// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

import "@openzeppelin/contracts/proxy/Clones.sol";
import "@openzeppelin/contracts/proxy/utils/Initializable.sol";
import "@openzeppelin/contracts/security/Pausable.sol";
import "@openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol";
import "@openzeppelin/contracts/utils/math/Math.sol";

import "contracts/interfaces/IPair.sol";
import "contracts/interfaces/IPairCallee.sol";
import "contracts/interfaces/IPairFactory.sol";
import "contracts/PairFees.sol";

// The base pair of pools, either stable or volatile
contract Pair is IPair, Initializable {
    string public name;
    string public symbol;
    uint8 public constant decimals = 18;

    bool public stable;

    uint256 public totalSupply;

    mapping(address => mapping(address => uint256)) public allowance;
    mapping(address => uint256) public balanceOf;

    bytes32 internal DOMAIN_SEPARATOR;
    // keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    bytes32 internal constant PERMIT_TYPEHASH = 0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;
    mapping(address => uint256) public nonces;

    uint256 internal constant MINIMUM_LIQUIDITY = 10 ** 3;

    address public token0;
    address public token1;
    address public fees;
    address factory;

    // Structure to capture time period obervations every 30 minutes, used for local oracles
    struct Observation {
        uint256 timestamp;
        uint256 reserve0Cumulative;
        uint256 reserve1Cumulative;
    }

    // Capture oracle reading every 30 minutes
    uint256 constant periodSize = 1800;

    Observation[] public observations;

    uint256 internal decimals0;
    uint256 internal decimals1;

    uint256 public reserve0;
    uint256 public reserve1;
    uint256 public blockTimestampLast;

    uint256 public reserve0CumulativeLast;
    uint256 public reserve1CumulativeLast;

    // index0 and index1 are used to accumulate fees, this is split out from normal trades to keep the swap "clean"
    // this further allows LP holders to easily claim fees for tokens they have/staked
    uint256 public index0;
    uint256 public index1;

    // position assigned to each LP to track their current index0 & index1 vs the global position
    mapping(address => uint256) public supplyIndex0;
    mapping(address => uint256) public supplyIndex1;

    // tracks the amount of unclaimed, but claimable tokens off of fees for token0 and token1
    mapping(address => uint256) public claimable0;
    mapping(address => uint256) public claimable1;

    event Fees(address indexed sender, uint256 amount0, uint256 amount1);
    event Mint(address indexed sender, uint256 amount0, uint256 amount1);
    event Burn(address indexed sender, uint256 amount0, uint256 amount1, address indexed to);
    event Swap(address indexed sender, uint256 amount0In, uint256 amount1In, uint256 amount0Out, uint256 amount1Out, address indexed to);
    event Sync(uint256 reserve0, uint256 reserve1);
    event Claim(address indexed sender, address indexed recipient, uint256 amount0, uint256 amount1);

    event Transfer(address indexed from, address indexed to, uint256 amount);
    event Approval(address indexed owner, address indexed spender, uint256 amount);

    function initialize(address _token0, address _token1, bool _stable) external initializer {
        factory = msg.sender;
        (token0, token1, stable) = (_token0, _token1, _stable);
        fees = address(new PairFees(_token0, _token1));
        if (_stable) {
            name = string(abi.encodePacked("StableV1 AMM - ", IERC20Metadata(_token0).symbol(), "/", IERC20Metadata(_token1).symbol()));
            symbol = string(abi.encodePacked("sAMM-", IERC20Metadata(_token0).symbol(), "/", IERC20Metadata(_token1).symbol()));
        } else {
            name = string(abi.encodePacked("VolatileV1 AMM - ", IERC20Metadata(_token0).symbol(), "/", IERC20Metadata(_token1).symbol()));
            symbol = string(abi.encodePacked("vAMM-", IERC20Metadata(_token0).symbol(), "/", IERC20Metadata(_token1).symbol()));
        }

        decimals0 = 10 ** IERC20Metadata(_token0).decimals();
        decimals1 = 10 ** IERC20Metadata(_token1).decimals();

        observations.push(Observation(block.timestamp, 0, 0));

        _unlocked = 1;
    }

    // simple re-entrancy check
    uint256 internal _unlocked;
    modifier lock() {
        require(_unlocked == 1);
        _unlocked = 2;
        _;
        _unlocked = 1;
    }

    function observationLength() external view returns (uint256) {
        return observations.length;
    }

    function lastObservation() public view returns (Observation memory) {
        return observations[observations.length - 1];
    }

    function metadata() external view returns (uint256 dec0, uint256 dec1, uint256 r0, uint256 r1, bool st, address t0, address t1) {
        return (decimals0, decimals1, reserve0, reserve1, stable, token0, token1);
    }

    function tokens() external view returns (address, address) {
        return (token0, token1);
    }

    // claim accumulated but unclaimed fees (viewable via claimable0 and claimable1)
    function claimFees() external returns (uint256 claimed0, uint256 claimed1) {
        _updateFor(msg.sender);

        claimed0 = claimable0[msg.sender];
        claimed1 = claimable1[msg.sender];

        if (claimed0 != 0 || claimed1 != 0) {
            claimable0[msg.sender] = 0;
            claimable1[msg.sender] = 0;

            PairFees(fees).claimFeesFor(msg.sender, claimed0, claimed1);

            emit Claim(msg.sender, msg.sender, claimed0, claimed1);
        }
    }

    // Accrue fees on token0 and token1
    function _updateFees(uint256 amount0, uint256 amount1) internal {
        if (amount0 != 0) {
            _safeTransfer(token0, fees, amount0); // transfer the fees out to PairFees
            uint256 _ratio = (amount0 * 1e18) / totalSupply; // 1e18 adjustment is removed during claim
            if (_ratio != 0) {
                index0 += _ratio;
            }
        }
        if (amount1 != 0) {
            _safeTransfer(token1, fees, amount1); // transfer the fees out to PairFees
            uint256 _ratio = (amount1 * 1e18) / totalSupply; // 1e18 adjustment is removed during claim
            if (_ratio != 0) {
                index1 += _ratio;
            }
        }
        if (amount0 != 0 || amount1 != 0) {
            PairFees(fees).notifyFeeAmounts(amount0, amount1);
            emit Fees(msg.sender, amount0, amount1);
        }
    }

    // this function MUST be called on any balance changes, otherwise can be used to infinitely claim fees
    // Fees are segregated from core funds, so fees can never put liquidity at risk
    function _updateFor(address recipient) internal {
        uint256 _supplied = balanceOf[recipient]; // get LP balance of `recipient`
        if (_supplied != 0) {
            uint256 _supplyIndex0 = supplyIndex0[recipient]; // get last adjusted index0 for recipient
            uint256 _supplyIndex1 = supplyIndex1[recipient];
            uint256 _index0 = index0; // get global index0 for accumulated fees
            uint256 _index1 = index1;
            supplyIndex0[recipient] = _index0; // update user current position to global position
            supplyIndex1[recipient] = _index1;
            uint256 _delta0 = _index0 - _supplyIndex0; // see if there is any difference that need to be accrued
            uint256 _delta1 = _index1 - _supplyIndex1;
            if (_delta0 != 0) {
                uint256 _share = (_supplied * _delta0) / 1e18; // add accrued difference for each supplied token
                claimable0[recipient] += _share;
            }
            if (_delta1 != 0) {
                uint256 _share = (_supplied * _delta1) / 1e18;
                claimable1[recipient] += _share;
            }
        } else {
            supplyIndex0[recipient] = index0; // new users are set to the default global state
            supplyIndex1[recipient] = index1;
        }
    }

    function getReserves() public view returns (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast) {
        _reserve0 = reserve0;
        _reserve1 = reserve1;
        _blockTimestampLast = blockTimestampLast;
    }

    // update reserves and, on the first call per block, price accumulators
    function _update(uint256 balance0, uint256 balance1, uint256 _reserve0, uint256 _reserve1) internal {
        uint256 blockTimestamp = block.timestamp;
        uint256 timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired
        if (timeElapsed != 0 && _reserve0 != 0 && _reserve1 != 0) {
            reserve0CumulativeLast += _reserve0 * timeElapsed;
            reserve1CumulativeLast += _reserve1 * timeElapsed;
        }

        Observation memory _point = lastObservation();
        timeElapsed = blockTimestamp - _point.timestamp; // compare the last observation with current timestamp, if greater than 30 minutes, record a new event
        if (timeElapsed > periodSize) {
            observations.push(Observation(blockTimestamp, reserve0CumulativeLast, reserve1CumulativeLast));
        }
        reserve0 = balance0;
        reserve1 = balance1;
        blockTimestampLast = blockTimestamp;
        emit Sync(reserve0, reserve1);
    }

    // produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    function currentCumulativePrices()
        public
        view
        returns (uint256 reserve0Cumulative, uint256 reserve1Cumulative, uint256 blockTimestamp)
    {
        blockTimestamp = block.timestamp;
        reserve0Cumulative = reserve0CumulativeLast;
        reserve1Cumulative = reserve1CumulativeLast;

        // if time has elapsed since the last update on the pair, mock the accumulated price values
        (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast) = getReserves();
        if (_blockTimestampLast != blockTimestamp) {
            // subtraction overflow is desired
            uint256 timeElapsed = blockTimestamp - _blockTimestampLast;
            reserve0Cumulative += _reserve0 * timeElapsed;
            reserve1Cumulative += _reserve1 * timeElapsed;
        }
    }

    // gives the current twap price measured from amountIn * tokenIn gives amountOut
    function current(address tokenIn, uint256 amountIn) external view returns (uint256 amountOut) {
        Observation memory _observation = lastObservation();
        (uint256 reserve0Cumulative, uint256 reserve1Cumulative, ) = currentCumulativePrices();
        if (block.timestamp == _observation.timestamp) {
            _observation = observations[observations.length - 2];
        }

        uint256 timeElapsed = block.timestamp - _observation.timestamp;
        uint256 _reserve0 = (reserve0Cumulative - _observation.reserve0Cumulative) / timeElapsed;
        uint256 _reserve1 = (reserve1Cumulative - _observation.reserve1Cumulative) / timeElapsed;
        amountOut = _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
    }

    // as per `current`, however allows user configured granularity, up to the full window size
    function quote(address tokenIn, uint256 amountIn, uint256 granularity) external view returns (uint256 amountOut) {
        uint256[] memory _prices = sample(tokenIn, amountIn, granularity, 1);
        uint256 priceAverageCumulative;
        for (uint256 i = _prices.length; i != 0; ) {
            unchecked {
                --i;
            }
            priceAverageCumulative += _prices[i];
        }
        return priceAverageCumulative / granularity;
    }

    // returns a memory set of twap prices
    function prices(address tokenIn, uint256 amountIn, uint256 points) external view returns (uint256[] memory) {
        return sample(tokenIn, amountIn, points, 1);
    }

    function sample(address tokenIn, uint256 amountIn, uint256 points, uint256 window) public view returns (uint256[] memory) {
        uint256[] memory _prices = new uint256[](points);

        uint256 length = observations.length - 1;
        uint256 nextIndex;
        uint256 index = 0;

        for (uint256 i = length - (points * window); i < length; ) {
            unchecked {
                nextIndex = i + window;
            }
            uint256 timeElapsed = observations[nextIndex].timestamp - observations[i].timestamp;
            uint256 _reserve0 = (observations[nextIndex].reserve0Cumulative - observations[i].reserve0Cumulative) / timeElapsed;
            uint256 _reserve1 = (observations[nextIndex].reserve1Cumulative - observations[i].reserve1Cumulative) / timeElapsed;
            _prices[index] = _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
            // index < length; length cannot overflow
            unchecked {
                ++index;
            }
            i = nextIndex;
        }
        return _prices;
    }

    // this low-level function should be called by addLiquidity functions in Router.sol, which performs important safety checks
    // standard uniswap v2 implementation
    function mint(address to) external lock returns (uint256 liquidity) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        uint256 _balance0 = IERC20(token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(token1).balanceOf(address(this));
        uint256 _amount0 = _balance0 - _reserve0;
        uint256 _amount1 = _balance1 - _reserve1;

        uint256 _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
        if (_totalSupply == 0) {
            liquidity = Math.sqrt(_amount0 * _amount1) - MINIMUM_LIQUIDITY;
            _mint(address(0), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens
        } else {
            liquidity = Math.min((_amount0 * _totalSupply) / _reserve0, (_amount1 * _totalSupply) / _reserve1);
        }
        require(liquidity != 0, "ILM"); // Pair: INSUFFICIENT_LIQUIDITY_MINTED
        _mint(to, liquidity);

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Mint(msg.sender, _amount0, _amount1);
    }

    // this low-level function should be called from a contract which performs important safety checks
    // standard uniswap v2 implementation
    function burn(address to) external lock returns (uint256 amount0, uint256 amount1) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        (address _token0, address _token1) = (token0, token1);
        uint256 _balance0 = IERC20(_token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(_token1).balanceOf(address(this));
        uint256 _liquidity = balanceOf[address(this)];

        uint256 _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
        amount0 = (_liquidity * _balance0) / _totalSupply; // using balances ensures pro-rata distribution
        amount1 = (_liquidity * _balance1) / _totalSupply; // using balances ensures pro-rata distribution
        require(amount0 != 0 && amount1 != 0, "ILB"); // Pair: INSUFFICIENT_LIQUIDITY_BURNED
        _burn(address(this), _liquidity);
        _safeTransfer(_token0, to, amount0);
        _safeTransfer(_token1, to, amount1);
        _balance0 = IERC20(_token0).balanceOf(address(this));
        _balance1 = IERC20(_token1).balanceOf(address(this));

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Burn(msg.sender, amount0, amount1, to);
    }

    // this low-level function should be called from a contract which performs important safety checks
    function swap(uint256 amount0Out, uint256 amount1Out, address to, bytes calldata data) external lock {
        require(!Pausable(factory).paused());
        require(amount0Out != 0 || amount1Out != 0, "IOA"); // Pair: INSUFFICIENT_OUTPUT_AMOUNT
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        require(amount0Out < _reserve0 && amount1Out < _reserve1, "IL"); // Pair: INSUFFICIENT_LIQUIDITY

        uint256 _balance0;
        uint256 _balance1;
        {
            // scope for _token{0,1}, avoids stack too deep errors
            (address _token0, address _token1) = (token0, token1);
            require(to != _token0 && to != _token1, "IT"); // Pair: INVALID_TO
            if (amount0Out != 0) _safeTransfer(_token0, to, amount0Out); // optimistically transfer tokens
            if (amount1Out != 0) _safeTransfer(_token1, to, amount1Out); // optimistically transfer tokens
            if (data.length != 0) IPairCallee(to).hook(msg.sender, amount0Out, amount1Out, data); // callback, used for flash loans
            _balance0 = IERC20(_token0).balanceOf(address(this));
            _balance1 = IERC20(_token1).balanceOf(address(this));
        }
        uint256 amount0In = _balance0 > _reserve0 - amount0Out ? _balance0 - (_reserve0 - amount0Out) : 0;
        uint256 amount1In = _balance1 > _reserve1 - amount1Out ? _balance1 - (_reserve1 - amount1Out) : 0;
        require(amount0In != 0 || amount1In != 0, "IIA"); // Pair: INSUFFICIENT_INPUT_AMOUNT
        {
            // scope for reserve{0,1}Adjusted, avoids stack too deep errors
            (address _token0, address _token1) = (token0, token1);
            _updateFees(
                IPairFactory(factory).getFeeAmount(stable, amount0In, msg.sender),
                IPairFactory(factory).getFeeAmount(stable, amount1In, msg.sender)
            ); // accrue fees for token0 and token1 and move them out of pool
            _balance0 = IERC20(_token0).balanceOf(address(this)); // since we removed tokens, we need to reconfirm balances, can also simply use previous balance - amountIn/ 10000, but doing balanceOf again as safety check
            _balance1 = IERC20(_token1).balanceOf(address(this));
            // The curve, either x3y+y3x for stable pools, or x*y for volatile pools
            require(_k(_balance0, _balance1) >= _k(_reserve0, _reserve1), "K"); // Pair: K
        }

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Swap(msg.sender, amount0In, amount1In, amount0Out, amount1Out, to);
    }

    // force balances to match reserves
    function skim(address to) external lock {
        (address _token0, address _token1) = (token0, token1);
        _safeTransfer(_token0, to, IERC20(_token0).balanceOf(address(this)) - (reserve0));
        _safeTransfer(_token1, to, IERC20(_token1).balanceOf(address(this)) - (reserve1));
    }

    // force reserves to match balances
    function sync() external lock {
        _update(IERC20(token0).balanceOf(address(this)), IERC20(token1).balanceOf(address(this)), reserve0, reserve1);
    }

    function _f(uint256 x0, uint256 y) internal pure returns (uint256) {
        return (x0 * ((((y * y) / 1e18) * y) / 1e18)) / 1e18 + (((((x0 * x0) / 1e18) * x0) / 1e18) * y) / 1e18;
    }

    function _d(uint256 x0, uint256 y) internal pure returns (uint256) {
        return (3 * x0 * ((y * y) / 1e18)) / 1e18 + ((((x0 * x0) / 1e18) * x0) / 1e18);
    }

    function _get_y(uint256 x0, uint256 xy, uint256 y) internal pure returns (uint256) {
        for (uint256 i = 255; i != 0; ) {
            uint256 y_prev = y;
            uint256 k = _f(x0, y);
            if (k < xy) {
                uint256 dy = ((xy - k) * 1e18) / _d(x0, y);
                y = y + dy;
            } else {
                uint256 dy = ((k - xy) * 1e18) / _d(x0, y);
                y = y - dy;
            }
            if (y > y_prev) {
                if (y - y_prev <= 1) {
                    return y;
                }
            } else {
                if (y_prev - y <= 1) {
                    return y;
                }
            }
            unchecked {
                --i;
            }
        }
        return y;
    }

    function getAmountOut(uint256 amountIn, address tokenIn) external view returns (uint256) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        amountIn -= IPairFactory(factory).getFeeAmount(stable, amountIn, msg.sender); // remove fee from amount received
        return _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
    }

    function _getAmountOut(uint256 amountIn, address tokenIn, uint256 _reserve0, uint256 _reserve1) internal view returns (uint256) {
        if (stable) {
            uint256 xy = _k(_reserve0, _reserve1);
            _reserve0 = (_reserve0 * 1e18) / decimals0;
            _reserve1 = (_reserve1 * 1e18) / decimals1;
            (uint256 reserveA, uint256 reserveB) = tokenIn == token0 ? (_reserve0, _reserve1) : (_reserve1, _reserve0);
            amountIn = tokenIn == token0 ? (amountIn * 1e18) / decimals0 : (amountIn * 1e18) / decimals1;
            uint256 y = reserveB - _get_y(amountIn + reserveA, xy, reserveB);
            return (y * (tokenIn == token0 ? decimals1 : decimals0)) / 1e18;
        } else {
            (uint256 reserveA, uint256 reserveB) = tokenIn == token0 ? (_reserve0, _reserve1) : (_reserve1, _reserve0);
            return (amountIn * reserveB) / (reserveA + amountIn);
        }
    }

    function _k(uint256 x, uint256 y) internal view returns (uint256) {
        if (stable) {
            uint256 _x = (x * 1e18) / decimals0;
            uint256 _y = (y * 1e18) / decimals1;
            uint256 _a = (_x * _y) / 1e18;
            uint256 _b = ((_x * _x) / 1e18 + (_y * _y) / 1e18);
            return (_a * _b) / 1e18; // x3y+y3x >= k
        } else {
            return x * y; // xy >= k
        }
    }

    function _mint(address dst, uint256 amount) internal {
        _updateFor(dst); // balances must be updated on mint/burn/transfer
        totalSupply += amount;
        balanceOf[dst] += amount;
        emit Transfer(address(0), dst, amount);
    }

    function _burn(address dst, uint256 amount) internal {
        _updateFor(dst);
        totalSupply -= amount;
        balanceOf[dst] -= amount;
        emit Transfer(dst, address(0), amount);
    }

    function approve(address spender, uint256 amount) external returns (bool) {
        allowance[msg.sender][spender] = amount;
        emit Approval(msg.sender, spender, amount);
        return true;
    }

    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external {
        require(deadline >= block.timestamp, "Pair: EXPIRED");
        DOMAIN_SEPARATOR = keccak256(
            abi.encode(
                keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"),
                keccak256(bytes(name)),
                keccak256(bytes("1")),
                block.chainid,
                address(this)
            )
        );
        bytes32 digest = keccak256(
            abi.encodePacked(
                "\x19\x01",
                DOMAIN_SEPARATOR,
                keccak256(abi.encode(PERMIT_TYPEHASH, owner, spender, value, nonces[owner]++, deadline))
            )
        );
        address recoveredAddress = ecrecover(digest, v, r, s);
        require(recoveredAddress != address(0) && recoveredAddress == owner, "Pair: INVALID_SIGNATURE");
        allowance[owner][spender] = value;

        emit Approval(owner, spender, value);
    }

    function transfer(address dst, uint256 amount) external returns (bool) {
        _transferTokens(msg.sender, dst, amount);
        return true;
    }

    function transferFrom(address src, address dst, uint256 amount) external returns (bool) {
        address spender = msg.sender;
        uint256 spenderAllowance = allowance[src][spender];

        if (spender != src && spenderAllowance != type(uint256).max) {
            uint256 newAllowance = spenderAllowance - amount;
            allowance[src][spender] = newAllowance;

            emit Approval(src, spender, newAllowance);
        }

        _transferTokens(src, dst, amount);
        return true;
    }

    function _transferTokens(address src, address dst, uint256 amount) internal {
        _updateFor(src); // update fee position for src
        _updateFor(dst); // update fee position for dst

        balanceOf[src] -= amount;
        balanceOf[dst] += amount;

        emit Transfer(src, dst, amount);
    }

    function _safeTransfer(address token, address to, uint256 value) internal {
        if (value != 0) {
            require(token.code.length > 0);
            (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.transfer.selector, to, value));
            require(success && (data.length == 0 || abi.decode(data, (bool))));
        }
    }
}

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

pragma solidity ^0.8.0;

/**
 * @dev https://eips.ethereum.org/EIPS/eip-1167[EIP 1167] is a standard for
 * deploying minimal proxy contracts, also known as "clones".
 *
 * > To simply and cheaply clone contract functionality in an immutable way, this standard specifies
 * > a minimal bytecode implementation that delegates all calls to a known, fixed address.
 *
 * The library includes functions to deploy a proxy using either `create` (traditional deployment) or `create2`
 * (salted deterministic deployment). It also includes functions to predict the addresses of clones deployed using the
 * deterministic method.
 *
 * _Available since v3.4._
 */
library Clones {
    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create opcode, which should never revert.
     */
    function clone(address implementation) internal returns (address instance) {
        /// @solidity memory-safe-assembly
        assembly {
            // Cleans the upper 96 bits of the `implementation` word, then packs the first 3 bytes
            // of the `implementation` address with the bytecode before the address.
            mstore(0x00, or(shr(0xe8, shl(0x60, implementation)), 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000))
            // Packs the remaining 17 bytes of `implementation` with the bytecode after the address.
            mstore(0x20, or(shl(0x78, implementation), 0x5af43d82803e903d91602b57fd5bf3))
            instance := create(0, 0x09, 0x37)
        }
        require(instance != address(0), "ERC1167: create failed");
    }

    /**
     * @dev Deploys and returns the address of a clone that mimics the behaviour of `implementation`.
     *
     * This function uses the create2 opcode and a `salt` to deterministically deploy
     * the clone. Using the same `implementation` and `salt` multiple time will revert, since
     * the clones cannot be deployed twice at the same address.
     */
    function cloneDeterministic(address implementation, bytes32 salt) internal returns (address instance) {
        /// @solidity memory-safe-assembly
        assembly {
            // Cleans the upper 96 bits of the `implementation` word, then packs the first 3 bytes
            // of the `implementation` address with the bytecode before the address.
            mstore(0x00, or(shr(0xe8, shl(0x60, implementation)), 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000))
            // Packs the remaining 17 bytes of `implementation` with the bytecode after the address.
            mstore(0x20, or(shl(0x78, implementation), 0x5af43d82803e903d91602b57fd5bf3))
            instance := create2(0, 0x09, 0x37, salt)
        }
        require(instance != address(0), "ERC1167: create2 failed");
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt,
        address deployer
    ) internal pure returns (address predicted) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(add(ptr, 0x38), deployer)
            mstore(add(ptr, 0x24), 0x5af43d82803e903d91602b57fd5bf3ff)
            mstore(add(ptr, 0x14), implementation)
            mstore(ptr, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73)
            mstore(add(ptr, 0x58), salt)
            mstore(add(ptr, 0x78), keccak256(add(ptr, 0x0c), 0x37))
            predicted := keccak256(add(ptr, 0x43), 0x55)
        }
    }

    /**
     * @dev Computes the address of a clone deployed using {Clones-cloneDeterministic}.
     */
    function predictDeterministicAddress(
        address implementation,
        bytes32 salt
    ) internal view returns (address predicted) {
        return predictDeterministicAddress(implementation, salt, address(this));
    }
}

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (security/Pausable.sol)

pragma solidity ^0.8.0;

import "../utils/Context.sol";

/**
 * @dev Contract module which allows children to implement an emergency stop
 * mechanism that can be triggered by an authorized account.
 *
 * This module is used through inheritance. It will make available the
 * modifiers `whenNotPaused` and `whenPaused`, which can be applied to
 * the functions of your contract. Note that they will not be pausable by
 * simply including this module, only once the modifiers are put in place.
 */
abstract contract Pausable is Context {
    /**
     * @dev Emitted when the pause is triggered by `account`.
     */
    event Paused(address account);

    /**
     * @dev Emitted when the pause is lifted by `account`.
     */
    event Unpaused(address account);

    bool private _paused;

    /**
     * @dev Initializes the contract in unpaused state.
     */
    constructor() {
        _paused = false;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    modifier whenNotPaused() {
        _requireNotPaused();
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    modifier whenPaused() {
        _requirePaused();
        _;
    }

    /**
     * @dev Returns true if the contract is paused, and false otherwise.
     */
    function paused() public view virtual returns (bool) {
        return _paused;
    }

    /**
     * @dev Throws if the contract is paused.
     */
    function _requireNotPaused() internal view virtual {
        require(!paused(), "Pausable: paused");
    }

    /**
     * @dev Throws if the contract is not paused.
     */
    function _requirePaused() internal view virtual {
        require(paused(), "Pausable: not paused");
    }

    /**
     * @dev Triggers stopped state.
     *
     * Requirements:
     *
     * - The contract must not be paused.
     */
    function _pause() internal virtual whenNotPaused {
        _paused = true;
        emit Paused(_msgSender());
    }

    /**
     * @dev Returns to normal state.
     *
     * Requirements:
     *
     * - The contract must be paused.
     */
    function _unpause() internal virtual whenPaused {
        _paused = false;
        emit Unpaused(_msgSender());
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

/**
 * @dev Interface for the optional metadata functions from the ERC20 standard.
 *
 * _Available since v4.1._
 */
interface IERC20Metadata is IERC20 {
    /**
     * @dev Returns the name of the token.
     */
    function name() external view returns (string memory);

    /**
     * @dev Returns the symbol of the token.
     */
    function symbol() external view returns (string memory);

    /**
     * @dev Returns the decimals places of the token.
     */
    function decimals() external view returns (uint8);
}

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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

pragma solidity ^0.8.1;

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

        return account.code.length > 0;
    }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

pragma solidity ^0.8.0;

/**
 * @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 Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

interface IPair {
    function initialize(address _token0, address _token1, bool _stable) external;

    function metadata() external view returns (uint256 dec0, uint256 dec1, uint256 r0, uint256 r1, bool st, address t0, address t1);

    function claimFees() external returns (uint256, uint256);

    function tokens() external view returns (address, address);

    function token0() external view returns (address);

    function token1() external view returns (address);

    function transferFrom(address src, address dst, uint256 amount) external returns (bool);

    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;

    function swap(uint256 amount0Out, uint256 amount1Out, address to, bytes calldata data) external;

    function burn(address to) external returns (uint256 amount0, uint256 amount1);

    function mint(address to) external returns (uint256 liquidity);

    function getReserves() external view returns (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast);

    function getAmountOut(uint256, address) external view returns (uint256);

    function name() external view returns (string memory);

    function symbol() external view returns (string memory);

    function totalSupply() external view returns (uint256);

    function decimals() external view returns (uint8);

    function claimable0(address _user) external view returns (uint256);

    function claimable1(address _user) external view returns (uint256);

    function stable() external view returns (bool);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

interface IPairCallee {
    function hook(address sender, uint256 amount0, uint256 amount1, bytes calldata data) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

interface IPairFactory {
    function allPairsLength() external view returns (uint256);

    function isPair(address pair) external view returns (bool);

    function allPairs(uint256 index) external view returns (address);

    function getPair(address tokenA, address token, bool stable) external view returns (address);

    function createPair(address tokenA, address tokenB, bool stable) external returns (address pair);

    function getFeeAmount(bool _stable, uint256 _amount, address _account) external view returns (uint256);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;

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

// Pair Fees contract is used as a 1:1 pair relationship to split out fees, this ensures that the curve does not need to be modified for LP shares
contract PairFees {
    address internal immutable pair; // The pair it is bonded to
    address internal immutable token0; // token0 of pair, saved localy and statically for gas optimization
    address internal immutable token1; // Token1 of pair, saved localy and statically for gas optimization

    uint256 private _reserve0;
    uint256 private _reserve1;

    constructor(address _token0, address _token1) {
        pair = msg.sender;
        token0 = _token0;
        token1 = _token1;
    }

    function _safeTransfer(address token, address to, uint256 value) internal {
        if (value != 0) {
            require(token.code.length != 0);
            (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.transfer.selector, to, value));
            require(success && (data.length == 0 || abi.decode(data, (bool))));
        }
    }

    // Allow the pair to transfer fees to users
    function claimFeesFor(address recipient, uint256 amount0, uint256 amount1) external {
        require(msg.sender == pair);
        if (amount0 != 0) {
            uint256 reserve0 = _reserve0;
            if (reserve0 >= amount0) {
                unchecked {
                    _reserve0 = reserve0 - amount0;
                    _safeTransfer(token0, recipient, amount0);
                }
            }
        }
        if (amount1 != 0) {
            uint256 reserve1 = _reserve1;
            if (reserve1 >= amount1) {
                unchecked {
                    _reserve1 = reserve1 - amount1;
                    _safeTransfer(token1, recipient, amount1);
                }
            }
        }
    }

    function skim() external returns (uint256 amount0, uint256 amount1) {
        uint256 balance0 = IERC20(token0).balanceOf(address(this));
        uint256 balance1 = IERC20(token1).balanceOf(address(this));
        uint256 reserve0 = _reserve0;
        uint256 reserve1 = _reserve1;
        if (balance0 > reserve0) {
            unchecked {
                _safeTransfer(token0, msg.sender, amount0 = balance0 - reserve0);
                _reserve0 = balance0;
            }
        }
        if (balance1 > reserve1) {
            unchecked {
                _safeTransfer(token1, msg.sender, amount1 = balance1 - reserve1);
                _reserve1 = balance1;
            }
        }
    }

    function notifyFeeAmounts(uint256 amount0, uint256 amount1) external {
        require(msg.sender == pair);
        if (amount0 != 0) _reserve0 = _reserve0 + amount0;
        if (amount1 != 0) _reserve1 = _reserve1 + amount1;
    }
}

{
  "viaIR": true,
  "optimizer": {
    "enabled": true,
    "runs": 1000
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "libraries": {}
}

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ockTimestamp","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"decimals","outputs":[{"internalType":"uint8","name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"fees","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"amountIn","type":"uint256"},{"internalType":"address","name":"tokenIn","type":"address"}],"name":"getAmountOut","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"getReserves","outputs":[{"internalType":"uint256","name":"_reserve0","type":"uint256"},{"internalType":"uint256","name":"_reserve1","type":"uint256"},{"internalType":"uint256","name":"_blockTimestampLast","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"index0","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"index1","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"_token0","type":"address"},{"internalType":"address","name":"_token1","type":"address"},{"internalType":"bool","name":"_stable","type":"bool"}],"name":"initialize","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"lastObservation","outputs":[{"components":[{"internalType":"uint256","name":"timestamp","type":"uint256"},{"internalType":"uint256","name":"reserve0Cumulative","type":"uint256"},{"internalType":"uint256","name":"reserve1Cumulative","type":"uint256"}],"internalType":"struct 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internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"token1","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"tokens","outputs":[{"internalType":"address","name":"","type":"address"},{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"totalSupply","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"dst","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transfer","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"src","type":"address"},{"internalType":"address","name":"dst","type":"address"},{"internalType":"uint256","name":"amount","type":"uint256"}],"name":"transferFrom","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"}]