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• library Math
•    - function max(uint256 a, uint256 b)
•    - function min(uint256 a, uint256 b)
•    - function average(uint256 a, uint256 b ...
•    - function ceilDiv(uint256 a, uint256 b ...
•    - function mulDiv(uint256 x, uint256 y, ...
•    - function mulDiv(uint256 x, uint256 y, ...
•    - function sqrt(uint256 a)
•    - function sqrt(uint256 a, Rounding rou ...
•    - function log2(uint256 value)
•    - function log2(uint256 value, Rounding ...
•    - function log10(uint256 value)
•    - function log10(uint256 value, Roundin ...
•    - function log256(uint256 value)
•    - function log256(uint256 value, Roundi ...
• interface IERC20
•    - function totalSupply()
•    - function transfer(address recipient, ...
•    - function decimals()
•    - function symbol()
•    - function balanceOf(address)
•    - function transferFrom(address sender, ...
•    - function allowance(address owner, add ...
•    - function approve(address spender, uin ...
• interface IPair
•    - function metadata()
•    - function tokens()
•    - function token0()
•    - function token1()
•    - function transferFrom(address src, ad ...
•    - function permit(address owner, addres ...
•    - function swap(uint amount0Out, uint a ...
•    - function burn(address to)
•    - function mint(address to)
•    - function getReserves()
•    - function getAmountOut(uint, address)
•    - function setHasGauge(bool value)
•    - function setExternalBribe(address _ex ...
•    - function hasGauge()
•    - function stable()
•    - function prices(address tokenIn, uint ...
• interface IPairCallee
•    - function hook(address sender, uint am ...
• interface IPairFactory
•    - function allPairsLength()
•    - function isPair(address pair)
•    - function isPaused()
•    - function pairCodeHash()
•    - function getFee(address pair)
•    - function getPair(address tokenA, addr ...
•    - function getInitializable()
•    - function createPair(address tokenA, a ...
•    - function voter()
•    - function tank()
• interface IBribe
•    - function _deposit(uint amount, uint t ...
•    - function _withdraw(uint amount, uint ...
•    - function getRewardForOwner(uint token ...
•    - function notifyRewardAmount(address t ...
•    - function left(address token)
•  contract Pair is IPair *
•    - function _safeApprove(address token, ...
•    - function tank()
•    - function setExternalBribe(address _ex ...
•    - function setHasGauge(bool value)
•    - function observationLength()
•    - function lastObservation()
•    - function metadata()
•    - function tokens()
•    - function _sendTokenFees(address token ...
•    - function getReserves()
•    - function _update(uint balance0, uint ...
•    - function currentCumulativePrices()
•    - function current(address tokenIn, uin ...
•    - function quote(address tokenIn, uint ...
•    - function prices(address tokenIn, uint ...
•    - function sample(address tokenIn, uint ...
•    - function mint(address to)
•    - function burn(address to)
•    - function swap(uint amount0Out, uint a ...
•    - function skim(address to)
•    - function sync()
•    - function _f(uint x0, uint y)
•    - function _d(uint x0, uint y)
•    - function _get_y(uint x0, uint xy, uin ...
•    - function getAmountOut(uint amountIn, ...
•    - function _getAmountOut(uint amountIn, ...
•    - function _k(uint x, uint y)
•    - function _mint(address dst, uint amou ...
•    - function _burn(address dst, uint amou ...
•    - function approve(address spender, uin ...
•    - function permit(address owner, addres ...
•    - function transfer(address dst, uint a ...
•    - function transferFrom(address src, ad ...
•    - function _transferTokens(address src, ...
•    - function _safeTransfer(address token, ...

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/**
 *Submitted for verification at ftmscan.com on 2023-07-24
*/

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


// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)
// 🐶👒


/**
 * @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);
        }
    }
}

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);
}

interface IPair {
    function metadata() external view returns (uint dec0, uint dec1, uint r0, uint r1, bool st, address t0, address t1);
    function tokens() external returns (address, address);
    function token0() external returns (address);
    function token1() external 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 setHasGauge(bool value) external;
    function setExternalBribe(address _externalBribe) external;
    function hasGauge() external view returns (bool);
    function stable() external view returns (bool);
    function prices(address tokenIn, uint amountIn, uint points) external view returns (uint[] memory);
}

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

interface IPairFactory {
    function allPairsLength() external view returns (uint);
    function isPair(address pair) external view returns (bool);
    function isPaused() external view returns (bool);
    function pairCodeHash() external pure returns (bytes32);
    function getFee(address pair) external view returns (uint256);
    function getPair(address tokenA, address token, bool stable) external view returns (address);
    function getInitializable() external view returns (address, address, bool);
    function createPair(address tokenA, address tokenB, bool stable) external returns (address pair);
    function voter() external view returns (address);
    function tank() external view returns (address);
}

interface IBribe {
    function _deposit(uint amount, uint tokenId) external;
    function _withdraw(uint amount, uint tokenId) external;
    function getRewardForOwner(uint tokenId, address[] memory tokens) external;
    function notifyRewardAmount(address token, uint amount) external;
    function left(address token) external view returns (uint);
}

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

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

    // Used to denote stable or volatile pair, not immutable since construction happens in the initialize method for CREATE2 deterministic addresses
    bool public immutable stable;

    uint public totalSupply = 0;

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

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

    uint internal constant MINIMUM_LIQUIDITY = 10**3;

    address public immutable token0;
    address public immutable token1;
    address immutable factory;
    address public externalBribe;
    address public voter;
    bool public hasGauge;

    // 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;

    event TankFees(address indexed token, uint amount, address tank);
    event GaugeFees(address indexed token, uint amount, address externalBribe);
    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 Transfer(address indexed from, address indexed to, uint amount);
    event Approval(address indexed owner, address indexed spender, uint amount);

    event ExternalBribeSet(address indexed externalBribe);
    event HasGaugeSet(bool value);

    constructor() {
        factory = msg.sender;
        voter = IPairFactory(msg.sender).voter();
        (address _token0, address _token1, bool _stable) = IPairFactory(msg.sender).getInitializable();
        (token0, token1, stable) = (_token0, _token1, _stable);
        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);
        _unlocked = 2;
        _;
        _unlocked = 1;
    }

    function _safeApprove(address token, address spender, uint value) internal {
        require(token.code.length > 0);
        (bool success, bytes memory data) = token.call(abi.encodeWithSelector(IERC20.approve.selector, spender, value));
        require(success && (data.length == 0 || abi.decode(data, (bool))));
    }

    function tank() public view returns (address) {
        return IPairFactory(factory).tank();
    }

    function setExternalBribe(address _externalBribe) external {
        require(msg.sender == voter, 'Only voter can set external bribe');
        externalBribe = _externalBribe;
        _safeApprove(token0, externalBribe, type(uint).max);
        _safeApprove(token1, externalBribe, type(uint).max);
        emit ExternalBribeSet(_externalBribe);
    }

    function setHasGauge(bool value) external {
        require(msg.sender == voter, 'Only voter can set has gauge');
        hasGauge = value;
        emit HasGaugeSet(value);
    }

    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 _sendTokenFees(address token, uint amount) internal {
        if (amount != 0) {
            if (hasGauge) {
                IBribe(externalBribe).notifyRewardAmount(token, amount); // transfer fees to exBribes
                emit GaugeFees(token, amount, externalBribe);
            } else {
                address _tank = tank();
                _safeTransfer(token, _tank, amount); // transfer the fees to tank MSig for gaugeless LPs
                emit TankFees(token, amount, _tank);
            }
        }
    }

    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) {
            // subtraction overflow is desired
            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);
    }

    // as per `current`, however allows user configured granularity, 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; // gas savings, must be defined here since totalSupply can update in _mintFee
        if (_totalSupply == 0) {
            liquidity = Math.sqrt(_amount0 * _amount1) - MINIMUM_LIQUIDITY;
            _mint(address(0), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens
        } else {
            liquidity = Math.min(_amount0 * _totalSupply / _reserve0, _amount1 * _totalSupply / _reserve1);
        }
        require(liquidity > 0, 'ILM'); // Pair: INSUFFICIENT_LIQUIDITY_MINTED
        _mint(to, liquidity);

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

    // this low-level function should be called from a contract which performs important safety checks
    // standard uniswap v2 implementation
    function burn(address to) external lock returns (uint amount0, uint amount1) {
        (uint _reserve0, uint _reserve1) = (reserve0, reserve1);
        (address _token0, address _token1) = (token0, token1);
        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());
        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);
        if (amount0In > 0) _sendTokenFees(token0, amount0In * IPairFactory(factory).getFee(address(this)) / 10000);
        if (amount1In > 0) _sendTokenFees(token1, amount1In * IPairFactory(factory).getFee(address(this)) / 10000);
        _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)) / 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 {
        totalSupply += amount;
        balanceOf[dst] += amount;
        emit Transfer(address(0), dst, amount);
    }

    function _burn(address dst, uint amount) internal {
        totalSupply -= amount;
        balanceOf[dst] -= amount;
        emit Transfer(dst, 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, 'Pair: EXPIRED');
        DOMAIN_SEPARATOR = keccak256(
            abi.encode(
                keccak256('EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)'),
                keccak256(bytes(name)),
                keccak256(bytes('1')),
                block.chainid,
                address(this)
            )
        );
        bytes32 digest = keccak256(
            abi.encodePacked(
                '\x19\x01',
                DOMAIN_SEPARATOR,
                keccak256(abi.encode(PERMIT_TYPEHASH, owner, spender, value, nonces[owner]++, deadline))
            )
        );
        address recoveredAddress = ecrecover(digest, v, r, s);
        require(recoveredAddress != address(0) && recoveredAddress == owner, 'Pair: INVALID_SIGNATURE');
        allowance[owner][spender] = value;

        emit Approval(owner, spender, value);
    }

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

• No Contract Security Audit Submitted- Submit Audit Here

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