;) {
            proof_[i] = TrieNode({ encoded: _proof[i], decoded: RLPReader.readList(_proof[i]) });
            unchecked {
                ++i;
            }
        }
    }
    /// @notice Picks out the ID for a node. Node ID is referred to as the "hash" within the
    ///         specification, but nodes < 32 bytes are not actually hashed.
    /// @param _node Node to pull an ID for.
    /// @return id_ ID for the node, depending on the size of its contents.
    function _getNodeID(RLPReader.RLPItem memory _node) private pure returns (bytes memory id_) {
        id_ = _node.length < 32 ? RLPReader.readRawBytes(_node) : RLPReader.readBytes(_node);
    }
    /// @notice Gets the path for a leaf or extension node.
    /// @param _node Node to get a path for.
    /// @return nibbles_ Node path, converted to an array of nibbles.
    function _getNodePath(TrieNode memory _node) private pure returns (bytes memory nibbles_) {
        nibbles_ = Bytes.toNibbles(RLPReader.readBytes(_node.decoded[0]));
    }
    /// @notice Utility; determines the number of nibbles shared between two nibble arrays.
    /// @param _a First nibble array.
    /// @param _b Second nibble array.
    /// @return shared_ Number of shared nibbles.
    function _getSharedNibbleLength(bytes memory _a, bytes memory _b) private pure returns (uint256 shared_) {
        uint256 max = (_a.length < _b.length) ? _a.length : _b.length;
        for (; shared_ < max && _a[shared_] == _b[shared_];) {
            unchecked {
                ++shared_;
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }
    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }
    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);
            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////
            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }
            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)
                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)
                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }
            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;
            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;
            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256
            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }
    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }
    /**
     * @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`.
        // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`.
        // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`.
        // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a
        // good first aproximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1;
        uint256 x = a;
        if (x >> 128 > 0) {
            x >>= 128;
            result <<= 64;
        }
        if (x >> 64 > 0) {
            x >>= 64;
            result <<= 32;
        }
        if (x >> 32 > 0) {
            x >>= 32;
            result <<= 16;
        }
        if (x >> 16 > 0) {
            x >>= 16;
            result <<= 8;
        }
        if (x >> 8 > 0) {
            x >>= 8;
            result <<= 4;
        }
        if (x >> 4 > 0) {
            x >>= 4;
            result <<= 2;
        }
        if (x >> 2 > 0) {
            result <<= 1;
        }
        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }
    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        uint256 result = sqrt(a);
        if (rounding == Rounding.Up && result * result < a) {
            result += 1;
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @title Burn
/// @notice Utilities for burning stuff.
library Burn {
    /// @notice Burns a given amount of ETH.
    /// @param _amount Amount of ETH to burn.
    function eth(uint256 _amount) internal {
        new Burner{ value: _amount }();
    }
    /// @notice Burns a given amount of gas.
    /// @param _amount Amount of gas to burn.
    function gas(uint256 _amount) internal view {
        uint256 i = 0;
        uint256 initialGas = gasleft();
        while (initialGas - gasleft() < _amount) {
            ++i;
        }
    }
}
/// @title Burner
/// @notice Burner self-destructs on creation and sends all ETH to itself, removing all ETH given to
///         the contract from the circulating supply. Self-destructing is the only way to remove ETH
///         from the circulating supply.
contract Burner {
    constructor() payable {
        selfdestruct(payable(address(this)));
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { SignedMath } from "@openzeppelin/contracts/utils/math/SignedMath.sol";
import { FixedPointMathLib } from "@rari-capital/solmate/src/utils/FixedPointMathLib.sol";
/// @title Arithmetic
/// @notice Even more math than before.
library Arithmetic {
    /// @notice Clamps a value between a minimum and maximum.
    /// @param _value The value to clamp.
    /// @param _min   The minimum value.
    /// @param _max   The maximum value.
    /// @return The clamped value.
    function clamp(int256 _value, int256 _min, int256 _max) internal pure returns (int256) {
        return SignedMath.min(SignedMath.max(_value, _min), _max);
    }
    /// @notice (c)oefficient (d)enominator (exp)onentiation function.
    ///         Returns the result of: c * (1 - 1/d)^exp.
    /// @param _coefficient Coefficient of the function.
    /// @param _denominator Fractional denominator.
    /// @param _exponent    Power function exponent.
    /// @return Result of c * (1 - 1/d)^exp.
    function cdexp(int256 _coefficient, int256 _denominator, int256 _exponent) internal pure returns (int256) {
        return (_coefficient * (FixedPointMathLib.powWad(1e18 - (1e18 / _denominator), _exponent * 1e18))) / 1e18;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.15;
import "src/dispute/lib/LibPosition.sol";
using LibClaim for Claim global;
using LibHash for Hash global;
using LibDuration for Duration global;
using LibClock for Clock global;
using LibGameId for GameId global;
using LibTimestamp for Timestamp global;
using LibVMStatus for VMStatus global;
using LibGameType for GameType global;
/// @notice A `Clock` represents a packed `Duration` and `Timestamp`
/// @dev The packed layout of this type is as follows:
/// ┌────────────┬────────────────┐
/// │    Bits    │     Value      │
/// ├────────────┼────────────────┤
/// │ [0, 64)    │ Duration       │
/// │ [64, 128)  │ Timestamp      │
/// └────────────┴────────────────┘
type Clock is uint128;
/// @title LibClock
/// @notice This library contains helper functions for working with the `Clock` type.
library LibClock {
    /// @notice Packs a `Duration` and `Timestamp` into a `Clock` type.
    /// @param _duration The `Duration` to pack into the `Clock` type.
    /// @param _timestamp The `Timestamp` to pack into the `Clock` type.
    /// @return clock_ The `Clock` containing the `_duration` and `_timestamp`.
    function wrap(Duration _duration, Timestamp _timestamp) internal pure returns (Clock clock_) {
        assembly {
            clock_ := or(shl(0x40, _duration), _timestamp)
        }
    }
    /// @notice Pull the `Duration` out of a `Clock` type.
    /// @param _clock The `Clock` type to pull the `Duration` out of.
    /// @return duration_ The `Duration` pulled out of `_clock`.
    function duration(Clock _clock) internal pure returns (Duration duration_) {
        // Shift the high-order 64 bits into the low-order 64 bits, leaving only the `duration`.
        assembly {
            duration_ := shr(0x40, _clock)
        }
    }
    /// @notice Pull the `Timestamp` out of a `Clock` type.
    /// @param _clock The `Clock` type to pull the `Timestamp` out of.
    /// @return timestamp_ The `Timestamp` pulled out of `_clock`.
    function timestamp(Clock _clock) internal pure returns (Timestamp timestamp_) {
        // Clean the high-order 192 bits by shifting the clock left and then right again, leaving
        // only the `timestamp`.
        assembly {
            timestamp_ := shr(0xC0, shl(0xC0, _clock))
        }
    }
    /// @notice Get the value of a `Clock` type in the form of the underlying uint128.
    /// @param _clock The `Clock` type to get the value of.
    /// @return clock_ The value of the `Clock` type as a uint128 type.
    function raw(Clock _clock) internal pure returns (uint128 clock_) {
        assembly {
            clock_ := _clock
        }
    }
}
/// @notice A `GameId` represents a packed 4 byte game ID, a 8 byte timestamp, and a 20 byte address.
/// @dev The packed layout of this type is as follows:
/// ┌───────────┬───────────┐
/// │   Bits    │   Value   │
/// ├───────────┼───────────┤
/// │ [0, 32)   │ Game Type │
/// │ [32, 96)  │ Timestamp │
/// │ [96, 256) │ Address   │
/// └───────────┴───────────┘
type GameId is bytes32;
/// @title LibGameId
/// @notice Utility functions for packing and unpacking GameIds.
library LibGameId {
    /// @notice Packs values into a 32 byte GameId type.
    /// @param _gameType The game type.
    /// @param _timestamp The timestamp of the game's creation.
    /// @param _gameProxy The game proxy address.
    /// @return gameId_ The packed GameId.
    function pack(
        GameType _gameType,
        Timestamp _timestamp,
        address _gameProxy
    )
        internal
        pure
        returns (GameId gameId_)
    {
        assembly {
            gameId_ := or(or(shl(224, _gameType), shl(160, _timestamp)), _gameProxy)
        }
    }
    /// @notice Unpacks values from a 32 byte GameId type.
    /// @param _gameId The packed GameId.
    /// @return gameType_ The game type.
    /// @return timestamp_ The timestamp of the game's creation.
    /// @return gameProxy_ The game proxy address.
    function unpack(GameId _gameId)
        internal
        pure
        returns (GameType gameType_, Timestamp timestamp_, address gameProxy_)
    {
        assembly {
            gameType_ := shr(224, _gameId)
            timestamp_ := and(shr(160, _gameId), 0xFFFFFFFFFFFFFFFF)
            gameProxy_ := and(_gameId, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
        }
    }
}
/// @notice A claim represents an MPT root representing the state of the fault proof program.
type Claim is bytes32;
/// @title LibClaim
/// @notice This library contains helper functions for working with the `Claim` type.
library LibClaim {
    /// @notice Get the value of a `Claim` type in the form of the underlying bytes32.
    /// @param _claim The `Claim` type to get the value of.
    /// @return claim_ The value of the `Claim` type as a bytes32 type.
    function raw(Claim _claim) internal pure returns (bytes32 claim_) {
        assembly {
            claim_ := _claim
        }
    }
    /// @notice Hashes a claim and a position together.
    /// @param _claim A Claim type.
    /// @param _position The position of `claim`.
    /// @param _challengeIndex The index of the claim being moved against.
    /// @return claimHash_ A hash of abi.encodePacked(claim, position|challengeIndex);
    function hashClaimPos(
        Claim _claim,
        Position _position,
        uint256 _challengeIndex
    )
        internal
        pure
        returns (Hash claimHash_)
    {
        assembly {
            mstore(0x00, _claim)
            mstore(0x20, or(shl(128, _position), and(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, _challengeIndex)))
            claimHash_ := keccak256(0x00, 0x40)
        }
    }
}
/// @notice A dedicated duration type.
/// @dev Unit: seconds
type Duration is uint64;
/// @title LibDuration
/// @notice This library contains helper functions for working with the `Duration` type.
library LibDuration {
    /// @notice Get the value of a `Duration` type in the form of the underlying uint64.
    /// @param _duration The `Duration` type to get the value of.
    /// @return duration_ The value of the `Duration` type as a uint64 type.
    function raw(Duration _duration) internal pure returns (uint64 duration_) {
        assembly {
            duration_ := _duration
        }
    }
}
/// @notice A custom type for a generic hash.
type Hash is bytes32;
/// @title LibHash
/// @notice This library contains helper functions for working with the `Hash` type.
library LibHash {
    /// @notice Get the value of a `Hash` type in the form of the underlying bytes32.
    /// @param _hash The `Hash` type to get the value of.
    /// @return hash_ The value of the `Hash` type as a bytes32 type.
    function raw(Hash _hash) internal pure returns (bytes32 hash_) {
        assembly {
            hash_ := _hash
        }
    }
}
/// @notice A dedicated timestamp type.
type Timestamp is uint64;
/// @title LibTimestamp
/// @notice This library contains helper functions for working with the `Timestamp` type.
library LibTimestamp {
    /// @notice Get the value of a `Timestamp` type in the form of the underlying uint64.
    /// @param _timestamp The `Timestamp` type to get the value of.
    /// @return timestamp_ The value of the `Timestamp` type as a uint64 type.
    function raw(Timestamp _timestamp) internal pure returns (uint64 timestamp_) {
        assembly {
            timestamp_ := _timestamp
        }
    }
}
/// @notice A `VMStatus` represents the status of a VM execution.
type VMStatus is uint8;
/// @title LibVMStatus
/// @notice This library contains helper functions for working with the `VMStatus` type.
library LibVMStatus {
    /// @notice Get the value of a `VMStatus` type in the form of the underlying uint8.
    /// @param _vmstatus The `VMStatus` type to get the value of.
    /// @return vmstatus_ The value of the `VMStatus` type as a uint8 type.
    function raw(VMStatus _vmstatus) internal pure returns (uint8 vmstatus_) {
        assembly {
            vmstatus_ := _vmstatus
        }
    }
}
/// @notice A `GameType` represents the type of game being played.
type GameType is uint32;
/// @title LibGameType
/// @notice This library contains helper functions for working with the `GameType` type.
library LibGameType {
    /// @notice Get the value of a `GameType` type in the form of the underlying uint32.
    /// @param _gametype The `GameType` type to get the value of.
    /// @return gametype_ The value of the `GameType` type as a uint32 type.
    function raw(GameType _gametype) internal pure returns (uint32 gametype_) {
        assembly {
            gametype_ := _gametype
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }
    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }
    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/AddressUpgradeable.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title IInitializable
/// @notice An interface for initializable contracts.
interface IInitializable {
    /// @notice Initializes the contract.
    /// @dev This function may only be called once.
    function initialize() external payable;
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @custom:attribution https://github.com/bakaoh/solidity-rlp-encode
/// @title RLPWriter
/// @author RLPWriter is a library for encoding Solidity types to RLP bytes. Adapted from Bakaoh's
///         RLPEncode library (https://github.com/bakaoh/solidity-rlp-encode) with minor
///         modifications to improve legibility.
library RLPWriter {
    /// @notice RLP encodes a byte string.
    /// @param _in The byte string to encode.
    /// @return out_ The RLP encoded string in bytes.
    function writeBytes(bytes memory _in) internal pure returns (bytes memory out_) {
        if (_in.length == 1 && uint8(_in[0]) < 128) {
            out_ = _in;
        } else {
            out_ = abi.encodePacked(_writeLength(_in.length, 128), _in);
        }
    }
    /// @notice RLP encodes a list of RLP encoded byte byte strings.
    /// @param _in The list of RLP encoded byte strings.
    /// @return list_ The RLP encoded list of items in bytes.
    function writeList(bytes[] memory _in) internal pure returns (bytes memory list_) {
        list_ = _flatten(_in);
        list_ = abi.encodePacked(_writeLength(list_.length, 192), list_);
    }
    /// @notice RLP encodes a string.
    /// @param _in The string to encode.
    /// @return out_ The RLP encoded string in bytes.
    function writeString(string memory _in) internal pure returns (bytes memory out_) {
        out_ = writeBytes(bytes(_in));
    }
    /// @notice RLP encodes an address.
    /// @param _in The address to encode.
    /// @return out_ The RLP encoded address in bytes.
    function writeAddress(address _in) internal pure returns (bytes memory out_) {
        out_ = writeBytes(abi.encodePacked(_in));
    }
    /// @notice RLP encodes a uint.
    /// @param _in The uint256 to encode.
    /// @return out_ The RLP encoded uint256 in bytes.
    function writeUint(uint256 _in) internal pure returns (bytes memory out_) {
        out_ = writeBytes(_toBinary(_in));
    }
    /// @notice RLP encodes a bool.
    /// @param _in The bool to encode.
    /// @return out_ The RLP encoded bool in bytes.
    function writeBool(bool _in) internal pure returns (bytes memory out_) {
        out_ = new bytes(1);
        out_[0] = (_in ? bytes1(0x01) : bytes1(0x80));
    }
    /// @notice Encode the first byte and then the `len` in binary form if `length` is more than 55.
    /// @param _len    The length of the string or the payload.
    /// @param _offset 128 if item is string, 192 if item is list.
    /// @return out_ RLP encoded bytes.
    function _writeLength(uint256 _len, uint256 _offset) private pure returns (bytes memory out_) {
        if (_len < 56) {
            out_ = new bytes(1);
            out_[0] = bytes1(uint8(_len) + uint8(_offset));
        } else {
            uint256 lenLen;
            uint256 i = 1;
            while (_len / i != 0) {
                lenLen++;
                i *= 256;
            }
            out_ = new bytes(lenLen + 1);
            out_[0] = bytes1(uint8(lenLen) + uint8(_offset) + 55);
            for (i = 1; i <= lenLen; i++) {
                out_[i] = bytes1(uint8((_len / (256 ** (lenLen - i))) % 256));
            }
        }
    }
    /// @notice Encode integer in big endian binary form with no leading zeroes.
    /// @param _x The integer to encode.
    /// @return out_ RLP encoded bytes.
    function _toBinary(uint256 _x) private pure returns (bytes memory out_) {
        bytes memory b = abi.encodePacked(_x);
        uint256 i = 0;
        for (; i < 32; i++) {
            if (b[i] != 0) {
                break;
            }
        }
        out_ = new bytes(32 - i);
        for (uint256 j = 0; j < out_.length; j++) {
            out_[j] = b[i++];
        }
    }
    /// @custom:attribution https://github.com/Arachnid/solidity-stringutils
    /// @notice Copies a piece of memory to another location.
    /// @param _dest Destination location.
    /// @param _src  Source location.
    /// @param _len  Length of memory to copy.
    function _memcpy(uint256 _dest, uint256 _src, uint256 _len) private pure {
        uint256 dest = _dest;
        uint256 src = _src;
        uint256 len = _len;
        for (; len >= 32; len -= 32) {
            assembly {
                mstore(dest, mload(src))
            }
            dest += 32;
            src += 32;
        }
        uint256 mask;
        unchecked {
            mask = 256 ** (32 - len) - 1;
        }
        assembly {
            let srcpart := and(mload(src), not(mask))
            let destpart := and(mload(dest), mask)
            mstore(dest, or(destpart, srcpart))
        }
    }
    /// @custom:attribution https://github.com/sammayo/solidity-rlp-encoder
    /// @notice Flattens a list of byte strings into one byte string.
    /// @param _list List of byte strings to flatten.
    /// @return out_ The flattened byte string.
    function _flatten(bytes[] memory _list) private pure returns (bytes memory out_) {
        if (_list.length == 0) {
            return new bytes(0);
        }
        uint256 len;
        uint256 i = 0;
        for (; i < _list.length; i++) {
            len += _list[i].length;
        }
        out_ = new bytes(len);
        uint256 flattenedPtr;
        assembly {
            flattenedPtr := add(out_, 0x20)
        }
        for (i = 0; i < _list.length; i++) {
            bytes memory item = _list[i];
            uint256 listPtr;
            assembly {
                listPtr := add(item, 0x20)
            }
            _memcpy(flattenedPtr, listPtr, item.length);
            flattenedPtr += _list[i].length;
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title Bytes
/// @notice Bytes is a library for manipulating byte arrays.
library Bytes {
    /// @custom:attribution https://github.com/GNSPS/solidity-bytes-utils
    /// @notice Slices a byte array with a given starting index and length. Returns a new byte array
    ///         as opposed to a pointer to the original array. Will throw if trying to slice more
    ///         bytes than exist in the array.
    /// @param _bytes Byte array to slice.
    /// @param _start Starting index of the slice.
    /// @param _length Length of the slice.
    /// @return Slice of the input byte array.
    function slice(bytes memory _bytes, uint256 _start, uint256 _length) internal pure returns (bytes memory) {
        unchecked {
            require(_length + 31 >= _length, "slice_overflow");
            require(_start + _length >= _start, "slice_overflow");
            require(_bytes.length >= _start + _length, "slice_outOfBounds");
        }
        bytes memory tempBytes;
        assembly {
            switch iszero(_length)
            case 0 {
                // Get a location of some free memory and store it in tempBytes as
                // Solidity does for memory variables.
                tempBytes := mload(0x40)
                // The first word of the slice result is potentially a partial
                // word read from the original array. To read it, we calculate
                // the length of that partial word and start copying that many
                // bytes into the array. The first word we copy will start with
                // data we don't care about, but the last `lengthmod` bytes will
                // land at the beginning of the contents of the new array. When
                // we're done copying, we overwrite the full first word with
                // the actual length of the slice.
                let lengthmod := and(_length, 31)
                // The multiplication in the next line is necessary
                // because when slicing multiples of 32 bytes (lengthmod == 0)
                // the following copy loop was copying the origin's length
                // and then ending prematurely not copying everything it should.
                let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                let end := add(mc, _length)
                for {
                    // The multiplication in the next line has the same exact purpose
                    // as the one above.
                    let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                } lt(mc, end) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } { mstore(mc, mload(cc)) }
                mstore(tempBytes, _length)
                //update free-memory pointer
                //allocating the array padded to 32 bytes like the compiler does now
                mstore(0x40, and(add(mc, 31), not(31)))
            }
            //if we want a zero-length slice let's just return a zero-length array
            default {
                tempBytes := mload(0x40)
                //zero out the 32 bytes slice we are about to return
                //we need to do it because Solidity does not garbage collect
                mstore(tempBytes, 0)
                mstore(0x40, add(tempBytes, 0x20))
            }
        }
        return tempBytes;
    }
    /// @notice Slices a byte array with a given starting index up to the end of the original byte
    ///         array. Returns a new array rathern than a pointer to the original.
    /// @param _bytes Byte array to slice.
    /// @param _start Starting index of the slice.
    /// @return Slice of the input byte array.
    function slice(bytes memory _bytes, uint256 _start) internal pure returns (bytes memory) {
        if (_start >= _bytes.length) {
            return bytes("");
        }
        return slice(_bytes, _start, _bytes.length - _start);
    }
    /// @notice Converts a byte array into a nibble array by splitting each byte into two nibbles.
    ///         Resulting nibble array will be exactly twice as long as the input byte array.
    /// @param _bytes Input byte array to convert.
    /// @return Resulting nibble array.
    function toNibbles(bytes memory _bytes) internal pure returns (bytes memory) {
        bytes memory _nibbles;
        assembly {
            // Grab a free memory offset for the new array
            _nibbles := mload(0x40)
            // Load the length of the passed bytes array from memory
            let bytesLength := mload(_bytes)
            // Calculate the length of the new nibble array
            // This is the length of the input array times 2
            let nibblesLength := shl(0x01, bytesLength)
            // Update the free memory pointer to allocate memory for the new array.
            // To do this, we add the length of the new array + 32 bytes for the array length
            // rounded up to the nearest 32 byte boundary to the current free memory pointer.
            mstore(0x40, add(_nibbles, and(not(0x1F), add(nibblesLength, 0x3F))))
            // Store the length of the new array in memory
            mstore(_nibbles, nibblesLength)
            // Store the memory offset of the _bytes array's contents on the stack
            let bytesStart := add(_bytes, 0x20)
            // Store the memory offset of the nibbles array's contents on the stack
            let nibblesStart := add(_nibbles, 0x20)
            // Loop through each byte in the input array
            for { let i := 0x00 } lt(i, bytesLength) { i := add(i, 0x01) } {
                // Get the starting offset of the next 2 bytes in the nibbles array
                let offset := add(nibblesStart, shl(0x01, i))
                // Load the byte at the current index within the `_bytes` array
                let b := byte(0x00, mload(add(bytesStart, i)))
                // Pull out the first nibble and store it in the new array
                mstore8(offset, shr(0x04, b))
                // Pull out the second nibble and store it in the new array
                mstore8(add(offset, 0x01), and(b, 0x0F))
            }
        }
        return _nibbles;
    }
    /// @notice Compares two byte arrays by comparing their keccak256 hashes.
    /// @param _bytes First byte array to compare.
    /// @param _other Second byte array to compare.
    /// @return True if the two byte arrays are equal, false otherwise.
    function equal(bytes memory _bytes, bytes memory _other) internal pure returns (bool) {
        return keccak256(_bytes) == keccak256(_other);
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.8;
import "./RLPErrors.sol";
/// @custom:attribution https://github.com/hamdiallam/Solidity-RLP
/// @title RLPReader
/// @notice RLPReader is a library for parsing RLP-encoded byte arrays into Solidity types. Adapted
///         from Solidity-RLP (https://github.com/hamdiallam/Solidity-RLP) by Hamdi Allam with
///         various tweaks to improve readability.
library RLPReader {
    /// @notice Custom pointer type to avoid confusion between pointers and uint256s.
    type MemoryPointer is uint256;
    /// @notice RLP item types.
    /// @custom:value DATA_ITEM Represents an RLP data item (NOT a list).
    /// @custom:value LIST_ITEM Represents an RLP list item.
    enum RLPItemType {
        DATA_ITEM,
        LIST_ITEM
    }
    /// @notice Struct representing an RLP item.
    /// @custom:field length Length of the RLP item.
    /// @custom:field ptr    Pointer to the RLP item in memory.
    struct RLPItem {
        uint256 length;
        MemoryPointer ptr;
    }
    /// @notice Max list length that this library will accept.
    uint256 internal constant MAX_LIST_LENGTH = 32;
    /// @notice Converts bytes to a reference to memory position and length.
    /// @param _in Input bytes to convert.
    /// @return out_ Output memory reference.
    function toRLPItem(bytes memory _in) internal pure returns (RLPItem memory out_) {
        // Empty arrays are not RLP items.
        if (_in.length == 0) revert EmptyItem();
        MemoryPointer ptr;
        assembly {
            ptr := add(_in, 32)
        }
        out_ = RLPItem({ length: _in.length, ptr: ptr });
    }
    /// @notice Reads an RLP list value into a list of RLP items.
    /// @param _in RLP list value.
    /// @return out_ Decoded RLP list items.
    function readList(RLPItem memory _in) internal pure returns (RLPItem[] memory out_) {
        (uint256 listOffset, uint256 listLength, RLPItemType itemType) = _decodeLength(_in);
        if (itemType != RLPItemType.LIST_ITEM) revert UnexpectedString();
        if (listOffset + listLength != _in.length) revert InvalidDataRemainder();
        // Solidity in-memory arrays can't be increased in size, but *can* be decreased in size by
        // writing to the length. Since we can't know the number of RLP items without looping over
        // the entire input, we'd have to loop twice to accurately size this array. It's easier to
        // simply set a reasonable maximum list length and decrease the size before we finish.
        out_ = new RLPItem[](MAX_LIST_LENGTH);
        uint256 itemCount = 0;
        uint256 offset = listOffset;
        while (offset < _in.length) {
            (uint256 itemOffset, uint256 itemLength,) = _decodeLength(
                RLPItem({ length: _in.length - offset, ptr: MemoryPointer.wrap(MemoryPointer.unwrap(_in.ptr) + offset) })
            );
            // We don't need to check itemCount < out.length explicitly because Solidity already
            // handles this check on our behalf, we'd just be wasting gas.
            out_[itemCount] = RLPItem({
                length: itemLength + itemOffset,
                ptr: MemoryPointer.wrap(MemoryPointer.unwrap(_in.ptr) + offset)
            });
            itemCount += 1;
            offset += itemOffset + itemLength;
        }
        // Decrease the array size to match the actual item count.
        assembly {
            mstore(out_, itemCount)
        }
    }
    /// @notice Reads an RLP list value into a list of RLP items.
    /// @param _in RLP list value.
    /// @return out_ Decoded RLP list items.
    function readList(bytes memory _in) internal pure returns (RLPItem[] memory out_) {
        out_ = readList(toRLPItem(_in));
    }
    /// @notice Reads an RLP bytes value into bytes.
    /// @param _in RLP bytes value.
    /// @return out_ Decoded bytes.
    function readBytes(RLPItem memory _in) internal pure returns (bytes memory out_) {
        (uint256 itemOffset, uint256 itemLength, RLPItemType itemType) = _decodeLength(_in);
        if (itemType != RLPItemType.DATA_ITEM) revert UnexpectedList();
        if (_in.length != itemOffset + itemLength) revert InvalidDataRemainder();
        out_ = _copy(_in.ptr, itemOffset, itemLength);
    }
    /// @notice Reads an RLP bytes value into bytes.
    /// @param _in RLP bytes value.
    /// @return out_ Decoded bytes.
    function readBytes(bytes memory _in) internal pure returns (bytes memory out_) {
        out_ = readBytes(toRLPItem(_in));
    }
    /// @notice Reads the raw bytes of an RLP item.
    /// @param _in RLP item to read.
    /// @return out_ Raw RLP bytes.
    function readRawBytes(RLPItem memory _in) internal pure returns (bytes memory out_) {
        out_ = _copy(_in.ptr, 0, _in.length);
    }
    /// @notice Decodes the length of an RLP item.
    /// @param _in RLP item to decode.
    /// @return offset_ Offset of the encoded data.
    /// @return length_ Length of the encoded data.
    /// @return type_ RLP item type (LIST_ITEM or DATA_ITEM).
    function _decodeLength(RLPItem memory _in)
        private
        pure
        returns (uint256 offset_, uint256 length_, RLPItemType type_)
    {
        // Short-circuit if there's nothing to decode, note that we perform this check when
        // the user creates an RLP item via toRLPItem, but it's always possible for them to bypass
        // that function and create an RLP item directly. So we need to check this anyway.
        if (_in.length == 0) revert EmptyItem();
        MemoryPointer ptr = _in.ptr;
        uint256 prefix;
        assembly {
            prefix := byte(0, mload(ptr))
        }
        if (prefix <= 0x7f) {
            // Single byte.
            return (0, 1, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xb7) {
            // Short string.
            // slither-disable-next-line variable-scope
            uint256 strLen = prefix - 0x80;
            if (_in.length <= strLen) revert ContentLengthMismatch();
            bytes1 firstByteOfContent;
            assembly {
                firstByteOfContent := and(mload(add(ptr, 1)), shl(248, 0xff))
            }
            if (strLen == 1 && firstByteOfContent < 0x80) revert InvalidHeader();
            return (1, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xbf) {
            // Long string.
            uint256 lenOfStrLen = prefix - 0xb7;
            if (_in.length <= lenOfStrLen) revert ContentLengthMismatch();
            bytes1 firstByteOfContent;
            assembly {
                firstByteOfContent := and(mload(add(ptr, 1)), shl(248, 0xff))
            }
            if (firstByteOfContent == 0x00) revert InvalidHeader();
            uint256 strLen;
            assembly {
                strLen := shr(sub(256, mul(8, lenOfStrLen)), mload(add(ptr, 1)))
            }
            if (strLen <= 55) revert InvalidHeader();
            if (_in.length <= lenOfStrLen + strLen) revert ContentLengthMismatch();
            return (1 + lenOfStrLen, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xf7) {
            // Short list.
            // slither-disable-next-line variable-scope
            uint256 listLen = prefix - 0xc0;
            if (_in.length <= listLen) revert ContentLengthMismatch();
            return (1, listLen, RLPItemType.LIST_ITEM);
        } else {
            // Long list.
            uint256 lenOfListLen = prefix - 0xf7;
            if (_in.length <= lenOfListLen) revert ContentLengthMismatch();
            bytes1 firstByteOfContent;
            assembly {
                firstByteOfContent := and(mload(add(ptr, 1)), shl(248, 0xff))
            }
            if (firstByteOfContent == 0x00) revert InvalidHeader();
            uint256 listLen;
            assembly {
                listLen := shr(sub(256, mul(8, lenOfListLen)), mload(add(ptr, 1)))
            }
            if (listLen <= 55) revert InvalidHeader();
            if (_in.length <= lenOfListLen + listLen) revert ContentLengthMismatch();
            return (1 + lenOfListLen, listLen, RLPItemType.LIST_ITEM);
        }
    }
    /// @notice Copies the bytes from a memory location.
    /// @param _src    Pointer to the location to read from.
    /// @param _offset Offset to start reading from.
    /// @param _length Number of bytes to read.
    /// @return out_ Copied bytes.
    function _copy(MemoryPointer _src, uint256 _offset, uint256 _length) private pure returns (bytes memory out_) {
        out_ = new bytes(_length);
        if (_length == 0) {
            return out_;
        }
        // Mostly based on Solidity's copy_memory_to_memory:
        // https://github.com/ethereum/solidity/blob/34dd30d71b4da730488be72ff6af7083cf2a91f6/libsolidity/codegen/YulUtilFunctions.cpp#L102-L114
        uint256 src = MemoryPointer.unwrap(_src) + _offset;
        assembly {
            let dest := add(out_, 32)
            let i := 0
            for { } lt(i, _length) { i := add(i, 32) } { mstore(add(dest, i), mload(add(src, i))) }
            if gt(i, _length) { mstore(add(dest, _length), 0) }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.
    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }
    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
        return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0.
    }
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return 0;
            // When the result is > (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 (x >= 135305999368893231589) revert("EXP_OVERFLOW");
            // 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;
            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));
        }
    }
    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            require(x > 0, "UNDEFINED");
            // 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.
            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            int256 k = int256(log2(uint256(x))) - 96;
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);
            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);
            // 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.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }
            // r 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
            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }
    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // Divide z by the denominator.
            z := div(z, denominator)
        }
    }
    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // First, divide z - 1 by the denominator and add 1.
            // We allow z - 1 to underflow if z is 0, because we multiply the
            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
        }
    }
    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }
                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)
                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }
                    // Store x squared.
                    let xx := mul(x, x)
                    // Round to the nearest number.
                    let xxRound := add(xx, half)
                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }
                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)
                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)
                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }
                        // Round to the nearest number.
                        let zxRound := add(zx, half)
                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }
                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }
    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.
            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.
            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, 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(y, 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }
    function log2(uint256 x) internal pure returns (uint256 r) {
        require(x > 0, "UNDEFINED");
        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))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.15;
using LibPosition for Position global;
/// @notice A `Position` represents a position of a claim within the game tree.
/// @dev This is represented as a "generalized index" where the high-order bit
/// is the level in the tree and the remaining bits is a unique bit pattern, allowing
/// a unique identifier for each node in the tree. Mathematically, it is calculated
/// as 2^{depth} + indexAtDepth.
type Position is uint128;
/// @title LibPosition
/// @notice This library contains helper functions for working with the `Position` type.
library LibPosition {
    /// @notice the `MAX_POSITION_BITLEN` is the number of bits that the `Position` type, and the implementation of
    ///         its behavior within this library, can safely support.
    uint8 internal constant MAX_POSITION_BITLEN = 126;
    /// @notice Computes a generalized index (2^{depth} + indexAtDepth).
    /// @param _depth The depth of the position.
    /// @param _indexAtDepth The index at the depth of the position.
    /// @return position_ The computed generalized index.
    function wrap(uint8 _depth, uint128 _indexAtDepth) internal pure returns (Position position_) {
        assembly {
            // gindex = 2^{_depth} + _indexAtDepth
            position_ := add(shl(_depth, 1), _indexAtDepth)
        }
    }
    /// @notice Pulls the `depth` out of a `Position` type.
    /// @param _position The generalized index to get the `depth` of.
    /// @return depth_ The `depth` of the `position` gindex.
    /// @custom:attribution Solady <https://github.com/Vectorized/Solady>
    function depth(Position _position) internal pure returns (uint8 depth_) {
        // Return the most significant bit offset, which signifies the depth of the gindex.
        assembly {
            depth_ := or(depth_, shl(6, lt(0xffffffffffffffff, shr(depth_, _position))))
            depth_ := or(depth_, shl(5, lt(0xffffffff, shr(depth_, _position))))
            // For the remaining 32 bits, use a De Bruijn lookup.
            _position := shr(depth_, _position)
            _position := or(_position, shr(1, _position))
            _position := or(_position, shr(2, _position))
            _position := or(_position, shr(4, _position))
            _position := or(_position, shr(8, _position))
            _position := or(_position, shr(16, _position))
            depth_ :=
                or(
                    depth_,
                    byte(
                        shr(251, mul(_position, shl(224, 0x07c4acdd))),
                        0x0009010a0d15021d0b0e10121619031e080c141c0f111807131b17061a05041f
                    )
                )
        }
    }
    /// @notice Pulls the `indexAtDepth` out of a `Position` type.
    ///         The `indexAtDepth` is the left/right index of a position at a specific depth within
    ///         the binary tree, starting from index 0. For example, at gindex 2, the `depth` = 1
    ///         and the `indexAtDepth` = 0.
    /// @param _position The generalized index to get the `indexAtDepth` of.
    /// @return indexAtDepth_ The `indexAtDepth` of the `position` gindex.
    function indexAtDepth(Position _position) internal pure returns (uint128 indexAtDepth_) {
        // Return bits p_{msb-1}...p_{0}. This effectively pulls the 2^{depth} out of the gindex,
        // leaving only the `indexAtDepth`.
        uint256 msb = depth(_position);
        assembly {
            indexAtDepth_ := sub(_position, shl(msb, 1))
        }
    }
    /// @notice Get the left child of `_position`.
    /// @param _position The position to get the left position of.
    /// @return left_ The position to the left of `position`.
    function left(Position _position) internal pure returns (Position left_) {
        assembly {
            left_ := shl(1, _position)
        }
    }
    /// @notice Get the right child of `_position`
    /// @param _position The position to get the right position of.
    /// @return right_ The position to the right of `position`.
    function right(Position _position) internal pure returns (Position right_) {
        assembly {
            right_ := or(1, shl(1, _position))
        }
    }
    /// @notice Get the parent position of `_position`.
    /// @param _position The position to get the parent position of.
    /// @return parent_ The parent position of `position`.
    function parent(Position _position) internal pure returns (Position parent_) {
        assembly {
            parent_ := shr(1, _position)
        }
    }
    /// @notice Get the deepest, right most gindex relative to the `position`. This is equivalent to
    ///         calling `right` on a position until the maximum depth is reached.
    /// @param _position The position to get the relative deepest, right most gindex of.
    /// @param _maxDepth The maximum depth of the game.
    /// @return rightIndex_ The deepest, right most gindex relative to the `position`.
    function rightIndex(Position _position, uint256 _maxDepth) internal pure returns (Position rightIndex_) {
        uint256 msb = depth(_position);
        assembly {
            let remaining := sub(_maxDepth, msb)
            rightIndex_ := or(shl(remaining, _position), sub(shl(remaining, 1), 1))
        }
    }
    /// @notice Get the deepest, right most trace index relative to the `position`. This is
    ///         equivalent to calling `right` on a position until the maximum depth is reached and
    ///         then finding its index at depth.
    /// @param _position The position to get the relative trace index of.
    /// @param _maxDepth The maximum depth of the game.
    /// @return traceIndex_ The trace index relative to the `position`.
    function traceIndex(Position _position, uint256 _maxDepth) internal pure returns (uint256 traceIndex_) {
        uint256 msb = depth(_position);
        assembly {
            let remaining := sub(_maxDepth, msb)
            traceIndex_ := sub(or(shl(remaining, _position), sub(shl(remaining, 1), 1)), shl(_maxDepth, 1))
        }
    }
    /// @notice Gets the position of the highest ancestor of `_position` that commits to the same
    ///         trace index.
    /// @param _position The position to get the highest ancestor of.
    /// @return ancestor_ The highest ancestor of `position` that commits to the same trace index.
    function traceAncestor(Position _position) internal pure returns (Position ancestor_) {
        // Create a field with only the lowest unset bit of `_position` set.
        Position lsb;
        assembly {
            lsb := and(not(_position), add(_position, 1))
        }
        // Find the index of the lowest unset bit within the field.
        uint256 msb = depth(lsb);
        // The highest ancestor that commits to the same trace index is the original position
        // shifted right by the index of the lowest unset bit.
        assembly {
            let a := shr(msb, _position)
            // Bound the ancestor to the minimum gindex, 1.
            ancestor_ := or(a, iszero(a))
        }
    }
    /// @notice Gets the position of the highest ancestor of `_position` that commits to the same
    ///         trace index, while still being below `_upperBoundExclusive`.
    /// @param _position The position to get the highest ancestor of.
    /// @param _upperBoundExclusive The exclusive upper depth bound, used to inform where to stop in order
    ///                             to not escape a sub-tree.
    /// @return ancestor_ The highest ancestor of `position` that commits to the same trace index.
    function traceAncestorBounded(
        Position _position,
        uint256 _upperBoundExclusive
    )
        internal
        pure
        returns (Position ancestor_)
    {
        // This function only works for positions that are below the upper bound.
        if (_position.depth() <= _upperBoundExclusive) {
            assembly {
                // Revert with `ClaimAboveSplit()`
                mstore(0x00, 0xb34b5c22)
                revert(0x1C, 0x04)
            }
        }
        // Grab the global trace ancestor.
        ancestor_ = traceAncestor(_position);
        // If the ancestor is above or at the upper bound, shift it to be below the upper bound.
        // This should be a special case that only covers positions that commit to the final leaf
        // in a sub-tree.
        if (ancestor_.depth() <= _upperBoundExclusive) {
            ancestor_ = ancestor_.rightIndex(_upperBoundExclusive + 1);
        }
    }
    /// @notice Get the move position of `_position`, which is the left child of:
    ///         1. `_position` if `_isAttack` is true.
    ///         2. `_position | 1` if `_isAttack` is false.
    /// @param _position The position to get the relative attack/defense position of.
    /// @param _isAttack Whether or not the move is an attack move.
    /// @return move_ The move position relative to `position`.
    function move(Position _position, bool _isAttack) internal pure returns (Position move_) {
        assembly {
            move_ := shl(1, or(iszero(_isAttack), _position))
        }
    }
    /// @notice Get the value of a `Position` type in the form of the underlying uint128.
    /// @param _position The position to get the value of.
    /// @return raw_ The value of the `position` as a uint128 type.
    function raw(Position _position) internal pure returns (uint128 raw_) {
        assembly {
            raw_ := _position
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @notice The length of an RLP item must be greater than zero to be decodable
error EmptyItem();
/// @notice The decoded item type for list is not a list item
error UnexpectedString();
/// @notice The RLP item has an invalid data remainder
error InvalidDataRemainder();
/// @notice Decoded item type for bytes is not a string item
error UnexpectedList();
/// @notice The length of the content must be greater than the RLP item length
error ContentLengthMismatch();
/// @notice Invalid RLP header for RLP item
error InvalidHeader();

// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Constants } from "../libraries/Constants.sol";
/// @title Proxy
/// @notice Proxy is a transparent proxy that passes through the call if the caller is the owner or
///         if the caller is address(0), meaning that the call originated from an off-chain
///         simulation.
contract Proxy {
    /// @notice An event that is emitted each time the implementation is changed. This event is part
    ///         of the EIP-1967 specification.
    /// @param implementation The address of the implementation contract
    event Upgraded(address indexed implementation);
    /// @notice An event that is emitted each time the owner is upgraded. This event is part of the
    ///         EIP-1967 specification.
    /// @param previousAdmin The previous owner of the contract
    /// @param newAdmin      The new owner of the contract
    event AdminChanged(address previousAdmin, address newAdmin);
    /// @notice A modifier that reverts if not called by the owner or by address(0) to allow
    ///         eth_call to interact with this proxy without needing to use low-level storage
    ///         inspection. We assume that nobody is able to trigger calls from address(0) during
    ///         normal EVM execution.
    modifier proxyCallIfNotAdmin() {
        if (msg.sender == _getAdmin() || msg.sender == address(0)) {
            _;
        } else {
            // This WILL halt the call frame on completion.
            _doProxyCall();
        }
    }
    /// @notice Sets the initial admin during contract deployment. Admin address is stored at the
    ///         EIP-1967 admin storage slot so that accidental storage collision with the
    ///         implementation is not possible.
    /// @param _admin Address of the initial contract admin. Admin as the ability to access the
    ///               transparent proxy interface.
    constructor(address _admin) {
        _changeAdmin(_admin);
    }
    // slither-disable-next-line locked-ether
    receive() external payable {
        // Proxy call by default.
        _doProxyCall();
    }
    // slither-disable-next-line locked-ether
    fallback() external payable {
        // Proxy call by default.
        _doProxyCall();
    }
    /// @notice Set the implementation contract address. The code at the given address will execute
    ///         when this contract is called.
    /// @param _implementation Address of the implementation contract.
    function upgradeTo(address _implementation) public virtual proxyCallIfNotAdmin {
        _setImplementation(_implementation);
    }
    /// @notice Set the implementation and call a function in a single transaction. Useful to ensure
    ///         atomic execution of initialization-based upgrades.
    /// @param _implementation Address of the implementation contract.
    /// @param _data           Calldata to delegatecall the new implementation with.
    function upgradeToAndCall(
        address _implementation,
        bytes calldata _data
    )
        public
        payable
        virtual
        proxyCallIfNotAdmin
        returns (bytes memory)
    {
        _setImplementation(_implementation);
        (bool success, bytes memory returndata) = _implementation.delegatecall(_data);
        require(success, "Proxy: delegatecall to new implementation contract failed");
        return returndata;
    }
    /// @notice Changes the owner of the proxy contract. Only callable by the owner.
    /// @param _admin New owner of the proxy contract.
    function changeAdmin(address _admin) public virtual proxyCallIfNotAdmin {
        _changeAdmin(_admin);
    }
    /// @notice Gets the owner of the proxy contract.
    /// @return Owner address.
    function admin() public virtual proxyCallIfNotAdmin returns (address) {
        return _getAdmin();
    }
    //// @notice Queries the implementation address.
    /// @return Implementation address.
    function implementation() public virtual proxyCallIfNotAdmin returns (address) {
        return _getImplementation();
    }
    /// @notice Sets the implementation address.
    /// @param _implementation New implementation address.
    function _setImplementation(address _implementation) internal {
        bytes32 proxyImplementation = Constants.PROXY_IMPLEMENTATION_ADDRESS;
        assembly {
            sstore(proxyImplementation, _implementation)
        }
        emit Upgraded(_implementation);
    }
    /// @notice Changes the owner of the proxy contract.
    /// @param _admin New owner of the proxy contract.
    function _changeAdmin(address _admin) internal {
        address previous = _getAdmin();
        bytes32 proxyOwner = Constants.PROXY_OWNER_ADDRESS;
        assembly {
            sstore(proxyOwner, _admin)
        }
        emit AdminChanged(previous, _admin);
    }
    /// @notice Performs the proxy call via a delegatecall.
    function _doProxyCall() internal {
        address impl = _getImplementation();
        require(impl != address(0), "Proxy: implementation not initialized");
        assembly {
            // Copy calldata into memory at 0x0....calldatasize.
            calldatacopy(0x0, 0x0, calldatasize())
            // Perform the delegatecall, make sure to pass all available gas.
            let success := delegatecall(gas(), impl, 0x0, calldatasize(), 0x0, 0x0)
            // Copy returndata into memory at 0x0....returndatasize. Note that this *will*
            // overwrite the calldata that we just copied into memory but that doesn't really
            // matter because we'll be returning in a second anyway.
            returndatacopy(0x0, 0x0, returndatasize())
            // Success == 0 means a revert. We'll revert too and pass the data up.
            if iszero(success) { revert(0x0, returndatasize()) }
            // Otherwise we'll just return and pass the data up.
            return(0x0, returndatasize())
        }
    }
    /// @notice Queries the implementation address.
    /// @return Implementation address.
    function _getImplementation() internal view returns (address) {
        address impl;
        bytes32 proxyImplementation = Constants.PROXY_IMPLEMENTATION_ADDRESS;
        assembly {
            impl := sload(proxyImplementation)
        }
        return impl;
    }
    /// @notice Queries the owner of the proxy contract.
    /// @return Owner address.
    function _getAdmin() internal view returns (address) {
        address owner;
        bytes32 proxyOwner = Constants.PROXY_OWNER_ADDRESS;
        assembly {
            owner := sload(proxyOwner)
        }
        return owner;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { ResourceMetering } from "../L1/ResourceMetering.sol";
/// @title Constants
/// @notice Constants is a library for storing constants. Simple! Don't put everything in here, just
///         the stuff used in multiple contracts. Constants that only apply to a single contract
///         should be defined in that contract instead.
library Constants {
    /// @notice Special address to be used as the tx origin for gas estimation calls in the
    ///         OptimismPortal and CrossDomainMessenger calls. You only need to use this address if
    ///         the minimum gas limit specified by the user is not actually enough to execute the
    ///         given message and you're attempting to estimate the actual necessary gas limit. We
    ///         use address(1) because it's the ecrecover precompile and therefore guaranteed to
    ///         never have any code on any EVM chain.
    address internal constant ESTIMATION_ADDRESS = address(1);
    /// @notice Value used for the L2 sender storage slot in both the OptimismPortal and the
    ///         CrossDomainMessenger contracts before an actual sender is set. This value is
    ///         non-zero to reduce the gas cost of message passing transactions.
    address internal constant DEFAULT_L2_SENDER = 0x000000000000000000000000000000000000dEaD;
    /// @notice The storage slot that holds the address of a proxy implementation.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)`
    bytes32 internal constant PROXY_IMPLEMENTATION_ADDRESS =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /// @notice The storage slot that holds the address of the owner.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)`
    bytes32 internal constant PROXY_OWNER_ADDRESS = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /// @notice Returns the default values for the ResourceConfig. These are the recommended values
    ///         for a production network.
    function DEFAULT_RESOURCE_CONFIG() internal pure returns (ResourceMetering.ResourceConfig memory) {
        ResourceMetering.ResourceConfig memory config = ResourceMetering.ResourceConfig({
            maxResourceLimit: 20_000_000,
            elasticityMultiplier: 10,
            baseFeeMaxChangeDenominator: 8,
            minimumBaseFee: 1 gwei,
            systemTxMaxGas: 1_000_000,
            maximumBaseFee: type(uint128).max
        });
        return config;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { Burn } from "../libraries/Burn.sol";
import { Arithmetic } from "../libraries/Arithmetic.sol";
/// @custom:upgradeable
/// @title ResourceMetering
/// @notice ResourceMetering implements an EIP-1559 style resource metering system where pricing
///         updates automatically based on current demand.
abstract contract ResourceMetering is Initializable {
    /// @notice Represents the various parameters that control the way in which resources are
    ///         metered. Corresponds to the EIP-1559 resource metering system.
    /// @custom:field prevBaseFee   Base fee from the previous block(s).
    /// @custom:field prevBoughtGas Amount of gas bought so far in the current block.
    /// @custom:field prevBlockNum  Last block number that the base fee was updated.
    struct ResourceParams {
        uint128 prevBaseFee;
        uint64 prevBoughtGas;
        uint64 prevBlockNum;
    }
    /// @notice Represents the configuration for the EIP-1559 based curve for the deposit gas
    ///         market. These values should be set with care as it is possible to set them in
    ///         a way that breaks the deposit gas market. The target resource limit is defined as
    ///         maxResourceLimit / elasticityMultiplier. This struct was designed to fit within a
    ///         single word. There is additional space for additions in the future.
    /// @custom:field maxResourceLimit             Represents the maximum amount of deposit gas that
    ///                                            can be purchased per block.
    /// @custom:field elasticityMultiplier         Determines the target resource limit along with
    ///                                            the resource limit.
    /// @custom:field baseFeeMaxChangeDenominator  Determines max change on fee per block.
    /// @custom:field minimumBaseFee               The min deposit base fee, it is clamped to this
    ///                                            value.
    /// @custom:field systemTxMaxGas               The amount of gas supplied to the system
    ///                                            transaction. This should be set to the same
    ///                                            number that the op-node sets as the gas limit
    ///                                            for the system transaction.
    /// @custom:field maximumBaseFee               The max deposit base fee, it is clamped to this
    ///                                            value.
    struct ResourceConfig {
        uint32 maxResourceLimit;
        uint8 elasticityMultiplier;
        uint8 baseFeeMaxChangeDenominator;
        uint32 minimumBaseFee;
        uint32 systemTxMaxGas;
        uint128 maximumBaseFee;
    }
    /// @notice EIP-1559 style gas parameters.
    ResourceParams public params;
    /// @notice Reserve extra slots (to a total of 50) in the storage layout for future upgrades.
    uint256[48] private __gap;
    /// @notice Meters access to a function based an amount of a requested resource.
    /// @param _amount Amount of the resource requested.
    modifier metered(uint64 _amount) {
        // Record initial gas amount so we can refund for it later.
        uint256 initialGas = gasleft();
        // Run the underlying function.
        _;
        // Run the metering function.
        _metered(_amount, initialGas);
    }
    /// @notice An internal function that holds all of the logic for metering a resource.
    /// @param _amount     Amount of the resource requested.
    /// @param _initialGas The amount of gas before any modifier execution.
    function _metered(uint64 _amount, uint256 _initialGas) internal {
        // Update block number and base fee if necessary.
        uint256 blockDiff = block.number - params.prevBlockNum;
        ResourceConfig memory config = _resourceConfig();
        int256 targetResourceLimit =
            int256(uint256(config.maxResourceLimit)) / int256(uint256(config.elasticityMultiplier));
        if (blockDiff > 0) {
            // Handle updating EIP-1559 style gas parameters. We use EIP-1559 to restrict the rate
            // at which deposits can be created and therefore limit the potential for deposits to
            // spam the L2 system. Fee scheme is very similar to EIP-1559 with minor changes.
            int256 gasUsedDelta = int256(uint256(params.prevBoughtGas)) - targetResourceLimit;
            int256 baseFeeDelta = (int256(uint256(params.prevBaseFee)) * gasUsedDelta)
                / (targetResourceLimit * int256(uint256(config.baseFeeMaxChangeDenominator)));
            // Update base fee by adding the base fee delta and clamp the resulting value between
            // min and max.
            int256 newBaseFee = Arithmetic.clamp({
                _value: int256(uint256(params.prevBaseFee)) + baseFeeDelta,
                _min: int256(uint256(config.minimumBaseFee)),
                _max: int256(uint256(config.maximumBaseFee))
            });
            // If we skipped more than one block, we also need to account for every empty block.
            // Empty block means there was no demand for deposits in that block, so we should
            // reflect this lack of demand in the fee.
            if (blockDiff > 1) {
                // Update the base fee by repeatedly applying the exponent 1-(1/change_denominator)
                // blockDiff - 1 times. Simulates multiple empty blocks. Clamp the resulting value
                // between min and max.
                newBaseFee = Arithmetic.clamp({
                    _value: Arithmetic.cdexp({
                        _coefficient: newBaseFee,
                        _denominator: int256(uint256(config.baseFeeMaxChangeDenominator)),
                        _exponent: int256(blockDiff - 1)
                    }),
                    _min: int256(uint256(config.minimumBaseFee)),
                    _max: int256(uint256(config.maximumBaseFee))
                });
            }
            // Update new base fee, reset bought gas, and update block number.
            params.prevBaseFee = uint128(uint256(newBaseFee));
            params.prevBoughtGas = 0;
            params.prevBlockNum = uint64(block.number);
        }
        // Make sure we can actually buy the resource amount requested by the user.
        params.prevBoughtGas += _amount;
        require(
            int256(uint256(params.prevBoughtGas)) <= int256(uint256(config.maxResourceLimit)),
            "ResourceMetering: cannot buy more gas than available gas limit"
        );
        // Determine the amount of ETH to be paid.
        uint256 resourceCost = uint256(_amount) * uint256(params.prevBaseFee);
        // We currently charge for this ETH amount as an L1 gas burn, so we convert the ETH amount
        // into gas by dividing by the L1 base fee. We assume a minimum base fee of 1 gwei to avoid
        // division by zero for L1s that don't support 1559 or to avoid excessive gas burns during
        // periods of extremely low L1 demand. One-day average gas fee hasn't dipped below 1 gwei
        // during any 1 day period in the last 5 years, so should be fine.
        uint256 gasCost = resourceCost / Math.max(block.basefee, 1 gwei);
        // Give the user a refund based on the amount of gas they used to do all of the work up to
        // this point. Since we're at the end of the modifier, this should be pretty accurate. Acts
        // effectively like a dynamic stipend (with a minimum value).
        uint256 usedGas = _initialGas - gasleft();
        if (gasCost > usedGas) {
            Burn.gas(gasCost - usedGas);
        }
    }
    /// @notice Virtual function that returns the resource config.
    ///         Contracts that inherit this contract must implement this function.
    /// @return ResourceConfig
    function _resourceConfig() internal virtual returns (ResourceConfig memory);
    /// @notice Sets initial resource parameter values.
    ///         This function must either be called by the initializer function of an upgradeable
    ///         child contract.
    // solhint-disable-next-line func-name-mixedcase
    function __ResourceMetering_init() internal onlyInitializing {
        params = ResourceParams({ prevBaseFee: 1 gwei, prevBoughtGas: 0, prevBlockNum: uint64(block.number) });
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/Address.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!Address.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }
    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }
    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);
            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////
            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }
            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)
                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)
                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }
            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;
            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;
            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256
            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }
    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }
    /**
     * @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`.
        // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`.
        // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`.
        // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a
        // good first aproximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1;
        uint256 x = a;
        if (x >> 128 > 0) {
            x >>= 128;
            result <<= 64;
        }
        if (x >> 64 > 0) {
            x >>= 64;
            result <<= 32;
        }
        if (x >> 32 > 0) {
            x >>= 32;
            result <<= 16;
        }
        if (x >> 16 > 0) {
            x >>= 16;
            result <<= 8;
        }
        if (x >> 8 > 0) {
            x >>= 8;
            result <<= 4;
        }
        if (x >> 4 > 0) {
            x >>= 4;
            result <<= 2;
        }
        if (x >> 2 > 0) {
            result <<= 1;
        }
        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }
    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        uint256 result = sqrt(a);
        if (rounding == Rounding.Up && result * result < a) {
            result += 1;
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @title Burn
/// @notice Utilities for burning stuff.
library Burn {
    /// @notice Burns a given amount of ETH.
    /// @param _amount Amount of ETH to burn.
    function eth(uint256 _amount) internal {
        new Burner{ value: _amount }();
    }
    /// @notice Burns a given amount of gas.
    /// @param _amount Amount of gas to burn.
    function gas(uint256 _amount) internal view {
        uint256 i = 0;
        uint256 initialGas = gasleft();
        while (initialGas - gasleft() < _amount) {
            ++i;
        }
    }
}
/// @title Burner
/// @notice Burner self-destructs on creation and sends all ETH to itself, removing all ETH given to
///         the contract from the circulating supply. Self-destructing is the only way to remove ETH
///         from the circulating supply.
contract Burner {
    constructor() payable {
        selfdestruct(payable(address(this)));
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { SignedMath } from "@openzeppelin/contracts/utils/math/SignedMath.sol";
import { FixedPointMathLib } from "@rari-capital/solmate/src/utils/FixedPointMathLib.sol";
/// @title Arithmetic
/// @notice Even more math than before.
library Arithmetic {
    /// @notice Clamps a value between a minimum and maximum.
    /// @param _value The value to clamp.
    /// @param _min   The minimum value.
    /// @param _max   The maximum value.
    /// @return The clamped value.
    function clamp(int256 _value, int256 _min, int256 _max) internal pure returns (int256) {
        return SignedMath.min(SignedMath.max(_value, _min), _max);
    }
    /// @notice (c)oefficient (d)enominator (exp)onentiation function.
    ///         Returns the result of: c * (1 - 1/d)^exp.
    /// @param _coefficient Coefficient of the function.
    /// @param _denominator Fractional denominator.
    /// @param _exponent    Power function exponent.
    /// @return Result of c * (1 - 1/d)^exp.
    function cdexp(int256 _coefficient, int256 _denominator, int256 _exponent) internal pure returns (int256) {
        return (_coefficient * (FixedPointMathLib.powWad(1e18 - (1e18 / _denominator), _exponent * 1e18))) / 1e18;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library 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
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev 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) {
        require(isContract(target), "Address: delegate call to non-contract");
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.
    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }
    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
        return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0.
    }
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return 0;
            // When the result is > (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 (x >= 135305999368893231589) revert("EXP_OVERFLOW");
            // 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;
            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));
        }
    }
    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            require(x > 0, "UNDEFINED");
            // 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.
            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            int256 k = int256(log2(uint256(x))) - 96;
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);
            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);
            // 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.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }
            // r 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
            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }
    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // Divide z by the denominator.
            z := div(z, denominator)
        }
    }
    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // First, divide z - 1 by the denominator and add 1.
            // We allow z - 1 to underflow if z is 0, because we multiply the
            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
        }
    }
    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }
                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)
                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }
                    // Store x squared.
                    let xx := mul(x, x)
                    // Round to the nearest number.
                    let xxRound := add(xx, half)
                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }
                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)
                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)
                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }
                        // Round to the nearest number.
                        let zxRound := add(zx, half)
                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }
                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }
    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.
            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.
            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, 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(y, 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }
    function log2(uint256 x) internal pure returns (uint256 r) {
        require(x > 0, "UNDEFINED");
        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))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { OwnableUpgradeable } from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
import { ISemver } from "src/universal/ISemver.sol";
import { ResourceMetering } from "src/L1/ResourceMetering.sol";
import { Storage } from "src/libraries/Storage.sol";
import { Constants } from "src/libraries/Constants.sol";
/// @title SystemConfig
/// @notice The SystemConfig contract is used to manage configuration of an Optimism network.
///         All configuration is stored on L1 and picked up by L2 as part of the derviation of
///         the L2 chain.
contract SystemConfig is OwnableUpgradeable, ISemver {
    /// @notice Enum representing different types of updates.
    /// @custom:value BATCHER              Represents an update to the batcher hash.
    /// @custom:value GAS_CONFIG           Represents an update to txn fee config on L2.
    /// @custom:value GAS_LIMIT            Represents an update to gas limit on L2.
    /// @custom:value UNSAFE_BLOCK_SIGNER  Represents an update to the signer key for unsafe
    ///                                    block distrubution.
    enum UpdateType {
        BATCHER,
        GAS_CONFIG,
        GAS_LIMIT,
        UNSAFE_BLOCK_SIGNER
    }
    /// @notice Struct representing the addresses of L1 system contracts. These should be the
    ///         proxies and are network specific.
    struct Addresses {
        address l1CrossDomainMessenger;
        address l1ERC721Bridge;
        address l1StandardBridge;
        address disputeGameFactory;
        address optimismPortal;
        address optimismMintableERC20Factory;
    }
    /// @notice Version identifier, used for upgrades.
    uint256 public constant VERSION = 0;
    /// @notice Storage slot that the unsafe block signer is stored at.
    ///         Storing it at this deterministic storage slot allows for decoupling the storage
    ///         layout from the way that `solc` lays out storage. The `op-node` uses a storage
    ///         proof to fetch this value.
    /// @dev    NOTE: this value will be migrated to another storage slot in a future version.
    ///         User input should not be placed in storage in this contract until this migration
    ///         happens. It is unlikely that keccak second preimage resistance will be broken,
    ///         but it is better to be safe than sorry.
    bytes32 public constant UNSAFE_BLOCK_SIGNER_SLOT = keccak256("systemconfig.unsafeblocksigner");
    /// @notice Storage slot that the L1CrossDomainMessenger address is stored at.
    bytes32 public constant L1_CROSS_DOMAIN_MESSENGER_SLOT =
        bytes32(uint256(keccak256("systemconfig.l1crossdomainmessenger")) - 1);
    /// @notice Storage slot that the L1ERC721Bridge address is stored at.
    bytes32 public constant L1_ERC_721_BRIDGE_SLOT = bytes32(uint256(keccak256("systemconfig.l1erc721bridge")) - 1);
    /// @notice Storage slot that the L1StandardBridge address is stored at.
    bytes32 public constant L1_STANDARD_BRIDGE_SLOT = bytes32(uint256(keccak256("systemconfig.l1standardbridge")) - 1);
    /// @notice Storage slot that the OptimismPortal address is stored at.
    bytes32 public constant OPTIMISM_PORTAL_SLOT = bytes32(uint256(keccak256("systemconfig.optimismportal")) - 1);
    /// @notice Storage slot that the OptimismMintableERC20Factory address is stored at.
    bytes32 public constant OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT =
        bytes32(uint256(keccak256("systemconfig.optimismmintableerc20factory")) - 1);
    /// @notice Storage slot that the batch inbox address is stored at.
    bytes32 public constant BATCH_INBOX_SLOT = bytes32(uint256(keccak256("systemconfig.batchinbox")) - 1);
    /// @notice Storage slot for block at which the op-node can start searching for logs from.
    bytes32 public constant START_BLOCK_SLOT = bytes32(uint256(keccak256("systemconfig.startBlock")) - 1);
    /// @notice Storage slot for the DisputeGameFactory address.
    bytes32 public constant DISPUTE_GAME_FACTORY_SLOT =
        bytes32(uint256(keccak256("systemconfig.disputegamefactory")) - 1);
    /// @notice The maximum gas limit that can be set for L2 blocks. This limit is used to enforce that the blocks
    ///         on L2 are not too large to process and prove. Over time, this value can be increased as various
    ///         optimizations and improvements are made to the system at large.
    uint64 internal constant MAX_GAS_LIMIT = 200_000_000;
    /// @notice Fixed L2 gas overhead. Used as part of the L2 fee calculation.
    uint256 public overhead;
    /// @notice Dynamic L2 gas overhead. Used as part of the L2 fee calculation.
    uint256 public scalar;
    /// @notice Identifier for the batcher.
    ///         For version 1 of this configuration, this is represented as an address left-padded
    ///         with zeros to 32 bytes.
    bytes32 public batcherHash;
    /// @notice L2 block gas limit.
    uint64 public gasLimit;
    /// @notice The configuration for the deposit fee market.
    ///         Used by the OptimismPortal to meter the cost of buying L2 gas on L1.
    ///         Set as internal with a getter so that the struct is returned instead of a tuple.
    ResourceMetering.ResourceConfig internal _resourceConfig;
    /// @notice Emitted when configuration is updated.
    /// @param version    SystemConfig version.
    /// @param updateType Type of update.
    /// @param data       Encoded update data.
    event ConfigUpdate(uint256 indexed version, UpdateType indexed updateType, bytes data);
    /// @notice Semantic version.
    /// @custom:semver 2.2.0
    string public constant version = "2.2.0";
    /// @notice Constructs the SystemConfig contract. Cannot set
    ///         the owner to `address(0)` due to the Ownable contract's
    ///         implementation, so set it to `address(0xdEaD)`
    /// @dev    START_BLOCK_SLOT is set to type(uint256).max here so that it will be a dead value
    ///         in the singleton and is skipped by initialize when setting the start block.
    constructor() {
        Storage.setUint(START_BLOCK_SLOT, type(uint256).max);
        initialize({
            _owner: address(0xdEaD),
            _overhead: 0,
            _scalar: 0,
            _batcherHash: bytes32(0),
            _gasLimit: 1,
            _unsafeBlockSigner: address(0),
            _config: ResourceMetering.ResourceConfig({
                maxResourceLimit: 1,
                elasticityMultiplier: 1,
                baseFeeMaxChangeDenominator: 2,
                minimumBaseFee: 0,
                systemTxMaxGas: 0,
                maximumBaseFee: 0
            }),
            _batchInbox: address(0),
            _addresses: SystemConfig.Addresses({
                l1CrossDomainMessenger: address(0),
                l1ERC721Bridge: address(0),
                l1StandardBridge: address(0),
                disputeGameFactory: address(0),
                optimismPortal: address(0),
                optimismMintableERC20Factory: address(0)
            })
        });
    }
    /// @notice Initializer.
    ///         The resource config must be set before the require check.
    /// @param _owner             Initial owner of the contract.
    /// @param _overhead          Initial overhead value.
    /// @param _scalar            Initial scalar value.
    /// @param _batcherHash       Initial batcher hash.
    /// @param _gasLimit          Initial gas limit.
    /// @param _unsafeBlockSigner Initial unsafe block signer address.
    /// @param _config            Initial ResourceConfig.
    /// @param _batchInbox        Batch inbox address. An identifier for the op-node to find
    ///                           canonical data.
    /// @param _addresses         Set of L1 contract addresses. These should be the proxies.
    function initialize(
        address _owner,
        uint256 _overhead,
        uint256 _scalar,
        bytes32 _batcherHash,
        uint64 _gasLimit,
        address _unsafeBlockSigner,
        ResourceMetering.ResourceConfig memory _config,
        address _batchInbox,
        SystemConfig.Addresses memory _addresses
    )
        public
        initializer
    {
        __Ownable_init();
        transferOwnership(_owner);
        // These are set in ascending order of their UpdateTypes.
        _setBatcherHash(_batcherHash);
        _setGasConfig({ _overhead: _overhead, _scalar: _scalar });
        _setGasLimit(_gasLimit);
        Storage.setAddress(UNSAFE_BLOCK_SIGNER_SLOT, _unsafeBlockSigner);
        Storage.setAddress(BATCH_INBOX_SLOT, _batchInbox);
        Storage.setAddress(L1_CROSS_DOMAIN_MESSENGER_SLOT, _addresses.l1CrossDomainMessenger);
        Storage.setAddress(L1_ERC_721_BRIDGE_SLOT, _addresses.l1ERC721Bridge);
        Storage.setAddress(L1_STANDARD_BRIDGE_SLOT, _addresses.l1StandardBridge);
        Storage.setAddress(DISPUTE_GAME_FACTORY_SLOT, _addresses.disputeGameFactory);
        Storage.setAddress(OPTIMISM_PORTAL_SLOT, _addresses.optimismPortal);
        Storage.setAddress(OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT, _addresses.optimismMintableERC20Factory);
        _setStartBlock();
        _setResourceConfig(_config);
        require(_gasLimit >= minimumGasLimit(), "SystemConfig: gas limit too low");
    }
    /// @notice Returns the minimum L2 gas limit that can be safely set for the system to
    ///         operate. The L2 gas limit must be larger than or equal to the amount of
    ///         gas that is allocated for deposits per block plus the amount of gas that
    ///         is allocated for the system transaction.
    ///         This function is used to determine if changes to parameters are safe.
    /// @return uint64 Minimum gas limit.
    function minimumGasLimit() public view returns (uint64) {
        return uint64(_resourceConfig.maxResourceLimit) + uint64(_resourceConfig.systemTxMaxGas);
    }
    /// @notice Returns the maximum L2 gas limit that can be safely set for the system to
    ///         operate. This bound is used to prevent the gas limit from being set too high
    ///         and causing the system to be unable to process and/or prove L2 blocks.
    /// @return uint64 Maximum gas limit.
    function maximumGasLimit() public pure returns (uint64) {
        return MAX_GAS_LIMIT;
    }
    /// @notice High level getter for the unsafe block signer address.
    ///         Unsafe blocks can be propagated across the p2p network if they are signed by the
    ///         key corresponding to this address.
    /// @return addr_ Address of the unsafe block signer.
    function unsafeBlockSigner() public view returns (address addr_) {
        addr_ = Storage.getAddress(UNSAFE_BLOCK_SIGNER_SLOT);
    }
    /// @notice Getter for the L1CrossDomainMessenger address.
    function l1CrossDomainMessenger() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_CROSS_DOMAIN_MESSENGER_SLOT);
    }
    /// @notice Getter for the L1ERC721Bridge address.
    function l1ERC721Bridge() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_ERC_721_BRIDGE_SLOT);
    }
    /// @notice Getter for the L1StandardBridge address.
    function l1StandardBridge() external view returns (address addr_) {
        addr_ = Storage.getAddress(L1_STANDARD_BRIDGE_SLOT);
    }
    /// @notice Getter for the DisputeGameFactory address.
    function disputeGameFactory() external view returns (address addr_) {
        addr_ = Storage.getAddress(DISPUTE_GAME_FACTORY_SLOT);
    }
    /// @notice Getter for the OptimismPortal address.
    function optimismPortal() external view returns (address addr_) {
        addr_ = Storage.getAddress(OPTIMISM_PORTAL_SLOT);
    }
    /// @notice Getter for the OptimismMintableERC20Factory address.
    function optimismMintableERC20Factory() external view returns (address addr_) {
        addr_ = Storage.getAddress(OPTIMISM_MINTABLE_ERC20_FACTORY_SLOT);
    }
    /// @notice Getter for the BatchInbox address.
    function batchInbox() external view returns (address addr_) {
        addr_ = Storage.getAddress(BATCH_INBOX_SLOT);
    }
    /// @notice Getter for the StartBlock number.
    function startBlock() external view returns (uint256 startBlock_) {
        startBlock_ = Storage.getUint(START_BLOCK_SLOT);
    }
    /// @notice Updates the unsafe block signer address. Can only be called by the owner.
    /// @param _unsafeBlockSigner New unsafe block signer address.
    function setUnsafeBlockSigner(address _unsafeBlockSigner) external onlyOwner {
        _setUnsafeBlockSigner(_unsafeBlockSigner);
    }
    /// @notice Updates the unsafe block signer address.
    /// @param _unsafeBlockSigner New unsafe block signer address.
    function _setUnsafeBlockSigner(address _unsafeBlockSigner) internal {
        Storage.setAddress(UNSAFE_BLOCK_SIGNER_SLOT, _unsafeBlockSigner);
        bytes memory data = abi.encode(_unsafeBlockSigner);
        emit ConfigUpdate(VERSION, UpdateType.UNSAFE_BLOCK_SIGNER, data);
    }
    /// @notice Updates the batcher hash. Can only be called by the owner.
    /// @param _batcherHash New batcher hash.
    function setBatcherHash(bytes32 _batcherHash) external onlyOwner {
        _setBatcherHash(_batcherHash);
    }
    /// @notice Internal function for updating the batcher hash.
    /// @param _batcherHash New batcher hash.
    function _setBatcherHash(bytes32 _batcherHash) internal {
        batcherHash = _batcherHash;
        bytes memory data = abi.encode(_batcherHash);
        emit ConfigUpdate(VERSION, UpdateType.BATCHER, data);
    }
    /// @notice Updates gas config. Can only be called by the owner.
    /// @param _overhead New overhead value.
    /// @param _scalar   New scalar value.
    function setGasConfig(uint256 _overhead, uint256 _scalar) external onlyOwner {
        _setGasConfig(_overhead, _scalar);
    }
    /// @notice Internal function for updating the gas config.
    /// @param _overhead New overhead value.
    /// @param _scalar   New scalar value.
    function _setGasConfig(uint256 _overhead, uint256 _scalar) internal {
        overhead = _overhead;
        scalar = _scalar;
        bytes memory data = abi.encode(_overhead, _scalar);
        emit ConfigUpdate(VERSION, UpdateType.GAS_CONFIG, data);
    }
    /// @notice Updates the L2 gas limit. Can only be called by the owner.
    /// @param _gasLimit New gas limit.
    function setGasLimit(uint64 _gasLimit) external onlyOwner {
        _setGasLimit(_gasLimit);
    }
    /// @notice Internal function for updating the L2 gas limit.
    /// @param _gasLimit New gas limit.
    function _setGasLimit(uint64 _gasLimit) internal {
        require(_gasLimit >= minimumGasLimit(), "SystemConfig: gas limit too low");
        require(_gasLimit <= maximumGasLimit(), "SystemConfig: gas limit too high");
        gasLimit = _gasLimit;
        bytes memory data = abi.encode(_gasLimit);
        emit ConfigUpdate(VERSION, UpdateType.GAS_LIMIT, data);
    }
    /// @notice Sets the start block in a backwards compatible way. Proxies
    ///         that were initialized before the startBlock existed in storage
    ///         can have their start block set by a user provided override.
    ///         A start block of 0 indicates that there is no override and the
    ///         start block will be set by `block.number`.
    /// @dev    This logic is used to patch legacy deployments with new storage values.
    ///         Use the override if it is provided as a non zero value and the value
    ///         has not already been set in storage. Use `block.number` if the value
    ///         has already been set in storage
    function _setStartBlock() internal {
        if (Storage.getUint(START_BLOCK_SLOT) == 0) {
            Storage.setUint(START_BLOCK_SLOT, block.number);
        }
    }
    /// @notice A getter for the resource config.
    ///         Ensures that the struct is returned instead of a tuple.
    /// @return ResourceConfig
    function resourceConfig() external view returns (ResourceMetering.ResourceConfig memory) {
        return _resourceConfig;
    }
    /// @notice An internal setter for the resource config.
    ///         Ensures that the config is sane before storing it by checking for invariants.
    ///         In the future, this method may emit an event that the `op-node` picks up
    ///         for when the resource config is changed.
    /// @param _config The new resource config.
    function _setResourceConfig(ResourceMetering.ResourceConfig memory _config) internal {
        // Min base fee must be less than or equal to max base fee.
        require(
            _config.minimumBaseFee <= _config.maximumBaseFee, "SystemConfig: min base fee must be less than max base"
        );
        // Base fee change denominator must be greater than 1.
        require(_config.baseFeeMaxChangeDenominator > 1, "SystemConfig: denominator must be larger than 1");
        // Max resource limit plus system tx gas must be less than or equal to the L2 gas limit.
        // The gas limit must be increased before these values can be increased.
        require(_config.maxResourceLimit + _config.systemTxMaxGas <= gasLimit, "SystemConfig: gas limit too low");
        // Elasticity multiplier must be greater than 0.
        require(_config.elasticityMultiplier > 0, "SystemConfig: elasticity multiplier cannot be 0");
        // No precision loss when computing target resource limit.
        require(
            ((_config.maxResourceLimit / _config.elasticityMultiplier) * _config.elasticityMultiplier)
                == _config.maxResourceLimit,
            "SystemConfig: precision loss with target resource limit"
        );
        _resourceConfig = _config;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (access/Ownable.sol)
pragma solidity ^0.8.0;
import "../utils/ContextUpgradeable.sol";
import "../proxy/utils/Initializable.sol";
/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;
    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }
    function __Ownable_init_unchained() internal onlyInitializing {
        _transferOwnership(_msgSender());
    }
    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }
    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }
    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }
    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }
    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title ISemver
/// @notice ISemver is a simple contract for ensuring that contracts are
///         versioned using semantic versioning.
interface ISemver {
    /// @notice Getter for the semantic version of the contract. This is not
    ///         meant to be used onchain but instead meant to be used by offchain
    ///         tooling.
    /// @return Semver contract version as a string.
    function version() external view returns (string memory);
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Initializable } from "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { Burn } from "src/libraries/Burn.sol";
import { Arithmetic } from "src/libraries/Arithmetic.sol";
/// @custom:upgradeable
/// @title ResourceMetering
/// @notice ResourceMetering implements an EIP-1559 style resource metering system where pricing
///         updates automatically based on current demand.
abstract contract ResourceMetering is Initializable {
    /// @notice Error returned when too much gas resource is consumed.
    error OutOfGas();
    /// @notice Represents the various parameters that control the way in which resources are
    ///         metered. Corresponds to the EIP-1559 resource metering system.
    /// @custom:field prevBaseFee   Base fee from the previous block(s).
    /// @custom:field prevBoughtGas Amount of gas bought so far in the current block.
    /// @custom:field prevBlockNum  Last block number that the base fee was updated.
    struct ResourceParams {
        uint128 prevBaseFee;
        uint64 prevBoughtGas;
        uint64 prevBlockNum;
    }
    /// @notice Represents the configuration for the EIP-1559 based curve for the deposit gas
    ///         market. These values should be set with care as it is possible to set them in
    ///         a way that breaks the deposit gas market. The target resource limit is defined as
    ///         maxResourceLimit / elasticityMultiplier. This struct was designed to fit within a
    ///         single word. There is additional space for additions in the future.
    /// @custom:field maxResourceLimit             Represents the maximum amount of deposit gas that
    ///                                            can be purchased per block.
    /// @custom:field elasticityMultiplier         Determines the target resource limit along with
    ///                                            the resource limit.
    /// @custom:field baseFeeMaxChangeDenominator  Determines max change on fee per block.
    /// @custom:field minimumBaseFee               The min deposit base fee, it is clamped to this
    ///                                            value.
    /// @custom:field systemTxMaxGas               The amount of gas supplied to the system
    ///                                            transaction. This should be set to the same
    ///                                            number that the op-node sets as the gas limit
    ///                                            for the system transaction.
    /// @custom:field maximumBaseFee               The max deposit base fee, it is clamped to this
    ///                                            value.
    struct ResourceConfig {
        uint32 maxResourceLimit;
        uint8 elasticityMultiplier;
        uint8 baseFeeMaxChangeDenominator;
        uint32 minimumBaseFee;
        uint32 systemTxMaxGas;
        uint128 maximumBaseFee;
    }
    /// @notice EIP-1559 style gas parameters.
    ResourceParams public params;
    /// @notice Reserve extra slots (to a total of 50) in the storage layout for future upgrades.
    uint256[48] private __gap;
    /// @notice Meters access to a function based an amount of a requested resource.
    /// @param _amount Amount of the resource requested.
    modifier metered(uint64 _amount) {
        // Record initial gas amount so we can refund for it later.
        uint256 initialGas = gasleft();
        // Run the underlying function.
        _;
        // Run the metering function.
        _metered(_amount, initialGas);
    }
    /// @notice An internal function that holds all of the logic for metering a resource.
    /// @param _amount     Amount of the resource requested.
    /// @param _initialGas The amount of gas before any modifier execution.
    function _metered(uint64 _amount, uint256 _initialGas) internal {
        // Update block number and base fee if necessary.
        uint256 blockDiff = block.number - params.prevBlockNum;
        ResourceConfig memory config = _resourceConfig();
        int256 targetResourceLimit =
            int256(uint256(config.maxResourceLimit)) / int256(uint256(config.elasticityMultiplier));
        if (blockDiff > 0) {
            // Handle updating EIP-1559 style gas parameters. We use EIP-1559 to restrict the rate
            // at which deposits can be created and therefore limit the potential for deposits to
            // spam the L2 system. Fee scheme is very similar to EIP-1559 with minor changes.
            int256 gasUsedDelta = int256(uint256(params.prevBoughtGas)) - targetResourceLimit;
            int256 baseFeeDelta = (int256(uint256(params.prevBaseFee)) * gasUsedDelta)
                / (targetResourceLimit * int256(uint256(config.baseFeeMaxChangeDenominator)));
            // Update base fee by adding the base fee delta and clamp the resulting value between
            // min and max.
            int256 newBaseFee = Arithmetic.clamp({
                _value: int256(uint256(params.prevBaseFee)) + baseFeeDelta,
                _min: int256(uint256(config.minimumBaseFee)),
                _max: int256(uint256(config.maximumBaseFee))
            });
            // If we skipped more than one block, we also need to account for every empty block.
            // Empty block means there was no demand for deposits in that block, so we should
            // reflect this lack of demand in the fee.
            if (blockDiff > 1) {
                // Update the base fee by repeatedly applying the exponent 1-(1/change_denominator)
                // blockDiff - 1 times. Simulates multiple empty blocks. Clamp the resulting value
                // between min and max.
                newBaseFee = Arithmetic.clamp({
                    _value: Arithmetic.cdexp({
                        _coefficient: newBaseFee,
                        _denominator: int256(uint256(config.baseFeeMaxChangeDenominator)),
                        _exponent: int256(blockDiff - 1)
                    }),
                    _min: int256(uint256(config.minimumBaseFee)),
                    _max: int256(uint256(config.maximumBaseFee))
                });
            }
            // Update new base fee, reset bought gas, and update block number.
            params.prevBaseFee = uint128(uint256(newBaseFee));
            params.prevBoughtGas = 0;
            params.prevBlockNum = uint64(block.number);
        }
        // Make sure we can actually buy the resource amount requested by the user.
        params.prevBoughtGas += _amount;
        if (int256(uint256(params.prevBoughtGas)) > int256(uint256(config.maxResourceLimit))) {
            revert OutOfGas();
        }
        // Determine the amount of ETH to be paid.
        uint256 resourceCost = uint256(_amount) * uint256(params.prevBaseFee);
        // We currently charge for this ETH amount as an L1 gas burn, so we convert the ETH amount
        // into gas by dividing by the L1 base fee. We assume a minimum base fee of 1 gwei to avoid
        // division by zero for L1s that don't support 1559 or to avoid excessive gas burns during
        // periods of extremely low L1 demand. One-day average gas fee hasn't dipped below 1 gwei
        // during any 1 day period in the last 5 years, so should be fine.
        uint256 gasCost = resourceCost / Math.max(block.basefee, 1 gwei);
        // Give the user a refund based on the amount of gas they used to do all of the work up to
        // this point. Since we're at the end of the modifier, this should be pretty accurate. Acts
        // effectively like a dynamic stipend (with a minimum value).
        uint256 usedGas = _initialGas - gasleft();
        if (gasCost > usedGas) {
            Burn.gas(gasCost - usedGas);
        }
    }
    /// @notice Virtual function that returns the resource config.
    ///         Contracts that inherit this contract must implement this function.
    /// @return ResourceConfig
    function _resourceConfig() internal virtual returns (ResourceConfig memory);
    /// @notice Sets initial resource parameter values.
    ///         This function must either be called by the initializer function of an upgradeable
    ///         child contract.
    function __ResourceMetering_init() internal onlyInitializing {
        if (params.prevBlockNum == 0) {
            params = ResourceParams({ prevBaseFee: 1 gwei, prevBoughtGas: 0, prevBlockNum: uint64(block.number) });
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/// @title Storage
/// @notice Storage handles reading and writing to arbitary storage locations
library Storage {
    /// @notice Returns an address stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getAddress(bytes32 _slot) internal view returns (address addr_) {
        assembly {
            addr_ := sload(_slot)
        }
    }
    /// @notice Stores an address in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _address The protocol version to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting addresses
    ///      in arbitrary storage slots.
    function setAddress(bytes32 _slot, address _address) internal {
        assembly {
            sstore(_slot, _address)
        }
    }
    /// @notice Returns a uint256 stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getUint(bytes32 _slot) internal view returns (uint256 value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
    /// @notice Stores a value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _value The protocol version to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setUint(bytes32 _slot, uint256 _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Returns a bytes32 stored in an arbitrary storage slot.
    ///         These storage slots decouple the storage layout from
    ///         solc's automation.
    /// @param _slot The storage slot to retrieve the address from.
    function getBytes32(bytes32 _slot) internal view returns (bytes32 value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
    /// @notice Stores a bytes32 value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the address in.
    /// @param _value The bytes32 value to store.
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setBytes32(bytes32 _slot, bytes32 _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Stores a bool value in an arbitrary storage slot, `_slot`.
    /// @param _slot The storage slot to store the bool in.
    /// @param _value The bool value to store
    /// @dev WARNING! This function must be used cautiously, as it allows for overwriting values
    ///      in arbitrary storage slots.
    function setBool(bytes32 _slot, bool _value) internal {
        assembly {
            sstore(_slot, _value)
        }
    }
    /// @notice Returns a bool stored in an arbitrary storage slot.
    /// @param _slot The storage slot to retrieve the bool from.
    function getBool(bytes32 _slot) internal view returns (bool value_) {
        assembly {
            value_ := sload(_slot)
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { ResourceMetering } from "src/L1/ResourceMetering.sol";
/// @title Constants
/// @notice Constants is a library for storing constants. Simple! Don't put everything in here, just
///         the stuff used in multiple contracts. Constants that only apply to a single contract
///         should be defined in that contract instead.
library Constants {
    /// @notice Special address to be used as the tx origin for gas estimation calls in the
    ///         OptimismPortal and CrossDomainMessenger calls. You only need to use this address if
    ///         the minimum gas limit specified by the user is not actually enough to execute the
    ///         given message and you're attempting to estimate the actual necessary gas limit. We
    ///         use address(1) because it's the ecrecover precompile and therefore guaranteed to
    ///         never have any code on any EVM chain.
    address internal constant ESTIMATION_ADDRESS = address(1);
    /// @notice Value used for the L2 sender storage slot in both the OptimismPortal and the
    ///         CrossDomainMessenger contracts before an actual sender is set. This value is
    ///         non-zero to reduce the gas cost of message passing transactions.
    address internal constant DEFAULT_L2_SENDER = 0x000000000000000000000000000000000000dEaD;
    /// @notice The storage slot that holds the address of a proxy implementation.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)`
    bytes32 internal constant PROXY_IMPLEMENTATION_ADDRESS =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /// @notice The storage slot that holds the address of the owner.
    /// @dev `bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)`
    bytes32 internal constant PROXY_OWNER_ADDRESS = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /// @notice Returns the default values for the ResourceConfig. These are the recommended values
    ///         for a production network.
    function DEFAULT_RESOURCE_CONFIG() internal pure returns (ResourceMetering.ResourceConfig memory) {
        ResourceMetering.ResourceConfig memory config = ResourceMetering.ResourceConfig({
            maxResourceLimit: 20_000_000,
            elasticityMultiplier: 10,
            baseFeeMaxChangeDenominator: 8,
            minimumBaseFee: 1 gwei,
            systemTxMaxGas: 1_000_000,
            maximumBaseFee: type(uint128).max
        });
        return config;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }
    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }
    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/AddressUpgradeable.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/Address.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!Address.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/Math.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }
    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }
    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }
            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }
            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1);
            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////
            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)
                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }
            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.
            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)
                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)
                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }
            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;
            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;
            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256
            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }
    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator,
        Rounding rounding
    ) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }
    /**
     * @dev Returns the square root of a number. It the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`.
        // We also know that `k`, the position of the most significant bit, is such that `msb(a) = 2**k`.
        // This gives `2**k < a <= 2**(k+1)` → `2**(k/2) <= sqrt(a) < 2 ** (k/2+1)`.
        // Using an algorithm similar to the msb conmputation, we are able to compute `result = 2**(k/2)` which is a
        // good first aproximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1;
        uint256 x = a;
        if (x >> 128 > 0) {
            x >>= 128;
            result <<= 64;
        }
        if (x >> 64 > 0) {
            x >>= 64;
            result <<= 32;
        }
        if (x >> 32 > 0) {
            x >>= 32;
            result <<= 16;
        }
        if (x >> 16 > 0) {
            x >>= 16;
            result <<= 8;
        }
        if (x >> 8 > 0) {
            x >>= 8;
            result <<= 4;
        }
        if (x >> 4 > 0) {
            x >>= 4;
            result <<= 2;
        }
        if (x >> 2 > 0) {
            result <<= 1;
        }
        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }
    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        uint256 result = sqrt(a);
        if (rounding == Rounding.Up && result * result < a) {
            result += 1;
        }
        return result;
    }
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/// @title Burn
/// @notice Utilities for burning stuff.
library Burn {
    /// @notice Burns a given amount of ETH.
    /// @param _amount Amount of ETH to burn.
    function eth(uint256 _amount) internal {
        new Burner{ value: _amount }();
    }
    /// @notice Burns a given amount of gas.
    /// @param _amount Amount of gas to burn.
    function gas(uint256 _amount) internal view {
        uint256 i = 0;
        uint256 initialGas = gasleft();
        while (initialGas - gasleft() < _amount) {
            ++i;
        }
    }
}
/// @title Burner
/// @notice Burner self-destructs on creation and sends all ETH to itself, removing all ETH given to
///         the contract from the circulating supply. Self-destructing is the only way to remove ETH
///         from the circulating supply.
contract Burner {
    constructor() payable {
        selfdestruct(payable(address(this)));
    }
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { SignedMath } from "@openzeppelin/contracts/utils/math/SignedMath.sol";
import { FixedPointMathLib } from "@rari-capital/solmate/src/utils/FixedPointMathLib.sol";
/// @title Arithmetic
/// @notice Even more math than before.
library Arithmetic {
    /// @notice Clamps a value between a minimum and maximum.
    /// @param _value The value to clamp.
    /// @param _min   The minimum value.
    /// @param _max   The maximum value.
    /// @return The clamped value.
    function clamp(int256 _value, int256 _min, int256 _max) internal pure returns (int256) {
        return SignedMath.min(SignedMath.max(_value, _min), _max);
    }
    /// @notice (c)oefficient (d)enominator (exp)onentiation function.
    ///         Returns the result of: c * (1 - 1/d)^exp.
    /// @param _coefficient Coefficient of the function.
    /// @param _denominator Fractional denominator.
    /// @param _exponent    Power function exponent.
    /// @return Result of c * (1 - 1/d)^exp.
    function cdexp(int256 _coefficient, int256 _denominator, int256 _exponent) internal pure returns (int256) {
        return (_coefficient * (FixedPointMathLib.powWad(1e18 - (1e18 / _denominator), _exponent * 1e18))) / 1e18;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Address.sol)
pragma solidity ^0.8.1;
/**
 * @dev Collection of functions related to the address type
 */
library 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
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.
        return account.code.length > 0;
    }
    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");
        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }
    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCall(target, data, "Address: low-level call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }
    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        require(isContract(target), "Address: call to non-contract");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }
    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev 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) {
        require(isContract(target), "Address: delegate call to non-contract");
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }
    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly
                /// @solidity memory-safe-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (utils/math/SignedMath.sol)
pragma solidity ^0.8.0;
/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a >= b ? a : b;
    }
    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }
    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }
    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}
// SPDX-License-Identifier: MIT
pragma solidity >=0.8.0;
/// @notice Arithmetic library with operations for fixed-point numbers.
/// @author Solmate (https://github.com/Rari-Capital/solmate/blob/main/src/utils/FixedPointMathLib.sol)
library FixedPointMathLib {
    /*//////////////////////////////////////////////////////////////
                    SIMPLIFIED FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    uint256 internal constant WAD = 1e18; // The scalar of ETH and most ERC20s.
    function mulWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, y, WAD); // Equivalent to (x * y) / WAD rounded down.
    }
    function mulWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, y, WAD); // Equivalent to (x * y) / WAD rounded up.
    }
    function divWadDown(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivDown(x, WAD, y); // Equivalent to (x * WAD) / y rounded down.
    }
    function divWadUp(uint256 x, uint256 y) internal pure returns (uint256) {
        return mulDivUp(x, WAD, y); // Equivalent to (x * WAD) / y rounded up.
    }
    function powWad(int256 x, int256 y) internal pure returns (int256) {
        // Equivalent to x to the power of y because x ** y = (e ** ln(x)) ** y = e ** (ln(x) * y)
        return expWad((lnWad(x) * y) / int256(WAD)); // Using ln(x) means x must be greater than 0.
    }
    function expWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            // When the result is < 0.5 we return zero. This happens when
            // x <= floor(log(0.5e18) * 1e18) ~ -42e18
            if (x <= -42139678854452767551) return 0;
            // When the result is > (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 (x >= 135305999368893231589) revert("EXP_OVERFLOW");
            // 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;
            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));
        }
    }
    function lnWad(int256 x) internal pure returns (int256 r) {
        unchecked {
            require(x > 0, "UNDEFINED");
            // 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.
            // Reduce range of x to (1, 2) * 2**96
            // ln(2^k * x) = k * ln(2) + ln(x)
            int256 k = int256(log2(uint256(x))) - 96;
            x <<= uint256(159 - k);
            x = int256(uint256(x) >> 159);
            // Evaluate using a (8, 8)-term rational approximation.
            // p is made monic, we will multiply by a scale factor later.
            int256 p = x + 3273285459638523848632254066296;
            p = ((p * x) >> 96) + 24828157081833163892658089445524;
            p = ((p * x) >> 96) + 43456485725739037958740375743393;
            p = ((p * x) >> 96) - 11111509109440967052023855526967;
            p = ((p * x) >> 96) - 45023709667254063763336534515857;
            p = ((p * x) >> 96) - 14706773417378608786704636184526;
            p = p * x - (795164235651350426258249787498 << 96);
            // 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.
            int256 q = x + 5573035233440673466300451813936;
            q = ((q * x) >> 96) + 71694874799317883764090561454958;
            q = ((q * x) >> 96) + 283447036172924575727196451306956;
            q = ((q * x) >> 96) + 401686690394027663651624208769553;
            q = ((q * x) >> 96) + 204048457590392012362485061816622;
            q = ((q * x) >> 96) + 31853899698501571402653359427138;
            q = ((q * x) >> 96) + 909429971244387300277376558375;
            assembly {
                // Div in assembly because solidity adds a zero check despite the unchecked.
                // The q polynomial is known not to have zeros in the domain.
                // No scaling required because p is already 2**96 too large.
                r := sdiv(p, q)
            }
            // r 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
            // mul s * 5e18 * 2**96, base is now 5**18 * 2**192
            r *= 1677202110996718588342820967067443963516166;
            // add ln(2) * k * 5e18 * 2**192
            r += 16597577552685614221487285958193947469193820559219878177908093499208371 * k;
            // add ln(2**96 / 10**18) * 5e18 * 2**192
            r += 600920179829731861736702779321621459595472258049074101567377883020018308;
            // base conversion: mul 2**18 / 2**192
            r >>= 174;
        }
    }
    /*//////////////////////////////////////////////////////////////
                    LOW LEVEL FIXED POINT OPERATIONS
    //////////////////////////////////////////////////////////////*/
    function mulDivDown(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // Divide z by the denominator.
            z := div(z, denominator)
        }
    }
    function mulDivUp(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 z) {
        assembly {
            // Store x * y in z for now.
            z := mul(x, y)
            // Equivalent to require(denominator != 0 && (x == 0 || (x * y) / x == y))
            if iszero(and(iszero(iszero(denominator)), or(iszero(x), eq(div(z, x), y)))) {
                revert(0, 0)
            }
            // First, divide z - 1 by the denominator and add 1.
            // We allow z - 1 to underflow if z is 0, because we multiply the
            // end result by 0 if z is zero, ensuring we return 0 if z is zero.
            z := mul(iszero(iszero(z)), add(div(sub(z, 1), denominator), 1))
        }
    }
    function rpow(
        uint256 x,
        uint256 n,
        uint256 scalar
    ) internal pure returns (uint256 z) {
        assembly {
            switch x
            case 0 {
                switch n
                case 0 {
                    // 0 ** 0 = 1
                    z := scalar
                }
                default {
                    // 0 ** n = 0
                    z := 0
                }
            }
            default {
                switch mod(n, 2)
                case 0 {
                    // If n is even, store scalar in z for now.
                    z := scalar
                }
                default {
                    // If n is odd, store x in z for now.
                    z := x
                }
                // Shifting right by 1 is like dividing by 2.
                let half := shr(1, scalar)
                for {
                    // Shift n right by 1 before looping to halve it.
                    n := shr(1, n)
                } n {
                    // Shift n right by 1 each iteration to halve it.
                    n := shr(1, n)
                } {
                    // Revert immediately if x ** 2 would overflow.
                    // Equivalent to iszero(eq(div(xx, x), x)) here.
                    if shr(128, x) {
                        revert(0, 0)
                    }
                    // Store x squared.
                    let xx := mul(x, x)
                    // Round to the nearest number.
                    let xxRound := add(xx, half)
                    // Revert if xx + half overflowed.
                    if lt(xxRound, xx) {
                        revert(0, 0)
                    }
                    // Set x to scaled xxRound.
                    x := div(xxRound, scalar)
                    // If n is even:
                    if mod(n, 2) {
                        // Compute z * x.
                        let zx := mul(z, x)
                        // If z * x overflowed:
                        if iszero(eq(div(zx, x), z)) {
                            // Revert if x is non-zero.
                            if iszero(iszero(x)) {
                                revert(0, 0)
                            }
                        }
                        // Round to the nearest number.
                        let zxRound := add(zx, half)
                        // Revert if zx + half overflowed.
                        if lt(zxRound, zx) {
                            revert(0, 0)
                        }
                        // Return properly scaled zxRound.
                        z := div(zxRound, scalar)
                    }
                }
            }
        }
    }
    /*//////////////////////////////////////////////////////////////
                        GENERAL NUMBER UTILITIES
    //////////////////////////////////////////////////////////////*/
    function sqrt(uint256 x) internal pure returns (uint256 z) {
        assembly {
            let y := x // We start y at x, which will help us make our initial estimate.
            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.
            // We check y >= 2^(k + 8) but shift right by k bits
            // each branch to ensure that if x >= 256, then y >= 256.
            if iszero(lt(y, 0x10000000000000000000000000000000000)) {
                y := shr(128, y)
                z := shl(64, z)
            }
            if iszero(lt(y, 0x1000000000000000000)) {
                y := shr(64, y)
                z := shl(32, z)
            }
            if iszero(lt(y, 0x10000000000)) {
                y := shr(32, y)
                z := shl(16, z)
            }
            if iszero(lt(y, 0x1000000)) {
                y := shr(16, y)
                z := shl(8, 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(y, 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
            // Since the ceil is rare, we save gas on the assignment and repeat division in the rare case.
            // If you don't care whether the floor or ceil square root is returned, you can remove this statement.
            z := sub(z, lt(div(x, z), z))
        }
    }
    function log2(uint256 x) internal pure returns (uint256 r) {
        require(x > 0, "UNDEFINED");
        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))))
            r := or(r, shl(2, lt(0xf, shr(r, x))))
            r := or(r, shl(1, lt(0x3, shr(r, x))))
            r := or(r, lt(0x1, shr(r, x)))
        }
    }
}