// File: @openzeppelin/contracts/token/ERC20/IERC20.sol



// 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);
}

// File: contracts/libraries/Math.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

// a library for performing various math operations

library Math {
    function min(uint x, uint y) internal pure returns (uint z) {
        z = x < y ? x : y;
    }

    // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
    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;
        }
    }
}

// File: contracts/libraries/SafeMath.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(
        uint256 a,
        uint256 b,
        string memory errorMessage
    ) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }

    function min(uint256 x, uint256 y) internal pure returns (uint256 z) {
        z = x < y ? x : y;
    }

    // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
    function sqrt(uint256 y) internal pure returns (uint256 z) {
        if (y > 3) {
            z = y;
            uint256 x = y / 2 + 1;
            while (x < z) {
                z = x;
                x = (y / x + x) / 2;
            }
        } else if (y != 0) {
            z = 1;
        }
    }
}

// File: contracts/libraries/UQ112x112.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))

// range: [0, 2**112 - 1]
// resolution: 1 / 2**112

library UQ112x112 {
    uint224 constant Q112 = 2 ** 112;

    // encode a uint112 as a UQ112x112
    function encode(uint112 y) internal pure returns (uint224 z) {
        z = uint224(y) * Q112; // never overflows
    }

    // divide a UQ112x112 by a uint112, returning a UQ112x112
    function uqdiv(uint224 x, uint112 y) internal pure returns (uint224 z) {
        z = x / uint224(y);
    }
}

// File: contracts/swap/interfaces/INineInchCallee.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

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

// File: contracts/swap/interfaces/INineInchERC20.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

interface INineInchERC20 {
    event Approval(address indexed owner, address indexed spender, uint value);
    event Transfer(address indexed from, address indexed to, uint value);

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

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

    function decimals() external pure returns (uint8);

    function totalSupply() external view returns (uint);

    function balanceOf(address owner) external view returns (uint);

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

    function approve(address spender, uint value) external returns (bool);

    function transfer(address to, uint value) external returns (bool);

    function transferFrom(
        address from,
        address to,
        uint value
    ) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);

    function PERMIT_TYPEHASH() external pure returns (bytes32);

    function nonces(address owner) external view returns (uint);

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

// File: contracts/swap/interfaces/INineInchFactory.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

interface INineInchFactory {
    event PairCreated(
        address indexed token0,
        address indexed token1,
        address pair,
        uint
    );

    function feeTo() external view returns (address);

    function feeToSetter() external view returns (address);

    function getPair(
        address tokenA,
        address tokenB
    ) external view returns (address pair);

    function allPairs(uint) external view returns (address pair);

    function allPairsLength() external view returns (uint);

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

    function setFeeTo(address) external;

    function setFeeToSetter(address) external;
}

// File: contracts/swap/interfaces/INineInchPair.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

interface INineInchPair {
    function name() external pure returns (string memory);

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

    function decimals() external pure returns (uint8);

    function totalSupply() external view returns (uint);

    function balanceOf(address owner) external view returns (uint);

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

    function approve(address spender, uint value) external returns (bool);

    function transfer(address to, uint value) external returns (bool);

    function transferFrom(
        address from,
        address to,
        uint value
    ) external returns (bool);

    function DOMAIN_SEPARATOR() external view returns (bytes32);

    function PERMIT_TYPEHASH() external view returns (bytes32);

    function nonces(address owner) external view returns (uint);

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

    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(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint);

    function factory() external view returns (address);

    function token0() external view returns (address);

    function token1() external view returns (address);

    function getReserves()
        external
        view
        returns (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast);

    function price0CumulativeLast() external view returns (uint);

    function price1CumulativeLast() external view returns (uint);

    function kLast() external view returns (uint);

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

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

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

    function skim(address to) external;

    function sync() external;

    function initialize(address, address) external;
}

// File: contracts/swap/NineInchERC20.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

import "./interfaces/INineInchERC20.sol";
import "../libraries/SafeMath.sol";

contract NineInchERC20 is INineInchERC20 {
    using SafeMath for uint;

    string public constant override name = unicode"🍆 9 LP";
    string public constant override symbol = unicode"🍆 9 LP";
    uint8 public constant override decimals = 18;
    uint public totalSupply;
    mapping(address => uint) public override balanceOf;
    mapping(address => mapping(address => uint)) public override allowance;

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

    constructor() {
        uint chainId;
        assembly {
            chainId := chainid()
        }
        DOMAIN_SEPARATOR = keccak256(
            abi.encode(
                keccak256(
                    "EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)"
                ),
                keccak256(bytes(name)),
                keccak256(bytes("1")),
                chainId,
                address(this)
            )
        );
    }

    function _mint(address to, uint value) internal {
        totalSupply = totalSupply.add(value);
        balanceOf[to] = balanceOf[to].add(value);
        emit Transfer(address(0), to, value);
    }

    function _burn(address from, uint value) internal {
        balanceOf[from] = balanceOf[from].sub(value);
        totalSupply = totalSupply.sub(value);
        emit Transfer(from, address(0), value);
    }

    function _approve(address owner, address spender, uint value) private {
        allowance[owner][spender] = value;
        emit Approval(owner, spender, value);
    }

    function _transfer(address from, address to, uint value) private {
        balanceOf[from] = balanceOf[from].sub(value);
        balanceOf[to] = balanceOf[to].add(value);
        emit Transfer(from, to, value);
    }

    function approve(address spender, uint value) external returns (bool) {
        _approve(msg.sender, spender, value);
        return true;
    }

    function transfer(address to, uint value) external returns (bool) {
        _transfer(msg.sender, to, value);
        return true;
    }

    function transferFrom(
        address from,
        address to,
        uint value
    ) external override returns (bool) {
        if (allowance[from][msg.sender] != type(uint).max) {
            allowance[from][msg.sender] = allowance[from][msg.sender].sub(
                value
            );
        }
        _transfer(from, to, value);
        return true;
    }

    function permit(
        address owner,
        address spender,
        uint value,
        uint deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) external {
        require(deadline >= block.timestamp, "NineInch: EXPIRED");
        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,
            "NineInch: INVALID_SIGNATURE"
        );
        _approve(owner, spender, value);
    }
}

// File: contracts/swap/NineInchFactory.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

import "./interfaces/INineInchFactory.sol";
import "./NineInchPair.sol";

contract NineInchFactory is INineInchFactory {
    bytes32 public constant INIT_CODE_PAIR_HASH =
        keccak256(abi.encodePacked(type(NineInchPair).creationCode));

    address public feeTo;
    address public feeToSetter;

    mapping(address => mapping(address => address)) public getPair;
    address[] public allPairs;

    constructor(address _feeToSetter) {
        require(_feeToSetter != address(0), "NineInchFactory: ZERO_ADDRESS");
        feeToSetter = _feeToSetter;
    }

    function allPairsLength() external view returns (uint) {
        return allPairs.length;
    }

    function createPair(
        address tokenA,
        address tokenB
    ) external returns (address pair) {
        require(
            tokenA != address(0) && tokenB != address(0),
            "NineInchFactory: ZERO_ADDRESS"
        );
        require(tokenA != tokenB, "NineInchFactory: IDENTICAL_ADDRESSES");
        (address token0, address token1) = tokenA < tokenB
            ? (tokenA, tokenB)
            : (tokenB, tokenA);
        require(token0 != address(0), "NineInchFactory: ZERO_ADDRESS");
        require(
            getPair[token0][token1] == address(0),
            "NineInchFactory: PAIR_EXISTS"
        ); // single check is sufficient
        bytes memory bytecode = type(NineInchPair).creationCode;
        bytes32 salt = keccak256(abi.encodePacked(token0, token1));
        assembly {
            pair := create2(0, add(bytecode, 32), mload(bytecode), salt)
        }
        INineInchPair(pair).initialize(token0, token1);
        getPair[token0][token1] = pair;
        getPair[token1][token0] = pair; // populate mapping in the reverse direction
        allPairs.push(pair);
        emit PairCreated(token0, token1, pair, allPairs.length);
    }

    function setFeeTo(address _feeTo) external {
        require(_feeTo != address(0), "NineInchFactory: ZERO_ADDRESS");
        require(msg.sender == feeToSetter, "NineInchFactory: FORBIDDEN");
        feeTo = _feeTo;
    }

    function setFeeToSetter(address _feeToSetter) external {
        require(_feeToSetter != address(0), "NineInchFactory: ZERO_ADDRESS");
        require(msg.sender == feeToSetter, "NineInchFactory: FORBIDDEN");
        feeToSetter = _feeToSetter;
    }
}

// File: contracts/swap/NineInchPair.sol



// SPDX-License-Identifier: GPLv3
pragma solidity 0.8.19;

import "./interfaces/INineInchFactory.sol";
import "./interfaces/INineInchCallee.sol";
import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "./interfaces/INineInchERC20.sol";
import "./NineInchERC20.sol";
import "./interfaces/INineInchPair.sol";
import "../libraries/SafeMath.sol";
import "../libraries/UQ112x112.sol";
import "../libraries/Math.sol";

contract NineInchPair is NineInchERC20 {
    using SafeMath for uint;
    using UQ112x112 for uint224;

    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(uint112 reserve0, uint112 reserve1);

    uint public constant MINIMUM_LIQUIDITY = 10 ** 3;
    bytes4 private constant SELECTOR =
        bytes4(keccak256(bytes("transfer(address,uint256)")));

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

    uint112 private reserve0; // uses single storage slot, accessible via getReserves
    uint112 private reserve1; // uses single storage slot, accessible via getReserves
    uint32 private blockTimestampLast; // uses single storage slot, accessible via getReserves

    uint public price0CumulativeLast;
    uint public price1CumulativeLast;
    uint public kLast; // reserve0 * reserve1, as of immediately after the most recent liquidity event

    uint private unlocked = 1;
    modifier lock() {
        require(unlocked == 1, "NineInch: LOCKED");
        unlocked = 0;
        _;
        unlocked = 1;
    }

    function getReserves()
        public
        view
        returns (
            uint112 _reserve0,
            uint112 _reserve1,
            uint32 _blockTimestampLast
        )
    {
        _reserve0 = reserve0;
        _reserve1 = reserve1;
        _blockTimestampLast = blockTimestampLast;
    }

    function _safeTransfer(address token, address to, uint value) private {
        (bool success, bytes memory data) = token.call(
            abi.encodeWithSelector(SELECTOR, to, value)
        );
        require(
            success && (data.length == 0 || abi.decode(data, (bool))),
            "NineInch: TRANSFER_FAILED"
        );
    }

    constructor() {
        factory = msg.sender;
    }

    // called once by the factory at time of deployment
    function initialize(address _token0, address _token1) external {
        require(
            _token0 != address(0) && _token1 != address(0),
            "NineInch: ZERO_ADDRESS"
        );
        require(_token0 != _token1, "NineInch: IDENTICAL_ADDRESSES");
        require(msg.sender == factory, "NineInch: FORBIDDEN"); // sufficient check
        token0 = _token0;
        token1 = _token1;
    }

    // update reserves and, on the first call per block, price accumulators
    function _update(
        uint balance0,
        uint balance1,
        uint112 _reserve0,
        uint112 _reserve1
    ) private {
        require(
            balance0 <= type(uint112).max && balance1 <= type(uint112).max,
            "NineInch: OVERFLOW"
        );
        uint32 blockTimestamp = uint32(block.timestamp % 2 ** 32);
        uint32 timeElapsed = blockTimestamp - blockTimestampLast; // overflow is desired
        if (timeElapsed > 0 && _reserve0 != 0 && _reserve1 != 0) {
            // * never overflows, and + overflow is desired
            price0CumulativeLast +=
                uint(UQ112x112.encode(_reserve1).uqdiv(_reserve0)) *
                timeElapsed;
            price1CumulativeLast +=
                uint(UQ112x112.encode(_reserve0).uqdiv(_reserve1)) *
                timeElapsed;
        }
        reserve0 = uint112(balance0);
        reserve1 = uint112(balance1);
        blockTimestampLast = blockTimestamp;
        emit Sync(reserve0, reserve1);
    }

    // if fee is on, mint liquidity equivalent to 1/6th of the growth in sqrt(k)
    function _mintFee(
        uint112 _reserve0,
        uint112 _reserve1
    ) private returns (bool feeOn) {
        address feeTo = INineInchFactory(factory).feeTo();
        feeOn = feeTo != address(0);
        uint _kLast = kLast; // gas savings
        if (feeOn) {
            if (_kLast != 0) {
                uint rootK = Math.sqrt(uint(_reserve0).mul(_reserve1));
                uint rootKLast = Math.sqrt(_kLast);
                if (rootK > rootKLast) {
                    uint numerator = totalSupply.mul(rootK.sub(rootKLast));
                    uint denominator = rootK.mul(7).add(rootKLast);
                    uint liquidity = numerator / denominator;
                    if (liquidity > 0) _mint(feeTo, liquidity);
                }
            }
        } else if (_kLast != 0) {
            kLast = 0;
        }
    }

    // this low-level function should be called from a contract which performs important safety checks
    function mint(address to) external lock returns (uint liquidity) {
        (uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
        uint balance0 = IERC20(token0).balanceOf(address(this));
        uint balance1 = IERC20(token1).balanceOf(address(this));
        uint amount0 = balance0.sub(_reserve0);
        uint amount1 = balance1.sub(_reserve1);

        bool feeOn = _mintFee(_reserve0, _reserve1);
        uint _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
        if (_totalSupply == 0) {
            liquidity = Math.sqrt(amount0.mul(amount1)).sub(MINIMUM_LIQUIDITY);
            _mint(address(0), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens
        } else {
            liquidity = Math.min(
                amount0.mul(_totalSupply) / _reserve0,
                amount1.mul(_totalSupply) / _reserve1
            );
        }
        require(liquidity > 0, "NineInch: INSUFFICIENT_LIQUIDITY_MINTED");
        _mint(to, liquidity);

        _update(balance0, balance1, _reserve0, _reserve1);
        if (feeOn) kLast = uint(reserve0).mul(reserve1); // reserve0 and reserve1 are up-to-date
        emit Mint(msg.sender, amount0, amount1);
    }

    // this low-level function should be called from a contract which performs important safety checks
    function burn(
        address to
    ) external lock returns (uint amount0, uint amount1) {
        (uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
        address _token0 = token0; // gas savings
        address _token1 = token1; // gas savings
        uint balance0 = IERC20(_token0).balanceOf(address(this));
        uint balance1 = IERC20(_token1).balanceOf(address(this));
        uint liquidity = balanceOf[address(this)];

        bool feeOn = _mintFee(_reserve0, _reserve1);
        uint _totalSupply = totalSupply; // gas savings, must be defined here since totalSupply can update in _mintFee
        amount0 = liquidity.mul(balance0) / _totalSupply; // using balances ensures pro-rata distribution
        amount1 = liquidity.mul(balance1) / _totalSupply; // using balances ensures pro-rata distribution
        require(
            amount0 > 0 && amount1 > 0,
            "NineInch: 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);
        if (feeOn) kLast = uint(reserve0).mul(reserve1); // reserve0 and reserve1 are up-to-date
        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(
            amount0Out > 0 || amount1Out > 0,
            "NineInch: INSUFFICIENT_OUTPUT_AMOUNT"
        );
        (uint112 _reserve0, uint112 _reserve1, ) = getReserves(); // gas savings
        require(
            amount0Out < _reserve0 && amount1Out < _reserve1,
            "NineInch: INSUFFICIENT_LIQUIDITY"
        );

        uint balance0;
        uint balance1;
        {
            // scope for _token{0,1}, avoids stack too deep errors
            address _token0 = token0;
            address _token1 = token1;
            require(to != _token0 && to != _token1, "NineInch: 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)
                INineInchCallee(to).nineInchCallee(
                    msg.sender,
                    amount0Out,
                    amount1Out,
                    data
                );
            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,
            "NineInch: INSUFFICIENT_INPUT_AMOUNT"
        );
        {
            // scope for reserve{0,1}Adjusted, avoids stack too deep errors
            uint balance0Adjusted = balance0.mul(10000).sub(amount0In.mul(29));
            uint balance1Adjusted = balance1.mul(10000).sub(amount1In.mul(29));
            require(
                balance0Adjusted.mul(balance1Adjusted) >=
                    uint(_reserve0).mul(_reserve1).mul(10000 ** 2),
                "NineInch: 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 = token0; // gas savings
        address _token1 = token1; // gas savings
        _safeTransfer(
            _token0,
            to,
            IERC20(_token0).balanceOf(address(this)).sub(reserve0)
        );
        _safeTransfer(
            _token1,
            to,
            IERC20(_token1).balanceOf(address(this)).sub(reserve1)
        );
    }

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