// SPDX-License-Identifier: MIT
pragma solidity ^0.6.12;
pragma experimental ABIEncoderV2;

interface IUniswapV2Factory {
    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;
}

interface IUniswapV2Pair {
    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;

    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;
}

// a library for handling binary fixed point numbers (https://en.wikipedia.org/wiki/Q_(number_format))
library FixedPoint {
    // range: [0, 2**112 - 1]
    // resolution: 1 / 2**112
    struct uq112x112 {
        uint224 _x;
    }

    // range: [0, 2**144 - 1]
    // resolution: 1 / 2**112
    struct uq144x112 {
        uint _x;
    }

    uint8 private constant RESOLUTION = 112;

    // encode a uint112 as a UQ112x112
    function encode(uint112 x) internal pure returns (uq112x112 memory) {
        return uq112x112(uint224(x) << RESOLUTION);
    }

    // encodes a uint144 as a UQ144x112
    function encode144(uint144 x) internal pure returns (uq144x112 memory) {
        return uq144x112(uint256(x) << RESOLUTION);
    }

    // divide a UQ112x112 by a uint112, returning a UQ112x112
    function div(uq112x112 memory self, uint112 x) internal pure returns (uq112x112 memory) {
        require(x != 0, 'FixedPoint: DIV_BY_ZERO');
        return uq112x112(self._x / uint224(x));
    }

    // multiply a UQ112x112 by a uint, returning a UQ144x112
    // reverts on overflow
    function mul(uq112x112 memory self, uint y) internal pure returns (uq144x112 memory) {
        uint z;
        require(y == 0 || (z = uint(self._x) * y) / y == uint(self._x), "FixedPoint: MULTIPLICATION_OVERFLOW");
        return uq144x112(z);
    }

    // returns a UQ112x112 which represents the ratio of the numerator to the denominator
    // equivalent to encode(numerator).div(denominator)
    function fraction(uint112 numerator, uint112 denominator) internal pure returns (uq112x112 memory) {
        require(denominator > 0, "FixedPoint: DIV_BY_ZERO");
        return uq112x112((uint224(numerator) << RESOLUTION) / denominator);
    }

    // decode a UQ112x112 into a uint112 by truncating after the radix point
    function decode(uq112x112 memory self) internal pure returns (uint112) {
        return uint112(self._x >> RESOLUTION);
    }

    // decode a UQ144x112 into a uint144 by truncating after the radix point
    function decode144(uq144x112 memory self) internal pure returns (uint144) {
        return uint144(self._x >> RESOLUTION);
    }
}

// library with helper methods for oracles that are concerned with computing average prices
library UniswapV2OracleLibrary {
    using FixedPoint for *;

    // helper function that returns the current block timestamp within the range of uint32, i.e. [0, 2**32 - 1]
    function currentBlockTimestamp() internal view returns (uint32) {
        return uint32(block.timestamp % 2 ** 32);
    }

    // produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    function currentCumulativePrices(
        address pair
    ) internal view returns (uint price0Cumulative, uint price1Cumulative, uint32 blockTimestamp) {
        blockTimestamp = currentBlockTimestamp();
        price0Cumulative = IUniswapV2Pair(pair).price0CumulativeLast();
        price1Cumulative = IUniswapV2Pair(pair).price1CumulativeLast();

        // if time has elapsed since the last update on the pair, mock the accumulated price values
        (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast) = IUniswapV2Pair(pair).getReserves();
        if (blockTimestampLast != blockTimestamp) {
            // subtraction overflow is desired
            uint32 timeElapsed = blockTimestamp - blockTimestampLast;
            // addition overflow is desired
            // counterfactual
            price0Cumulative += uint(FixedPoint.fraction(reserve1, reserve0)._x) * timeElapsed;
            // counterfactual
            price1Cumulative += uint(FixedPoint.fraction(reserve0, reserve1)._x) * timeElapsed;
        }
    }
}

// a library for performing overflow-safe math, courtesy of DappHub (https://github.com/dapphub/ds-math)

/**
 * @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 addition of two unsigned integers, reverting with custom message on overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, errorMessage);

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on underflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot underflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction underflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on underflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     * - Subtraction cannot underflow.
     */
    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 multiplication of two unsigned integers, reverting on overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b, string memory errorMessage) 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, errorMessage);

        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) {
        // Solidity only automatically asserts when dividing by 0
        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;
    }
}

library UniswapV2Library {
    using SafeMath for uint;

    // returns sorted token addresses, used to handle return values from pairs sorted in this order
    function sortTokens(address tokenA, address tokenB) internal pure returns (address token0, address token1) {
        require(tokenA != tokenB, 'UniswapV2Library: IDENTICAL_ADDRESSES');
        (token0, token1) = tokenA < tokenB ? (tokenA, tokenB) : (tokenB, tokenA);
        require(token0 != address(0), 'UniswapV2Library: ZERO_ADDRESS');
    }

    // calculates the CREATE2 address for a pair without making any external calls
    function pairFor(address factory, address tokenA, address tokenB) internal pure returns (address pair) {
        (address token0, address token1) = sortTokens(tokenA, tokenB);
        pair = address(uint(keccak256(abi.encodePacked(
                hex'ff',
                factory,
                keccak256(abi.encodePacked(token0, token1)),
                hex'96e8ac4277198ff8b6f785478aa9a39f403cb768dd02cbee326c3e7da348845f' // init code hash
            ))));
    }

    // fetches and sorts the reserves for a pair
    function getReserves(address factory, address tokenA, address tokenB) internal view returns (uint reserveA, uint reserveB) {
        (address token0,) = sortTokens(tokenA, tokenB);
        (uint reserve0, uint reserve1,) = IUniswapV2Pair(pairFor(factory, tokenA, tokenB)).getReserves();
        (reserveA, reserveB) = tokenA == token0 ? (reserve0, reserve1) : (reserve1, reserve0);
    }

    // given some amount of an asset and pair reserves, returns an equivalent amount of the other asset
    function quote(uint amountA, uint reserveA, uint reserveB) internal pure returns (uint amountB) {
        require(amountA > 0, 'UniswapV2Library: INSUFFICIENT_AMOUNT');
        require(reserveA > 0 && reserveB > 0, 'UniswapV2Library: INSUFFICIENT_LIQUIDITY');
        amountB = amountA.mul(reserveB) / reserveA;
    }

    // given an input amount of an asset and pair reserves, returns the maximum output amount of the other asset
    function getAmountOut(uint amountIn, uint reserveIn, uint reserveOut) internal pure returns (uint amountOut) {
        require(amountIn > 0, 'UniswapV2Library: INSUFFICIENT_INPUT_AMOUNT');
        require(reserveIn > 0 && reserveOut > 0, 'UniswapV2Library: INSUFFICIENT_LIQUIDITY');
        uint amountInWithFee = amountIn.mul(997);
        uint numerator = amountInWithFee.mul(reserveOut);
        uint denominator = reserveIn.mul(1000).add(amountInWithFee);
        amountOut = numerator / denominator;
    }

    // given an output amount of an asset and pair reserves, returns a required input amount of the other asset
    function getAmountIn(uint amountOut, uint reserveIn, uint reserveOut) internal pure returns (uint amountIn) {
        require(amountOut > 0, 'UniswapV2Library: INSUFFICIENT_OUTPUT_AMOUNT');
        require(reserveIn > 0 && reserveOut > 0, 'UniswapV2Library: INSUFFICIENT_LIQUIDITY');
        uint numerator = reserveIn.mul(amountOut).mul(1000);
        uint denominator = reserveOut.sub(amountOut).mul(997);
        amountIn = (numerator / denominator).add(1);
    }

    // performs chained getAmountOut calculations on any number of pairs
    function getAmountsOut(address factory, uint amountIn, address[] memory path) internal view returns (uint[] memory amounts) {
        require(path.length >= 2, 'UniswapV2Library: INVALID_PATH');
        amounts = new uint[](path.length);
        amounts[0] = amountIn;
        for (uint i; i < path.length - 1; i++) {
            (uint reserveIn, uint reserveOut) = getReserves(factory, path[i], path[i + 1]);
            amounts[i + 1] = getAmountOut(amounts[i], reserveIn, reserveOut);
        }
    }

    // performs chained getAmountIn calculations on any number of pairs
    function getAmountsIn(address factory, uint amountOut, address[] memory path) internal view returns (uint[] memory amounts) {
        require(path.length >= 2, 'UniswapV2Library: INVALID_PATH');
        amounts = new uint[](path.length);
        amounts[amounts.length - 1] = amountOut;
        for (uint i = path.length - 1; i > 0; i--) {
            (uint reserveIn, uint reserveOut) = getReserves(factory, path[i - 1], path[i]);
            amounts[i - 1] = getAmountIn(amounts[i], reserveIn, reserveOut);
        }
    }
}

interface WETH9 {
    function withdraw(uint wad) external;
}

interface IUniswapV2Router {
    function swapExactTokensForTokens(
        uint amountIn,
        uint amountOutMin,
        address[] calldata path,
        address to,
        uint deadline
    ) external returns (uint[] memory amounts);
}

interface ILock3r {
    function isMinLocker(address locker, uint minBond, uint earned, uint age) external returns (bool);
    function receipt(address credit, address locker, uint amount) external;
    function unbond(address bonding, uint amount) external;
    function withdraw(address bonding) external;
    function bonds(address locker, address credit) external view returns (uint);
    function unbondings(address locker, address credit) external view returns (uint);
    function approve(address spender, uint amount) external returns (bool);
    function jobs(address job) external view returns (bool);
    function balanceOf(address account) external view returns (uint256);
    function worked(address locker) external;
    function LK3RH() external view returns (ILock3rV1Helper);
}

interface ILock3rV1Helper {
    function getQuoteLimit(uint gasUsed) external view returns (uint);
}

// sliding oracle that uses observations collected to provide moving price averages in the past
contract Lock3rOracle {
    using FixedPoint for *;
    using SafeMath for uint;

    struct Observation {
        uint timestamp;
        uint price0Cumulative;
        uint price1Cumulative;
    }
    
    uint public minKeep = 150e18;

    modifier locker() {
        require(LK3R.isMinLocker(msg.sender, minKeep, 0, 0), "::isLocker: locker is not registered");
        _;
    }

    modifier upkeep() {
        uint _gasUsed = gasleft();
        require(LK3R.isMinLocker(msg.sender, minKeep, 0, 0), "::isLocker: locker is not registered");
        _;
        uint _received = LK3R.LK3RH().getQuoteLimit(_gasUsed.sub(gasleft()));
        LK3R.receipt(address(LK3R), address(this), _received);
        _received = _swap(_received);
        msg.sender.transfer(_received);
    }

    address public governance;
    address public pendingGovernance;
    
    function setMinKeep(uint _keep) external {
        require(msg.sender == governance, "setGovernance: !gov");
        minKeep = _keep;
    }

    /**
     * @notice Allows governance to change governance (for future upgradability)
     * @param _governance new governance address to set
     */
    function setGovernance(address _governance) external {
        require(msg.sender == governance, "setGovernance: !gov");
        pendingGovernance = _governance;
    }

    /**
     * @notice Allows pendingGovernance to accept their role as governance (protection pattern)
     */
    function acceptGovernance() external {
        require(msg.sender == pendingGovernance, "acceptGovernance: !pendingGov");
        governance = pendingGovernance;
    }

    ILock3r public constant LK3R = ILock3r(0xe3f3869dDD41C23Eff3630F58E5bFA584C770D67);
    WETH9 public constant WETH = WETH9(0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2);
    IUniswapV2Router public constant UNI = IUniswapV2Router(0x7a250d5630B4cF539739dF2C5dAcb4c659F2488D);

    address public constant factory = 0x5C69bEe701ef814a2B6a3EDD4B1652CB9cc5aA6f;
    // this is redundant with granularity and windowSize, but stored for gas savings & informational purposes.
    uint public constant periodSize = 1800;

    address[] internal _pairs;
    mapping(address => bool) internal _known;

    function pairs() external view returns (address[] memory) {
        return _pairs;
    }

    mapping(address => Observation[]) public observations;
    
    function observationLength(address pair) external view returns (uint) {
        return observations[pair].length;
    }
    
    function pairFor(address tokenA, address tokenB) external pure returns (address) {
        return UniswapV2Library.pairFor(factory, tokenA, tokenB);
    }
    
    function pairForWETH(address tokenA) external pure returns (address) {
        return UniswapV2Library.pairFor(factory, tokenA, address(WETH));
    }

    constructor() public {
        governance = msg.sender;
    }

    function updatePair(address pair) external locker returns (bool) {
        return _update(pair);
    }

    function update(address tokenA, address tokenB) external locker returns (bool) {
        address pair = UniswapV2Library.pairFor(factory, tokenA, tokenB);
        return _update(pair);
    }

    function add(address tokenA, address tokenB) external {
        require(msg.sender == governance, "UniswapV2Oracle::add: !gov");
        address pair = UniswapV2Library.pairFor(factory, tokenA, tokenB);
        require(!_known[pair], "known");
        _known[pair] = true;
        _pairs.push(pair);

        (uint price0Cumulative, uint price1Cumulative,) = UniswapV2OracleLibrary.currentCumulativePrices(pair);
        observations[pair].push(Observation(block.timestamp, price0Cumulative, price1Cumulative));
    }

    function work() public upkeep {
        bool worked = _updateAll();
        require(worked, "UniswapV2Oracle: !work");
    }

    function workForFree() public locker {
        bool worked = _updateAll();
        require(worked, "UniswapV2Oracle: !work");
    }
    
    function lastObservation(address pair) public view returns (Observation memory) {
        return observations[pair][observations[pair].length-1];
    }

    function _updateAll() internal returns (bool updated) {
        for (uint i = 0; i < _pairs.length; i++) {
            if (_update(_pairs[i])) {
                updated = true;
            }
        }
    }

    function updateFor(uint i, uint length) external locker returns (bool updated) {
        for (; i < length; i++) {
            if (_update(_pairs[i])) {
                updated = true;
            }
        }
    }

    function workable(address pair) public view returns (bool) {
        return (block.timestamp - lastObservation(pair).timestamp) > periodSize;
    }

    function workable() external view returns (bool) {
        for (uint i = 0; i < _pairs.length; i++) {
            if (workable(_pairs[i])) {
                return true;
            }
        }
        return false;
    }

    function _update(address pair) internal returns (bool) {
        // we only want to commit updates once per period (i.e. windowSize / granularity)
        Observation memory _point = lastObservation(pair);
        uint timeElapsed = block.timestamp - _point.timestamp;
        if (timeElapsed > periodSize) {
            (uint price0Cumulative, uint price1Cumulative,) = UniswapV2OracleLibrary.currentCumulativePrices(pair);
            observations[pair].push(Observation(block.timestamp, price0Cumulative, price1Cumulative));
            return true;
        }
        return false;
    }

    function computeAmountOut(
        uint priceCumulativeStart, uint priceCumulativeEnd,
        uint timeElapsed, uint amountIn
    ) private pure returns (uint amountOut) {
        // overflow is desired.
        FixedPoint.uq112x112 memory priceAverage = FixedPoint.uq112x112(
            uint224((priceCumulativeEnd - priceCumulativeStart) / timeElapsed)
        );
        amountOut = priceAverage.mul(amountIn).decode144();
    }

    function _valid(address pair, uint age) internal view returns (bool) {
        return (block.timestamp - lastObservation(pair).timestamp) <= age;
    }

    function current(address tokenIn, uint amountIn, address tokenOut) external view returns (uint amountOut) {
        address pair = UniswapV2Library.pairFor(factory, tokenIn, tokenOut);
        require(_valid(pair, periodSize.mul(2)), "UniswapV2Oracle::quote: stale prices");
        (address token0,) = UniswapV2Library.sortTokens(tokenIn, tokenOut);

        Observation memory _observation = lastObservation(pair);
        (uint price0Cumulative, uint price1Cumulative,) = UniswapV2OracleLibrary.currentCumulativePrices(pair);
        if (block.timestamp == _observation.timestamp) {
            _observation = observations[pair][observations[pair].length-2];
        }
        
        uint timeElapsed = block.timestamp - _observation.timestamp;
        timeElapsed = timeElapsed == 0 ? 1 : timeElapsed;
        if (token0 == tokenIn) {
            return computeAmountOut(_observation.price0Cumulative, price0Cumulative, timeElapsed, amountIn);
        } else {
            return computeAmountOut(_observation.price1Cumulative, price1Cumulative, timeElapsed, amountIn);
        }
    }

    function quote(address tokenIn, uint amountIn, address tokenOut, uint granularity) external view returns (uint amountOut) {
        address pair = UniswapV2Library.pairFor(factory, tokenIn, tokenOut);
        require(_valid(pair, periodSize.mul(granularity)), "UniswapV2Oracle::quote: stale prices");
        (address token0,) = UniswapV2Library.sortTokens(tokenIn, tokenOut);

        uint priceAverageCumulative = 0;
        uint length = observations[pair].length-1;
        uint i = length.sub(granularity);


        uint nextIndex = 0;
        if (token0 == tokenIn) {
            for (; i < length; i++) {
                nextIndex = i+1;
                priceAverageCumulative += computeAmountOut(
                    observations[pair][i].price0Cumulative,
                    observations[pair][nextIndex].price0Cumulative, 
                    observations[pair][nextIndex].timestamp - observations[pair][i].timestamp, amountIn);
            }
        } else {
            for (; i < length; i++) {
                nextIndex = i+1;
                priceAverageCumulative += computeAmountOut(
                    observations[pair][i].price1Cumulative,
                    observations[pair][nextIndex].price1Cumulative, 
                    observations[pair][nextIndex].timestamp - observations[pair][i].timestamp, amountIn);
            }
        }
        return priceAverageCumulative.div(granularity);
    }
    
    function prices(address tokenIn, uint amountIn, address tokenOut, uint points) external view returns (uint[] memory) {
        return sample(tokenIn, amountIn, tokenOut, points, 1);
    }
    
    function sample(address tokenIn, uint amountIn, address tokenOut, uint points, uint window) public view returns (uint[] memory) {
        address pair = UniswapV2Library.pairFor(factory, tokenIn, tokenOut);
        (address token0,) = UniswapV2Library.sortTokens(tokenIn, tokenOut);
        uint[] memory _prices = new uint[](points);
        
        uint length = observations[pair].length-1;
        uint i = length.sub(points * window);
        uint nextIndex = 0;
        uint index = 0;
        
        if (token0 == tokenIn) {
            for (; i < length; i+=window) {
                nextIndex = i + window;
                _prices[index] = computeAmountOut(
                    observations[pair][i].price0Cumulative,
                    observations[pair][nextIndex].price0Cumulative, 
                    observations[pair][nextIndex].timestamp - observations[pair][i].timestamp, amountIn);
                index = index + 1;
            }
        } else {
            for (; i < length; i+=window) {
                nextIndex = i + window;
                _prices[index] = computeAmountOut(
                    observations[pair][i].price1Cumulative,
                    observations[pair][nextIndex].price1Cumulative, 
                    observations[pair][nextIndex].timestamp - observations[pair][i].timestamp, amountIn);
                index = index + 1;
            }
        }
        return _prices;
    }
    
    function hourly(address tokenIn, uint amountIn, address tokenOut, uint points) external view returns (uint[] memory) {
        return sample(tokenIn, amountIn, tokenOut, points, 2);
    }
    
    function daily(address tokenIn, uint amountIn, address tokenOut, uint points) external view returns (uint[] memory) {
        return sample(tokenIn, amountIn, tokenOut, points, 48);
    }
    
    function weekly(address tokenIn, uint amountIn, address tokenOut, uint points) external view returns (uint[] memory) {
        return sample(tokenIn, amountIn, tokenOut, points, 336);
    }
    
    function realizedVolatility(address tokenIn, uint amountIn, address tokenOut, uint points, uint window) external view returns (uint) {
        return stddev(sample(tokenIn, amountIn, tokenOut, points, window));
    }
    
    function realizedVolatilityHourly(address tokenIn, uint amountIn, address tokenOut) external view returns (uint) {
        return stddev(sample(tokenIn, amountIn, tokenOut, 1, 2));
    }
    
    function realizedVolatilityDaily(address tokenIn, uint amountIn, address tokenOut) external view returns (uint) {
        return stddev(sample(tokenIn, amountIn, tokenOut, 1, 48));
    }
    
    function realizedVolatilityWeekly(address tokenIn, uint amountIn, address tokenOut) external view returns (uint) {
        return stddev(sample(tokenIn, amountIn, tokenOut, 1, 336));
    }
    
    /**
     * @dev sqrt calculates the square root of a given number x
     * @dev for precision into decimals the number must first
     * @dev be multiplied by the precision factor desired
     * @param x uint256 number for the calculation of square root
     */
    function sqrt(uint256 x) public pure returns (uint256) {
        uint256 c = (x + 1) / 2;
        uint256 b = x;
        while (c < b) {
            b = c;
            c = (x / c + c) / 2;
        }
        return b;
    }
    
    /**
     * @dev stddev calculates the standard deviation for an array of integers
     * @dev precision is the same as sqrt above meaning for higher precision
     * @dev the decimal place must be moved prior to passing the params
     * @param numbers uint[] array of numbers to be used in calculation
     */
    function stddev(uint[] memory numbers) public pure returns (uint256 sd) {
        uint sum = 0;
        for(uint i = 0; i < numbers.length; i++) {
            sum += numbers[i];
        }
        uint256 mean = sum / numbers.length;        // Integral value; float not supported in Solidity
        sum = 0;
        uint i;
        for(i = 0; i < numbers.length; i++) {
            sum += (numbers[i] - mean) ** 2;
        }
        sd = sqrt(sum / (numbers.length - 1));      //Integral value; float not supported in Solidity
        return sd;
    }
    
    
    /**
     * @dev blackScholesEstimate calculates a rough price estimate for an ATM option
     * @dev input parameters should be transformed prior to being passed to the function
     * @dev so as to remove decimal places otherwise results will be far less accurate
     * @param _vol uint256 volatility of the underlying converted to remove decimals
     * @param _underlying uint256 price of the underlying asset
     * @param _time uint256 days to expiration in years multiplied to remove decimals
     */
    function blackScholesEstimate(
        uint256 _vol,
        uint256 _underlying,
        uint256 _time
    ) public pure returns (uint256 estimate) {
        estimate = 40 * _vol * _underlying * sqrt(_time);
        return estimate;
    }
    
    /**
     * @dev fromReturnsBSestimate first calculates the stddev of an array of price returns
     * @dev then uses that as the volatility param for the blackScholesEstimate
     * @param _numbers uint256[] array of price returns for volatility calculation
     * @param _underlying uint256 price of the underlying asset
     * @param _time uint256 days to expiration in years multiplied to remove decimals
     */
    function retBasedBlackScholesEstimate(
        uint256[] memory _numbers,
        uint256 _underlying,
        uint256 _time
    ) public pure {
        uint _vol = stddev(_numbers);
        blackScholesEstimate(_vol, _underlying, _time);
    }
    
    receive() external payable {}
    
    function _swap(uint _amount) internal returns (uint) {
        LK3R.approve(address(UNI), _amount);
        
        address[] memory path = new address[](2);
        path[0] = address(LK3R);
        path[1] = address(WETH);

        uint[] memory amounts = UNI.swapExactTokensForTokens(_amount, uint256(0), path, address(this), now.add(1800));
        WETH.withdraw(amounts[1]);
        return amounts[1];
    }
}