// 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;
// Contracts
import { OwnableUpgradeable } from "@openzeppelin/contracts-upgradeable/access/OwnableUpgradeable.sol";
// Libraries
import { LibClone } from "@solady/utils/LibClone.sol";
import { GameType, Claim, GameId, Timestamp, Hash, LibGameId } from "src/dispute/lib/Types.sol";
import { NoImplementation, IncorrectBondAmount, GameAlreadyExists } from "src/dispute/lib/Errors.sol";
// Interfaces
import { ISemver } from "interfaces/universal/ISemver.sol";
import { IDisputeGame } from "interfaces/dispute/IDisputeGame.sol";
/// @custom:proxied true
/// @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, ISemver {
    /// @dev Allows for the creation of clone proxies with immutable arguments.
    using LibClone for address;
    /// @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 Semantic version.
    /// @custom:semver 1.0.1
    string public constant version = "1.0.1";
    /// @notice `gameImpls` is a mapping that maps `GameType`s to their respective
    ///         `IDisputeGame` implementations.
    mapping(GameType => IDisputeGame) public gameImpls;
    /// @notice Returns the required bonds for initializing a dispute game of the given type.
    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() {
        _disableInitializers();
    }
    /// @notice Initializes the contract.
    /// @param _owner The owner of the contract.
    function initialize(address _owner) external initializer {
        __Ownable_init();
        _transferOwnership(_owner);
    }
    /// @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_) {
        gameCount_ = _disputeGameList.length;
    }
    /// @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_)
    {
        Hash uuid = getGameUUID(_gameType, _rootClaim, _extraData);
        (, Timestamp timestamp, address proxy) = _disputeGames[uuid].unpack();
        (proxy_, timestamp_) = (IDisputeGame(proxy), 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_)
    {
        (GameType gameType, Timestamp timestamp, address proxy) = _disputeGameList[_index].unpack();
        (gameType_, timestamp_, proxy_) = (gameType, timestamp, IDisputeGame(proxy));
    }
    /// @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_)
    {
        // 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);
    }
    /// @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 calldata _extraData
    )
        public
        pure
        returns (Hash uuid_)
    {
        uuid_ = Hash.wrap(keccak256(abi.encode(_gameType, _rootClaim, _extraData)));
    }
    /// @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_)
    {
        // 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--;
            }
        }
    }
    /// @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 onlyOwner {
        gameImpls[_gameType] = _impl;
        emit ImplementationSet(address(_impl), _gameType);
    }
    /// @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 onlyOwner {
        initBonds[_gameType] = _initBond;
        emit InitBondUpdated(_gameType, _initBond);
    }
}
// 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 ^0.8.4;
/// @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
pragma solidity ^0.8.15;
// Libraries
import {
    Position,
    Hash,
    GameType,
    VMStatus,
    Timestamp,
    Duration,
    Clock,
    GameId,
    Claim,
    LibGameId,
    LibClock
} from "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 The game's bond distribution type. Games are expected to start in the `UNDECIDED`
///         state, and then choose either `NORMAL` or `REFUND`.
enum BondDistributionMode {
    // Bond distribution strategy has not been chosen.
    UNDECIDED,
    // Bonds should be distributed as normal.
    NORMAL,
    // Bonds should be refunded to claimants.
    REFUND
}
/// @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 that uses the cannon vm.
    GameType internal constant PERMISSIONED_CANNON = GameType.wrap(1);
    /// @notice A dispute game type that uses the asterisc vm.
    GameType internal constant ASTERISC = GameType.wrap(2);
    /// @notice A dispute game type that uses the asterisc vm with Kona.
    GameType internal constant ASTERISC_KONA = GameType.wrap(3);
    /// @notice A dispute game type that uses OP Succinct
    GameType internal constant OP_SUCCINCT = GameType.wrap(6);
    /// @notice A dispute game type with short game duration for testing withdrawals.
    ///         Not intended for production use.
    GameType internal constant FAST = GameType.wrap(254);
    /// @notice A dispute game type that uses an alphabet vm.
    ///         Not intended for production use.
    GameType internal constant ALPHABET = GameType.wrap(255);
    /// @notice A dispute game type that uses RISC Zero's Kailua
    GameType internal constant KAILUA = GameType.wrap(1337);
}
/// @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
pragma solidity ^0.8.15;
// Libraries
import { GameType, Hash, Claim } from "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 PreimageOracle challenge period is too high.
error InvalidChallengePeriod();
/// @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();
/// @notice Thrown when the game is not yet finalized.
error GameNotFinalized();
/// @notice Thrown when an invalid bond distribution mode is supplied.
error InvalidBondDistributionMode();
/// @notice Thrown when the game is not yet resolved.
error GameNotResolved();
/// @notice Thrown when a reserved game type is used.
error ReservedGameType();
////////////////////////////////////////////////////////////////
//              `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 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;
import { IInitializable } from "interfaces/dispute/IInitializable.sol";
import { Timestamp, GameStatus, GameType, Claim, Hash } from "src/dispute/lib/Types.sol";
interface IDisputeGame is IInitializable {
    event Resolved(GameStatus indexed status);
    function createdAt() external view returns (Timestamp);
    function resolvedAt() external view returns (Timestamp);
    function status() external view returns (GameStatus);
    function gameType() external view returns (GameType gameType_);
    function gameCreator() external pure returns (address creator_);
    function rootClaim() external pure returns (Claim rootClaim_);
    function l1Head() external pure returns (Hash l1Head_);
    function l2BlockNumber() external pure returns (uint256 l2BlockNumber_);
    function extraData() external pure returns (bytes memory extraData_);
    function resolve() external returns (GameStatus status_);
    function gameData() external view returns (GameType gameType_, Claim rootClaim_, bytes memory extraData_);
    function wasRespectedGameTypeWhenCreated() external view returns (bool);
}
// 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 ^0.8.15;
// Libraries
import { Position } from "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
pragma solidity ^0.8.0;
interface IInitializable {
    function initialize() external payable;
}
// 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;
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
        }
    }
}