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// SPDX-License-Identifier: MIT OR GPL-3.0-or-later
pragma solidity 0.8.13;

import './libraries/Math.sol';
import './interfaces/IERC20.sol';
import './interfaces/IPair.sol';
import './interfaces/IPairGenerator.sol';
import './interfaces/IPairCallee.sol';
import './interfaces/IPairFactory.sol';
import './PairFees.sol';
import {REFERRAL_FEE_DENOMINATOR} from './libraries/Constants.sol';

import {ECDSA} from "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";

// The base pair of pools, either stable or volatile
contract Pair is IPair {

    string public name;
    string public symbol;
    uint8 public constant decimals = 18;

    bool public immutable stable;

    uint public totalSupply = 0;

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

    bytes32 internal constant PERMIT_TYPEHASH = 0x6e71edae12b1b97f4d1f60370fef10105fa2faae0126114a169c64845d6126c9;
    mapping(address => uint) public nonces;

    uint internal constant MINIMUM_LIQUIDITY = 10**3;

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

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

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

    Observation[] public observations;

    uint internal immutable decimals0;
    uint internal immutable decimals1;

    uint public reserve0;
    uint public reserve1;
    uint public blockTimestampLast;

    uint public reserve0CumulativeLast;
    uint 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
    uint public index0 = 0;
    uint public index1 = 0;

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

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

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

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

    constructor() {
        factory = IPairGenerator(msg.sender).factory();
        (address _token0, address _token1, bool _stable) = IPairGenerator(msg.sender).getInitializable();
        (token0, token1, stable) = (_token0, _token1, _stable);
        fees = address(new PairFees(_token0, _token1));
        if (_stable) {
            name = string(abi.encodePacked("StableV1 AMM - ", IERC20(_token0).symbol(), "/", IERC20(_token1).symbol()));
            symbol = string(abi.encodePacked("sAMM-", IERC20(_token0).symbol(), "/", IERC20(_token1).symbol()));
        } else {
            name = string(abi.encodePacked("VolatileV1 AMM - ", IERC20(_token0).symbol(), "/", IERC20(_token1).symbol()));
            symbol = string(abi.encodePacked("vAMM-", IERC20(_token0).symbol(), "/", IERC20(_token1).symbol()));
        }

        decimals0 = 10**IERC20(_token0).decimals();
        decimals1 = 10**IERC20(_token1).decimals();

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

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

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

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

    function metadata() external view returns (uint dec0, uint dec1, uint r0, uint 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);
    }

    function isStable() external view returns(bool) {
        return stable;
    }

    // claim accumulated but unclaimed fees (viewable via claimable0 and claimable1)
    function claimFees() external returns (uint claimed0, uint 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
    function _update0(uint amount) internal {
        // get referral fee
        address _dibs = IPairFactory(factory).dibs();
        uint256 _maxRef = IPairFactory(factory).getReferralFee(address(this));
        uint256 _referralFee = (_dibs != address(0)) ? (amount * _maxRef / REFERRAL_FEE_DENOMINATOR) : 0;
        if (_referralFee > 0) {
            _safeTransfer(token0, _dibs, _referralFee); // Transfer referral fees
            amount -= _referralFee;
        }
        _safeTransfer(token0, fees, amount); // transfer the fees out to PairFees
        uint256 _ratio = amount * 1e18 / totalSupply; // 1e18 adjustment is removed during claim
        if (_ratio > 0) {
            index0 += _ratio;
        }
        emit Fees(msg.sender, amount+_referralFee, 0);
    }

    // Accrue fees on token1
    function _update1(uint amount) internal {
        // get referral fee
        address _dibs = IPairFactory(factory).dibs();
        uint256 _maxRef = IPairFactory(factory).getReferralFee(address(this));
        uint256 _referralFee = (_dibs != address(0)) ? (amount * _maxRef / REFERRAL_FEE_DENOMINATOR) : 0;
         if (_referralFee > 0) {
             _safeTransfer(token1, _dibs, _referralFee); // transfer the fees out to Dibs address(Foundation address)
            amount -= _referralFee;
         }
        _safeTransfer(token1, fees, amount); // transfer the fees out to PairFees

        uint256 _ratio = amount * 1e18 / totalSupply;

        if (_ratio > 0) {
            index1 += _ratio;
        }

        emit Fees(msg.sender, 0, amount+_referralFee);
    }

    // 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 {
        uint _supplied = balanceOf[recipient]; // get LP balance of `recipient`
        if (_supplied > 0) {
            uint _supplyIndex0 = supplyIndex0[recipient]; // get last adjusted index0 for recipient
            uint _supplyIndex1 = supplyIndex1[recipient];
            uint _index0 = index0; // get global index0 for accumulated fees
            uint _index1 = index1;
            supplyIndex0[recipient] = _index0; // update user current position to global position
            supplyIndex1[recipient] = _index1;
            uint _delta0 = _index0 - _supplyIndex0; // see if there is any difference that need to be accrued
            uint _delta1 = _index1 - _supplyIndex1;
            if (_delta0 > 0) {
                uint _share = _supplied * _delta0 / 1e18; // add accrued difference for each supplied token
                claimable0[recipient] += _share;
            }
            if (_delta1 > 0) {
                uint _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 (uint _reserve0, uint _reserve1, uint _blockTimestampLast) {
        _reserve0 = reserve0;
        _reserve1 = reserve1;
        _blockTimestampLast = blockTimestampLast;
    }

    // update reserves and, on the first call per block, price accumulators
    function _update(uint balance0, uint balance1, uint _reserve0, uint _reserve1) internal {
        uint blockTimestamp = block.timestamp;
        uint 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 (uint reserve0Cumulative, uint reserve1Cumulative, uint blockTimestamp) {
        blockTimestamp = block.timestamp;
        reserve0Cumulative = reserve0CumulativeLast;
        reserve1Cumulative = reserve1CumulativeLast;

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

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

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

    // Similar in purpose to `current`, but more secure as it averages sampled prices over a user-defined granularity (minimum 1, up to the full window size)
    function quote(address tokenIn, uint amountIn, uint granularity) external view returns (uint amountOut) {
        uint [] memory _prices = sample(tokenIn, amountIn, granularity, 1);
        uint priceAverageCumulative;
        for (uint i = 0; i < _prices.length; i++) {
            priceAverageCumulative += _prices[i];
        }
        return priceAverageCumulative / granularity;
    }

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

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

        uint length = observations.length-1;
        uint i = length - (points * window);
        uint nextIndex = 0;
        uint index = 0;

        for (; i < length; i+=window) {
            nextIndex = i + window;
            uint timeElapsed = observations[nextIndex].timestamp - observations[i].timestamp;
            uint _reserve0 = (observations[nextIndex].reserve0Cumulative - observations[i].reserve0Cumulative) / timeElapsed;
            uint _reserve1 = (observations[nextIndex].reserve1Cumulative - observations[i].reserve1Cumulative) / timeElapsed;
            _prices[index] = _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
            // index < length; length cannot overflow
            unchecked {
                index = index + 1;
            }
        }
        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 (uint liquidity) {
        (uint _reserve0, uint _reserve1) = (reserve0, reserve1);
        uint _balance0 = IERC20(token0).balanceOf(address(this));
        uint _balance1 = IERC20(token1).balanceOf(address(this));
        uint _amount0 = _balance0 - _reserve0;
        uint _amount1 = _balance1 - _reserve1;

        uint _totalSupply = totalSupply;
        if (_totalSupply == 0) {
            // Calculate initial liquidity (includes MINIMUM_LIQUIDITY)
            uint totalLiquidity = Math.sqrt(_amount0 * _amount1);

            // Use minimum liquidity based on pair type
            uint minimumLiquidity;
            if (stable) {
                // For stable pairs, use dynamic minimum liquidity to ensure squared terms are not zero
                minimumLiquidity = _getMinimumLiquidity(_amount0, _amount1);
            } else {
                // For volatile pairs, use static minimum liquidity
                minimumLiquidity = MINIMUM_LIQUIDITY;
            }
            require(totalLiquidity > minimumLiquidity, "INSUFFICIENT_LIQUIDITY");

            // For stable pairs, ensure minimum liquidity provides sufficient k value for permanent protection
            // This prevents the rounding error vulnerability where k could become 0 after burning liquidity
            if (stable) {
                // Calculate the minimum reserves that would correspond to minimum liquidity tokens
                // This ensures that even the permanent minimum liquidity provides k > 0
                uint minReserve0 = (_amount0 * minimumLiquidity) / totalLiquidity;
                uint minReserve1 = (_amount1 * minimumLiquidity) / totalLiquidity;

                // Ensure these minimum reserves would produce k > 0
                // We check the actual k value that would result from these minimum reserves
                require(_k(minReserve0, minReserve1) > 0, "MINIMUM_LIQUIDITY_TOO_SMALL");
            }

            // Mint liquidity (excluding minimum liquidity) to the user and lock minimum liquidity permanently
            liquidity = totalLiquidity - minimumLiquidity;
            _mint(address(0), minimumLiquidity); // 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(to, _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 (uint amount0, uint amount1) {
        (uint _reserve0, uint _reserve1) = (reserve0, reserve1);
        uint _balance0 = IERC20(token0).balanceOf(address(this));
        uint _balance1 = IERC20(token1).balanceOf(address(this));
        uint _liquidity = balanceOf[address(this)];

        uint _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(uint amount0Out, uint amount1Out, address to, bytes calldata data) external lock {
        require(!IPairFactory(factory).isPaused(), "PAUSED");
        require(amount0Out > 0 || amount1Out > 0, 'IOA'); // Pair: INSUFFICIENT_OUTPUT_AMOUNT
        (uint _reserve0, uint _reserve1) =  (reserve0, reserve1);
        require(amount0Out < _reserve0 && amount1Out < _reserve1, 'IL'); // Pair: INSUFFICIENT_LIQUIDITY

        uint _balance0;
        uint _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));
        }

        uint amount0In = _balance0 > _reserve0 - amount0Out ? _balance0 - (_reserve0 - amount0Out) : 0;
        uint 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);
        uint256 pairFee = IPairFactory(factory).getFee(address(this), stable);
        if (amount0In > 0) _update0(amount0In * pairFee / 10000); // accrue fees for token0 and move them out of pool
        if (amount1In > 0) _update1(amount1In * pairFee / 10000); // accrue fees for 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(uint x0, uint y) internal pure returns (uint) {
        return x0*(y*y/1e18*y/1e18)/1e18+(x0*x0/1e18*x0/1e18)*y/1e18;
    }

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

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

    function getAmountOut(uint amountIn, address tokenIn) external view returns (uint) {
        (uint _reserve0, uint _reserve1) = (reserve0, reserve1);
        amountIn -= amountIn * IPairFactory(factory).getFee(address(this), stable) / 10000; // remove fee from amount received
        return _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
    }

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

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

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

    function approve(address spender, uint amount) external returns (bool) {
        allowance[msg.sender][spender] = amount;

        emit Approval(msg.sender, spender, amount);
        return true;
    }

    function permit(address owner, address spender, uint value, uint deadline, uint8 v, bytes32 r, bytes32 s) external {
        require(deadline >= block.timestamp, 'EXP');
        bytes32 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 = ECDSA.recover(digest, v, r, s);
        require(recoveredAddress == owner, 'ISIG');
        allowance[owner][spender] = value;

        emit Approval(owner, spender, value);
    }

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

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

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

            emit Approval(src, spender, newAllowance);
        }

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

    function _transferTokens(address src, address dst, uint 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 {
        require(token.code.length > 0, "CODELEN");
        (bool success, bytes memory data) = token.call(abi.encodeCall(IERC20.transfer, (to, value)));
        require(success && (data.length == 0 || abi.decode(data, (bool))), "IST");
    }

    function _getMinimumLiquidity(uint amount0, uint amount1) internal view returns (uint) {
        uint totalLiquidity = Math.sqrt(amount0 * amount1);

        // We need minimum reserves to satisfy:
        // _x >= 1e14 where _x = minReserve0 * 1e18 / decimals0
        // _y >= 1e14 where _y = minReserve1 * 1e18 / decimals1

        // This means:
        // minReserve0 >= 1e14 * decimals0 / 1e18
        // minReserve1 >= 1e14 * decimals1 / 1e18
        // minReserve0 >= decimals0 / 1e4
        // minReserve1 >= decimals1 / 1e4

        // Since minReserve0 = (amount0 * minimumLiquidity) / totalLiquidity
        // We can solve for minimumLiquidity:
        // minimumLiquidity >= (decimals0 / 1e4) * totalLiquidity / amount0
        // minimumLiquidity >= (decimals1 / 1e4) * totalLiquidity / amount1

        uint minLiquidity0 = (decimals0 * totalLiquidity) / (1e4 * amount0);
        uint minLiquidity1 = (decimals1 * totalLiquidity) / (1e4 * amount1);
        //

        // Use the maximum of the two requirements
        return Math.max(minLiquidity0, minLiquidity1);
    }
}

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

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 message) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32")
            mstore(0x1c, hash)
            message := keccak256(0x00, 0x3c)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 data) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, "\x19\x01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            data := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Data with intended validator, created from a
     * `validator` and `data` according to the version 0 of EIP-191.
     *
     * See {recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x00", validator, 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
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}

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

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

interface IERC20 {
    function totalSupply() external view returns (uint256);
    function transfer(address recipient, uint amount) external returns (bool);
    function decimals() external view returns (uint8);
    function symbol() external view returns (string memory);
    function balanceOf(address) external view returns (uint);
    function transferFrom(address sender, address recipient, uint amount) external returns (bool);
    function allowance(address owner, address spender) external view returns (uint);
    function approve(address spender, uint value) external returns (bool);

    event Transfer(address indexed from, address indexed to, uint value);
    event Approval(address indexed owner, address indexed spender, uint value);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

interface IPair {
    function metadata() external view returns (uint dec0, uint dec1, uint r0, uint r1, bool st, address t0, address t1);
    function claimFees() external returns (uint, uint);
    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, uint amount) external returns (bool);
    function permit(address owner, address spender, uint value, uint deadline, uint8 v, bytes32 r, bytes32 s) external;
    function swap(uint amount0Out, uint amount1Out, address to, bytes calldata data) external;
    function burn(address to) external returns (uint amount0, uint amount1);
    function mint(address to) external returns (uint liquidity);
    function getReserves() external view returns (uint _reserve0, uint _reserve1, uint _blockTimestampLast);
    function getAmountOut(uint, address) external view returns (uint);

    function name() external view returns(string memory);
    function symbol() external view returns(string memory);
    function totalSupply() external view returns (uint);
    function decimals() external view returns (uint8);

    function claimable0(address _user) external view returns (uint);
    function claimable1(address _user) external view returns (uint);

    function isStable() external view returns(bool);
    function allowance(address owner, address spender) external view returns (uint);
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

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

// SPDX-License-Identifier: MIT OR GPL-3.0-or-later
pragma solidity 0.8.13;

interface IPairFactory {
    function allPairsLength() external view returns (uint);
    function isPair(address pair) external view returns (bool);
    function allPairs(uint index) external view returns (address);
    function pairCodeHash() external view returns (bytes32);
    function pairGenerator() 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 getFee(address _pairAddress, bool _stable) external view returns(uint256);
    function dibs() external view returns (address);
    function getReferralFee(address _pairAddress) external view returns (uint256);
    function isPaused() external view returns (bool);
}

// SPDX-License-Identifier: MIT OR GPL-3.0-or-later
pragma solidity 0.8.13;

interface IPairGenerator {
    function factory() external view returns (address);
    function pairCodeHash() external pure returns (bytes32);
    function getInitializable() external view returns (address, address, bool);
    function createPair(address token0, address token1, bool stable) external returns (address pair);
}

// SPDX-License-Identifier: GPL-3.0-or-later
pragma solidity 0.8.13;

// Define constants as standalone constants that can be imported by name
uint256 constant MAX_FEE = 500; // 5% maximum fee
uint256 constant MAX_REFERRAL_FEE_CAP = 500; // 5% max referral fee
uint256 constant REFERRAL_FEE_DENOMINATOR = 10000; // basis points denominator

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

library Math {
    function max(uint a, uint b) internal pure returns (uint) {
        return a >= b ? a : b;
    }
    function min(uint a, uint b) internal pure returns (uint) {
        return a < b ? a : b;
    }
    function sqrt(uint y) internal pure returns (uint z) {
        if (y > 3) {
            z = y;
            uint x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }
    function cbrt(uint256 n) internal pure returns (uint256) { unchecked {
        uint256 x = 0;
        for (uint256 y = 1 << 255; y > 0; y >>= 3) {
            x <<= 1;
            uint256 z = 3 * x * (x + 1) + 1;
            if (n / y >= z) {
                n -= y * z;
                x += 1;
            }
        }
        return x;
    }}
}

// SPDX-License-Identifier: MIT
pragma solidity 0.8.13;

import './interfaces/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

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

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

    // Allow the pair to transfer fees to users
    function claimFeesFor(address recipient, uint amount0, uint amount1) external {
        require(msg.sender == pair);
        if (amount0 > 0) _safeTransfer(token0, recipient, amount0);
        if (amount1 > 0) _safeTransfer(token1, recipient, amount1);
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "metadata": {
    "useLiteralContent": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  }
}

• No Contract Security Audit Submitted- Submit Audit Here

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