// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/**
 * @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 The storage slot that holds the address of the implementation.
     *         bytes32(uint256(keccak256('eip1967.proxy.implementation')) - 1)
     */
    bytes32 internal constant IMPLEMENTATION_KEY =
        0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
    /**
     * @notice The storage slot that holds the address of the owner.
     *         bytes32(uint256(keccak256('eip1967.proxy.admin')) - 1)
     */
    bytes32 internal constant OWNER_KEY =
        0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;
    /**
     * @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 {
        assembly {
            sstore(IMPLEMENTATION_KEY, _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();
        assembly {
            sstore(OWNER_KEY, _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;
        assembly {
            impl := sload(IMPLEMENTATION_KEY)
        }
        return impl;
    }
    /**
     * @notice Queries the owner of the proxy contract.
     *
     * @return Owner address.
     */
    function _getAdmin() internal view returns (address) {
        address owner;
        assembly {
            owner := sload(OWNER_KEY)
        }
        return owner;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
import { Address } from "@openzeppelin/contracts/utils/Address.sol";
import { Math } from "@openzeppelin/contracts/utils/math/Math.sol";
import { ReentrancyGuardUpgradeable } 
    from "@openzeppelin/contracts-upgradeable/security/ReentrancyGuardUpgradeable.sol";
import { SafeCall } from "@eth-optimism-bedrock/contracts/libraries/SafeCall.sol";
/**
 * @title BalanceTracker
 * @dev Funds system addresses and sends the remaining profits to the profit wallet.
 */
contract BalanceTracker is ReentrancyGuardUpgradeable {
    using Address for address;
    /*//////////////////////////////////////////////////////////////
                            Constants
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev The maximum number of system addresses that can be funded.
     */
    uint256 public constant MAX_SYSTEM_ADDRESS_COUNT = 20;
    
    /*//////////////////////////////////////////////////////////////
                            Immutables
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev The address of the wallet receiving profits.
     */
    address payable public immutable PROFIT_WALLET;
    
    /*//////////////////////////////////////////////////////////////
                            VARIABLES
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev The system addresses being funded.
     */
    address payable[] public systemAddresses;
    /**
     * @dev The target balances for system addresses.
     */
    uint256[] public targetBalances;
    /*//////////////////////////////////////////////////////////////
                            Events
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev Emitted when the BalanceTracker sends funds to a system address.
     * @param _systemAddress The system address being funded.
     * @param _success A boolean denoting whether a fund send occurred and its success or failure.
     * @param _balanceNeeded The amount of funds the given system address needs to reach its target balance.
     * @param _balanceSent The amount of funds sent to the system address.
     */
    event ProcessedFunds(
        address indexed _systemAddress,
        bool indexed _success,
        uint256 _balanceNeeded,
        uint256 _balanceSent
    );
    /**
     * @dev Emitted when the BalanceTracker attempts to send funds to the profit wallet.
     * @param _profitWallet The address of the profit wallet.
     * @param _success A boolean denoting the success or failure of fund send.
     * @param _balanceSent The amount of funds sent to the profit wallet.
     */
    event SentProfit(
        address indexed _profitWallet,
        bool indexed _success,
        uint256 _balanceSent
    );
    /**
     * @dev Emitted when funds are received.
     * @param _sender The address sending funds.
     * @param _amount The amount of funds received from the sender.
     */
    event ReceivedFunds(
        address indexed _sender,
        uint256 _amount
    );
    
    /*//////////////////////////////////////////////////////////////
                            Constructor
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev Constructor for the BalanceTracker contract that sets an immutable variable.
     * @param _profitWallet The address to send remaining ETH profits to.
     */
    constructor(
        address payable _profitWallet
    ) {
        require(_profitWallet != address(0), "BalanceTracker: PROFIT_WALLET cannot be address(0)");
        
        PROFIT_WALLET = _profitWallet;
        _disableInitializers();
    }
    /*//////////////////////////////////////////////////////////////
                            External Functions
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev Initializes the BalanceTracker contract.
     * @param _systemAddresses The system addresses being funded.
     * @param _targetBalances The target balances for system addresses.
     */
    function initialize(
        address payable[] memory _systemAddresses,
        uint256[] memory _targetBalances
    ) external initializer {
        uint256 systemAddresesLength = _systemAddresses.length;
        require(systemAddresesLength > 0, 
            "BalanceTracker: systemAddresses cannot have a length of zero");
        require(systemAddresesLength <= MAX_SYSTEM_ADDRESS_COUNT, 
            "BalanceTracker: systemAddresses cannot have a length greater than 20");
        require(systemAddresesLength == _targetBalances.length, 
            "BalanceTracker: systemAddresses and targetBalances length must be equal");
        for (uint256 i; i < systemAddresesLength;) {
            require(_systemAddresses[i] != address(0), "BalanceTracker: systemAddresses cannot contain address(0)");
            require(_targetBalances[i] > 0, "BalanceTracker: targetBalances cannot contain 0 target");
            unchecked { i++; }
        }
        systemAddresses = _systemAddresses;
        targetBalances = _targetBalances;
        __ReentrancyGuard_init();
    }
    /**
     * @dev Funds system addresses and sends remaining profits to the profit wallet.
     * 
     */
    function processFees() external nonReentrant {
        uint256 systemAddresesLength = systemAddresses.length;
        require(systemAddresesLength > 0, 
            "BalanceTracker: systemAddresses cannot have a length of zero");
        // Refills balances of systems addresses up to their target balances
        for (uint256 i; i < systemAddresesLength;) {
            refillBalanceIfNeeded(systemAddresses[i], targetBalances[i]);
            unchecked { i++; }
        }
        // Send remaining profits to profit wallet
        uint256 valueToSend = address(this).balance;
        bool success = SafeCall.send(PROFIT_WALLET, gasleft(), valueToSend);
        emit SentProfit(PROFIT_WALLET, success, valueToSend);
    }
    /**
     * @dev Fallback function to receive funds from L2 fee withdrawals and additional top up funds if
     *      L2 fees are insufficient to fund L1 system addresses.
     */
    receive() external payable {
        emit ReceivedFunds(msg.sender, msg.value);
    }
    /*//////////////////////////////////////////////////////////////
                            Internal Functions
    //////////////////////////////////////////////////////////////*/
    /**
     * @dev Checks the balance of the target address and refills it back up to the target balance if needed.
     * @param _systemAddress The system address being funded.
     * @param _targetBalance The target balance for the system address being funded.
     */
    function refillBalanceIfNeeded(address _systemAddress, uint256 _targetBalance) internal {
         uint256 systemAddressBalance = _systemAddress.balance;
        if (systemAddressBalance >= _targetBalance) {
            emit ProcessedFunds(_systemAddress, false, 0, 0);
            return;
        }
        
        uint256 valueNeeded = _targetBalance - systemAddressBalance;
        uint256 balanceTrackerBalance = address(this).balance;
        uint256 valueToSend = valueNeeded > balanceTrackerBalance ? balanceTrackerBalance : valueNeeded;
        bool success = SafeCall.send(_systemAddress, gasleft(), valueToSend);
        emit ProcessedFunds(_systemAddress, success, valueNeeded, valueToSend);
    }
}
// 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 v4.7.0) (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
// OpenZeppelin Contracts v4.4.1 (security/ReentrancyGuard.sol)
pragma solidity ^0.8.0;
import "../proxy/utils/Initializable.sol";
/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuardUpgradeable is Initializable {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.
    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;
    uint256 private _status;
    function __ReentrancyGuard_init() internal onlyInitializing {
        __ReentrancyGuard_init_unchained();
    }
    function __ReentrancyGuard_init_unchained() internal onlyInitializing {
        _status = _NOT_ENTERED;
    }
    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");
        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
        _;
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }
    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
// SPDX-License-Identifier: MIT
pragma solidity 0.8.15;
/**
 * @title SafeCall
 * @notice Perform low level safe calls
 */
library SafeCall {
    /**
     * @notice Performs a low level call without copying any returndata.
     * @dev Passes no calldata to the call context.
     *
     * @param _target   Address to call
     * @param _gas      Amount of gas to pass to the call
     * @param _value    Amount of value to pass to the call
     */
    function send(
        address _target,
        uint256 _gas,
        uint256 _value
    ) internal returns (bool) {
        bool _success;
        assembly {
            _success := call(
                _gas, // gas
                _target, // recipient
                _value, // ether value
                0, // inloc
                0, // inlen
                0, // outloc
                0 // outlen
            )
        }
        return _success;
    }
    /**
     * @notice Perform a low level call without copying any returndata
     *
     * @param _target   Address to call
     * @param _gas      Amount of gas to pass to the call
     * @param _value    Amount of value to pass to the call
     * @param _calldata Calldata to pass to the call
     */
    function call(
        address _target,
        uint256 _gas,
        uint256 _value,
        bytes memory _calldata
    ) internal returns (bool) {
        bool _success;
        assembly {
            _success := call(
                _gas, // gas
                _target, // recipient
                _value, // ether value
                add(_calldata, 32), // inloc
                mload(_calldata), // inlen
                0, // outloc
                0 // outlen
            )
        }
        return _success;
    }
    /**
     * @notice Helper function to determine if there is sufficient gas remaining within the context
     *         to guarantee that the minimum gas requirement for a call will be met as well as
     *         optionally reserving a specified amount of gas for after the call has concluded.
     * @param _minGas      The minimum amount of gas that may be passed to the target context.
     * @param _reservedGas Optional amount of gas to reserve for the caller after the execution
     *                     of the target context.
     * @return `true` if there is enough gas remaining to safely supply `_minGas` to the target
     *         context as well as reserve `_reservedGas` for the caller after the execution of
     *         the target context.
     * @dev !!!!! FOOTGUN ALERT !!!!!
     *      1.) The 40_000 base buffer is to account for the worst case of the dynamic cost of the
     *          `CALL` opcode's `address_access_cost`, `positive_value_cost`, and
     *          `value_to_empty_account_cost` factors with an added buffer of 5,700 gas. It is
     *          still possible to self-rekt by initiating a withdrawal with a minimum gas limit
     *          that does not account for the `memory_expansion_cost` & `code_execution_cost`
     *          factors of the dynamic cost of the `CALL` opcode.
     *      2.) This function should *directly* precede the external call if possible. There is an
     *          added buffer to account for gas consumed between this check and the call, but it
     *          is only 5,700 gas.
     *      3.) Because EIP-150 ensures that a maximum of 63/64ths of the remaining gas in the call
     *          frame may be passed to a subcontext, we need to ensure that the gas will not be
     *          truncated.
     *      4.) Use wisely. This function is not a silver bullet.
     */
    function hasMinGas(uint256 _minGas, uint256 _reservedGas) internal view returns (bool) {
        bool _hasMinGas;
        assembly {
            // Equation: gas × 63 ≥ minGas × 64 + 63(40_000 + reservedGas)
            _hasMinGas := iszero(
                lt(mul(gas(), 63), add(mul(_minGas, 64), mul(add(40000, _reservedGas), 63)))
            )
        }
        return _hasMinGas;
    }
    /**
     * @notice Perform a low level call without copying any returndata. This function
     *         will revert if the call cannot be performed with the specified minimum
     *         gas.
     *
     * @param _target   Address to call
     * @param _minGas   The minimum amount of gas that may be passed to the call
     * @param _value    Amount of value to pass to the call
     * @param _calldata Calldata to pass to the call
     */
    function callWithMinGas(
        address _target,
        uint256 _minGas,
        uint256 _value,
        bytes memory _calldata
    ) internal returns (bool) {
        bool _success;
        bool _hasMinGas = hasMinGas(_minGas, 0);
        assembly {
            // Assertion: gasleft() >= (_minGas * 64) / 63 + 40_000
            if iszero(_hasMinGas) {
                // Store the "Error(string)" selector in scratch space.
                mstore(0, 0x08c379a0)
                // Store the pointer to the string length in scratch space.
                mstore(32, 32)
                // Store the string.
                //
                // SAFETY:
                // - We pad the beginning of the string with two zero bytes as well as the
                // length (24) to ensure that we override the free memory pointer at offset
                // 0x40. This is necessary because the free memory pointer is likely to
                // be greater than 1 byte when this function is called, but it is incredibly
                // unlikely that it will be greater than 3 bytes. As for the data within
                // 0x60, it is ensured that it is 0 due to 0x60 being the zero offset.
                // - It's fine to clobber the free memory pointer, we're reverting.
                mstore(88, 0x0000185361666543616c6c3a204e6f7420656e6f75676820676173)
                // Revert with 'Error("SafeCall: Not enough gas")'
                revert(28, 100)
            }
            // The call will be supplied at least ((_minGas * 64) / 63) gas due to the
            // above assertion. This ensures that, in all circumstances (except for when the
            // `_minGas` does not account for the `memory_expansion_cost` and `code_execution_cost`
            // factors of the dynamic cost of the `CALL` opcode), the call will receive at least
            // the minimum amount of gas specified.
            _success := call(
                gas(), // gas
                _target, // recipient
                _value, // ether value
                add(_calldata, 32), // inloc
                mload(_calldata), // inlen
                0x00, // outloc
                0x00 // outlen
            )
        }
        return _success;
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (proxy/utils/Initializable.sol)
pragma solidity ^0.8.2;
import "../../utils/AddressUpgradeable.sol";
/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;
    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;
    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);
    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts. Equivalent to `reinitializer(1)`.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }
    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * `initializer` is equivalent to `reinitializer(1)`, so a reinitializer may be used after the original
     * initialization step. This is essential to configure modules that are added through upgrades and that require
     * initialization.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }
    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }
    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized < type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }
}
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (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);
            }
        }
    }
}