// File: contracts/AloePoolCapped.sol



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

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "./AloePool.sol";

contract AloePoolCapped is AloePool {
    using SafeERC20 for IERC20;

    address public immutable MULTISIG;
    uint256 public maxTotalSupply = 100000000000000000000;

    constructor(address predictions, address multisig) AloePool(predictions) {
        MULTISIG = multisig;
    }

    modifier restricted() {
        require(msg.sender == MULTISIG, "Not authorized");
        _;
    }

    function deposit(
        uint256 amount0Max,
        uint256 amount1Max,
        uint256 amount0Min,
        uint256 amount1Min
    )
        public
        override
        lock
        returns (
            uint256 shares,
            uint256 amount0,
            uint256 amount1
        )
    {
        (shares, amount0, amount1) = super.deposit(amount0Max, amount1Max, amount0Min, amount1Min);
        require(totalSupply() <= maxTotalSupply, "Aloe: Pool already full");
    }

    /**
     * @notice Removes tokens accidentally sent to this vault.
     */
    function sweep(
        IERC20 token,
        uint256 amount,
        address to
    ) external restricted {
        require(token != TOKEN0 && token != TOKEN1, "Not sweepable");
        token.safeTransfer(to, amount);
    }

    /**
     * @notice Used to change deposit cap for a guarded launch or to ensure
     * vault doesn't grow too large relative to the UNI_POOL. Cap is on total
     * supply rather than amounts of TOKEN0 and TOKEN1 as those amounts
     * fluctuate naturally over time.
     */
    function setMaxTotalSupply(uint256 _maxTotalSupply) external restricted {
        maxTotalSupply = _maxTotalSupply;
    }

    function toggleRebalances() external restricted {
        allowRebalances = !allowRebalances;
    }

    function setK(uint48 _K) external restricted {
        K = _K;
    }
}

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



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender, address recipient, uint256 amount) external returns (bool);

    /**
     * @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);
}

// File: @openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../../../utils/Address.sol";

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using Address for address;

    function safeTransfer(IERC20 token, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transfer.selector, to, value));
    }

    function safeTransferFrom(IERC20 token, address from, address to, uint256 value) internal {
        _callOptionalReturn(token, abi.encodeWithSelector(token.transferFrom.selector, from, to, value));
    }

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        // solhint-disable-next-line max-line-length
        require((value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender) + value;
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        unchecked {
            uint256 oldAllowance = token.allowance(address(this), spender);
            require(oldAllowance >= value, "SafeERC20: decreased allowance below zero");
            uint256 newAllowance = oldAllowance - value;
            _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
        }
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) { // Return data is optional
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// File: contracts/AloePool.sol



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

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol";

import "./libraries/FullMath.sol";
import "./libraries/LiquidityAmounts.sol";
import "./libraries/Math.sol";
import "./libraries/TickMath.sol";

import "./interfaces/IAloePredictions.sol";
import "./interfaces/IAloePredictionsImmutables.sol";

import "./AloePoolERC20.sol";
import "./UniswapMinter.sol";

uint256 constant TWO_144 = 2**144;

struct PDF {
    bool isInverted;
    uint176 mean;
    uint128 sigmaL;
    uint128 sigmaU;
}

contract AloePool is AloePoolERC20, UniswapMinter {
    using SafeERC20 for IERC20;

    event Deposit(address indexed sender, uint256 shares, uint256 amount0, uint256 amount1);

    event Withdraw(address indexed sender, uint256 shares, uint256 amount0, uint256 amount1);

    event Snapshot(int24 tick, uint256 totalAmount0, uint256 totalAmount1, uint256 totalSupply);

    /// @dev The number of standard deviations to +/- from mean when setting position bounds
    uint48 public K = 5;

    /// @dev The number of seconds to look back when computing current price. Makes manipulation harder
    uint32 public constant CURRENT_PRICE_WINDOW = 360;

    /// @dev The predictions market that provides this pool with next-price distribution data
    IAloePredictions public immutable PREDICTIONS;

    /// @dev The most recent predictions market epoch during which this pool was rebalanced
    uint24 public epoch;

    /// @dev The elastic position stretches to accomodate unpredictable price movements
    Ticks public elastic;

    /// @dev The cushion position consumes leftover funds after `elastic` is stretched
    Ticks public cushion;

    /// @dev The excess position is made up of funds that didn't fit into `elastic` when rebalancing
    Ticks public excess;

    /// @dev The current statistics from prediction market (representing a probability density function)
    PDF public pdf;

    /// @dev Whether the pool had excess token0 as of the most recent rebalance
    bool public didHaveExcessToken0;

    /// @dev For reentrancy check
    bool private locked;

    bool public allowRebalances = true;

    modifier lock() {
        require(!locked, "Aloe: Locked");
        locked = true;
        _;
        locked = false;
    }

    constructor(address predictions)
        AloePoolERC20()
        UniswapMinter(IUniswapV3Pool(IAloePredictionsImmutables(predictions).UNI_POOL()))
    {
        PREDICTIONS = IAloePredictions(predictions);
    }

    /**
     * @notice Calculates the vault's total holdings of TOKEN0 and TOKEN1 - in
     * other words, how much of each token the vault would hold if it withdrew
     * all its liquidity from Uniswap.
     */
    function getReserves() public view returns (uint256 reserve0, uint256 reserve1) {
        reserve0 = TOKEN0.balanceOf(address(this));
        reserve1 = TOKEN1.balanceOf(address(this));
        uint256 temp0;
        uint256 temp1;
        (temp0, temp1) = _collectableAmountsAsOfLastPoke(elastic);
        reserve0 += temp0;
        reserve1 += temp1;
        (temp0, temp1) = _collectableAmountsAsOfLastPoke(cushion);
        reserve0 += temp0;
        reserve1 += temp1;
        (temp0, temp1) = _collectableAmountsAsOfLastPoke(excess);
        reserve0 += temp0;
        reserve1 += temp1;
    }

    function getNextElasticTicks() public view returns (Ticks memory) {
        // Define the window over which we want to fetch price
        uint32[] memory secondsAgos = new uint32[](2);
        secondsAgos[0] = CURRENT_PRICE_WINDOW;
        secondsAgos[1] = 0;

        // Fetch price and account for possible inversion
        (int56[] memory tickCumulatives, ) = UNI_POOL.observe(secondsAgos);
        uint176 price =
            TickMath.getSqrtRatioAtTick(
                int24((tickCumulatives[1] - tickCumulatives[0]) / int56(uint56(CURRENT_PRICE_WINDOW)))
            );
        if (pdf.isInverted) price = type(uint160).max / price;
        price = uint176(FullMath.mulDiv(price, price, TWO_144));

        return _getNextElasticTicks(price, pdf.mean, pdf.sigmaL, pdf.sigmaU, pdf.isInverted);
    }

    function _getNextElasticTicks(
        uint176 price,
        uint176 mean,
        uint128 sigmaL,
        uint128 sigmaU,
        bool areInverted
    ) private view returns (Ticks memory ticks) {
        uint48 n;
        uint176 widthL;
        uint176 widthU;

        if (price < mean) {
            n = uint48((mean - price) / sigmaL);
            widthL = uint176(sigmaL) * uint176(K + n);
            widthU = uint176(sigmaU) * uint176(K);
        } else {
            n = uint48((price - mean) / sigmaU);
            widthL = uint176(sigmaL) * uint176(K);
            widthU = uint176(sigmaU) * uint176(K + n);
        }

        uint176 l = mean > widthL ? mean - widthL : 1;
        uint176 u = mean < type(uint176).max - widthU ? mean + widthU : type(uint176).max;
        uint160 sqrtPriceX96;

        if (areInverted) {
            sqrtPriceX96 = uint160(uint256(type(uint128).max) / Math.sqrt(u << 80));
            ticks.lower = TickMath.getTickAtSqrtRatio(sqrtPriceX96);
            sqrtPriceX96 = uint160(uint256(type(uint128).max) / Math.sqrt(l << 80));
            ticks.upper = TickMath.getTickAtSqrtRatio(sqrtPriceX96);
        } else {
            sqrtPriceX96 = uint160(Math.sqrt(l << 80) << 32);
            ticks.lower = TickMath.getTickAtSqrtRatio(sqrtPriceX96);
            sqrtPriceX96 = uint160(Math.sqrt(u << 80) << 32);
            ticks.upper = TickMath.getTickAtSqrtRatio(sqrtPriceX96);
        }
    }

    /**
     * @notice Deposits tokens in proportion to the vault's current holdings.
     * @dev These tokens sit in the vault and are not used for liquidity on
     * Uniswap until the next rebalance. Also note it's not necessary to check
     * if user manipulated price to deposit cheaper, as the value of range
     * orders can only by manipulated higher.
     * @dev LOCK MODIFIER IS APPLIED IN AloePoolCapped!!!
     * @param amount0Max Max amount of TOKEN0 to deposit
     * @param amount1Max Max amount of TOKEN1 to deposit
     * @param amount0Min Ensure `amount0` is greater than this
     * @param amount1Min Ensure `amount1` is greater than this
     * @return shares Number of shares minted
     * @return amount0 Amount of TOKEN0 deposited
     * @return amount1 Amount of TOKEN1 deposited
     */
    function deposit(
        uint256 amount0Max,
        uint256 amount1Max,
        uint256 amount0Min,
        uint256 amount1Min
    )
        public
        virtual
        returns (
            uint256 shares,
            uint256 amount0,
            uint256 amount1
        )
    {
        require(amount0Max != 0 || amount1Max != 0, "Aloe: 0 deposit");

        _uniswapPoke(elastic);
        _uniswapPoke(cushion);
        _uniswapPoke(excess);

        (shares, amount0, amount1) = _computeLPShares(amount0Max, amount1Max);
        require(shares != 0, "Aloe: 0 shares");
        require(amount0 >= amount0Min, "Aloe: amount0 too low");
        require(amount1 >= amount1Min, "Aloe: amount1 too low");

        // Pull in tokens from sender
        if (amount0 != 0) TOKEN0.safeTransferFrom(msg.sender, address(this), amount0);
        if (amount1 != 0) TOKEN1.safeTransferFrom(msg.sender, address(this), amount1);

        // Mint shares
        _mint(msg.sender, shares);
        emit Deposit(msg.sender, shares, amount0, amount1);
    }

    /// @dev Calculates the largest possible `amount0` and `amount1` such that
    /// they're in the same proportion as total amounts, but not greater than
    /// `amount0Max` and `amount1Max` respectively.
    function _computeLPShares(uint256 amount0Max, uint256 amount1Max)
        internal
        view
        returns (
            uint256 shares,
            uint256 amount0,
            uint256 amount1
        )
    {
        uint256 totalSupply = totalSupply();
        (uint256 reserve0, uint256 reserve1) = getReserves();

        // If total supply > 0, pool can't be empty
        assert(totalSupply == 0 || reserve0 != 0 || reserve1 != 0);

        if (totalSupply == 0) {
            // For first deposit, just use the amounts desired
            amount0 = amount0Max;
            amount1 = amount1Max;
            shares = amount0 > amount1 ? amount0 : amount1; // max
        } else if (reserve0 == 0) {
            amount1 = amount1Max;
            shares = FullMath.mulDiv(amount1, totalSupply, reserve1);
        } else if (reserve1 == 0) {
            amount0 = amount0Max;
            shares = FullMath.mulDiv(amount0, totalSupply, reserve0);
        } else {
            amount0 = FullMath.mulDiv(amount1Max, reserve0, reserve1);

            if (amount0 < amount0Max) {
                amount1 = amount1Max;
                shares = FullMath.mulDiv(amount1, totalSupply, reserve1);
            } else {
                amount0 = amount0Max;
                amount1 = FullMath.mulDiv(amount0, reserve1, reserve0);
                shares = FullMath.mulDiv(amount0, totalSupply, reserve0);
            }
        }
    }

    /**
     * @notice Withdraws tokens in proportion to the vault's holdings.
     * @param shares Shares burned by sender
     * @param amount0Min Revert if resulting `amount0` is smaller than this
     * @param amount1Min Revert if resulting `amount1` is smaller than this
     * @return amount0 Amount of TOKEN0 sent to recipient
     * @return amount1 Amount of TOKEN1 sent to recipient
     */
    function withdraw(
        uint256 shares,
        uint256 amount0Min,
        uint256 amount1Min
    ) external lock returns (uint256 amount0, uint256 amount1) {
        require(shares != 0, "Aloe: 0 shares");
        uint256 totalSupply = totalSupply() + 1;

        // Calculate token amounts proportional to unused balances
        amount0 = FullMath.mulDiv(TOKEN0.balanceOf(address(this)), shares, totalSupply);
        amount1 = FullMath.mulDiv(TOKEN1.balanceOf(address(this)), shares, totalSupply);

        // Withdraw proportion of liquidity from Uniswap pool
        uint256 temp0;
        uint256 temp1;
        (temp0, temp1) = _uniswapExitFraction(shares, totalSupply, elastic);
        amount0 += temp0;
        amount1 += temp1;
        (temp0, temp1) = _uniswapExitFraction(shares, totalSupply, cushion);
        amount0 += temp0;
        amount1 += temp1;
        (temp0, temp1) = _uniswapExitFraction(shares, totalSupply, excess);
        amount0 += temp0;
        amount1 += temp1;

        // Check constraints
        require(amount0 >= amount0Min, "Aloe: amount0 too low");
        require(amount1 >= amount1Min, "Aloe: amount1 too low");

        // Transfer tokens
        if (amount0 != 0) TOKEN0.safeTransfer(msg.sender, amount0);
        if (amount1 != 0) TOKEN1.safeTransfer(msg.sender, amount1);

        // Burn shares
        _burn(msg.sender, shares);
        emit Withdraw(msg.sender, shares, amount0, amount1);
    }

    /// @dev Withdraws share of liquidity in a range from Uniswap pool. All fee earnings
    /// will be collected and left unused afterwards
    function _uniswapExitFraction(
        uint256 numerator,
        uint256 denominator,
        Ticks memory ticks
    ) internal returns (uint256 amount0, uint256 amount1) {
        assert(numerator < denominator);

        (uint128 liquidity, , , , ) = _position(ticks);
        liquidity = uint128(FullMath.mulDiv(liquidity, numerator, denominator));

        uint256 earned0;
        uint256 earned1;
        (amount0, amount1, earned0, earned1) = _uniswapExit(ticks, liquidity);

        // Add share of fees
        amount0 += FullMath.mulDiv(earned0, numerator, denominator);
        amount1 += FullMath.mulDiv(earned1, numerator, denominator);
    }

    function rebalance() external lock {
        require(allowRebalances, "Disabled");
        uint24 _epoch = PREDICTIONS.epoch();
        require(_epoch > epoch, "Aloe: Too early");

        // Update P.D.F from prediction market
        (pdf.isInverted, pdf.mean, pdf.sigmaL, pdf.sigmaU) = PREDICTIONS.current();
        epoch = _epoch;

        int24 tickSpacing = TICK_SPACING;
        (uint160 sqrtPriceX96, int24 tick, , , , , ) = UNI_POOL.slot0();

        // Exit all current Uniswap positions
        {
            (uint128 liquidityElastic, , , , ) = _position(elastic);
            (uint128 liquidityCushion, , , , ) = _position(cushion);
            (uint128 liquidityExcess, , , , ) = _position(excess);
            _uniswapExit(elastic, liquidityElastic);
            _uniswapExit(cushion, liquidityCushion);
            _uniswapExit(excess, liquidityExcess);
        }

        // Emit snapshot to record balances and supply
        uint256 balance0 = TOKEN0.balanceOf(address(this));
        uint256 balance1 = TOKEN1.balanceOf(address(this));
        emit Snapshot(tick, balance0, balance1, totalSupply());

        // Place elastic order on Uniswap
        Ticks memory elasticNew = _coerceTicksToSpacing(getNextElasticTicks());
        uint128 liquidity = _liquidityForAmounts(elasticNew, sqrtPriceX96, balance0, balance1);
        delete lastMintedAmount0;
        delete lastMintedAmount1;
        _uniswapEnter(elasticNew, liquidity);
        elastic = elasticNew;

        // Place excess order on Uniswap
        Ticks memory active = _coerceTicksToSpacing(Ticks(tick, tick));
        if (lastMintedAmount0 * balance1 < lastMintedAmount1 * balance0) {
            _placeExcessUpper(active, TOKEN0.balanceOf(address(this)), tickSpacing);
            didHaveExcessToken0 = true;
        } else {
            _placeExcessLower(active, TOKEN1.balanceOf(address(this)), tickSpacing);
            didHaveExcessToken0 = false;
        }
    }

    function shouldStretch() external view returns (bool) {
        Ticks memory elasticNew = _coerceTicksToSpacing(getNextElasticTicks());
        return elasticNew.lower != elastic.lower || elasticNew.upper != elastic.upper;
    }

    function stretch() external lock {
        require(allowRebalances, "Disabled");
        int24 tickSpacing = TICK_SPACING;
        (uint160 sqrtPriceX96, int24 tick, , , , , ) = UNI_POOL.slot0();

        // Check if stretching is necessary
        Ticks memory elasticNew = _coerceTicksToSpacing(getNextElasticTicks());
        require(elasticNew.lower != elastic.lower || elasticNew.upper != elastic.upper, "Aloe: Already stretched");

        // Exit previous elastic and cushion, and place as much value as possible in new elastic
        (uint256 elastic0, uint256 elastic1, , , uint256 available0, uint256 available1) =
            _exit2Enter1(sqrtPriceX96, elastic, cushion, elasticNew);
        elastic = elasticNew;

        // Place new cushion
        Ticks memory active = _coerceTicksToSpacing(Ticks(tick, tick));
        if (lastMintedAmount0 * elastic1 < lastMintedAmount1 * elastic0) {
            _placeCushionUpper(active, available0, tickSpacing);
        } else {
            _placeCushionLower(active, available1, tickSpacing);
        }
    }

    function snipe() external lock {
        require(allowRebalances, "Disabled");
        int24 tickSpacing = TICK_SPACING;
        (uint160 sqrtPriceX96, int24 tick, , , , uint8 feeProtocol, ) = UNI_POOL.slot0();

        (
            uint256 excess0,
            uint256 excess1,
            uint256 maxReward0,
            uint256 maxReward1,
            uint256 available0,
            uint256 available1
        ) = _exit2Enter1(sqrtPriceX96, excess, cushion, elastic);

        Ticks memory active = _coerceTicksToSpacing(Ticks(tick, tick));
        uint128 reward = UNI_FEE;

        if (didHaveExcessToken0) {
            // Reward caller
            if (feeProtocol >> 4 != 0) reward -= UNI_FEE / (feeProtocol >> 4);
            reward = (uint128(excess1) * reward) / 1e6;
            assert(reward <= maxReward1);
            if (reward != 0) TOKEN1.safeTransfer(msg.sender, reward);

            // Replace excess and cushion positions
            if (excess0 >= available0) {
                // We converted so much token0 to token1 that the cushion has to go
                // on the other side now
                _placeExcessUpper(active, available0, tickSpacing);
                _placeCushionLower(active, available1, tickSpacing);
            } else {
                // Both excess and cushion still have token0 to eat through
                _placeExcessUpper(active, excess0, tickSpacing);
                _placeCushionUpper(active, available0 - excess0, tickSpacing);
            }
        } else {
            // Reward caller
            if (feeProtocol % 16 != 0) reward -= UNI_FEE / (feeProtocol % 16);
            reward = (uint128(excess0) * reward) / 1e6;
            assert(reward <= maxReward0);
            if (reward != 0) TOKEN0.safeTransfer(msg.sender, reward);

            // Replace excess and cushion positions
            if (excess1 >= available1) {
                // We converted so much token1 to token0 that the cushion has to go
                // on the other side now
                _placeExcessLower(active, available1, tickSpacing);
                _placeCushionUpper(active, available0, tickSpacing);
            } else {
                // Both excess and cushion still have token1 to eat through
                _placeExcessLower(active, excess1, tickSpacing);
                _placeCushionLower(active, available1 - excess1, tickSpacing);
            }
        }
    }

    /// @dev Exits positions a and b, and moves as much value as possible to position c.
    /// Position a must have non-zero liquidity.
    function _exit2Enter1(
        uint160 sqrtPriceX96,
        Ticks memory a,
        Ticks memory b,
        Ticks memory c
    )
        private
        returns (
            uint256 a0,
            uint256 a1,
            uint256 aEarned0,
            uint256 aEarned1,
            uint256 available0,
            uint256 available1
        )
    {
        // Exit position A
        (uint128 liquidity, , , , ) = _position(a);
        require(liquidity != 0, "Aloe: Expected liquidity");
        (a0, a1, aEarned0, aEarned1) = _uniswapExit(a, liquidity);

        // Exit position B if it exists
        uint256 b0;
        uint256 b1;
        (liquidity, , , , ) = _position(b);
        if (liquidity != 0) {
            (b0, b1, , ) = _uniswapExit(b, liquidity);
        }

        // Add to position c
        available0 = a0 + b0;
        available1 = a1 + b1;
        liquidity = _liquidityForAmounts(c, sqrtPriceX96, available0, available1);
        delete lastMintedAmount0;
        delete lastMintedAmount1;
        _uniswapEnter(c, liquidity);

        unchecked {
            available0 = available0 > lastMintedAmount0 ? available0 - lastMintedAmount0 : 0;
            available1 = available1 > lastMintedAmount1 ? available1 - lastMintedAmount1 : 0;
        }
    }

    function _placeCushionLower(
        Ticks memory active,
        uint256 balance1,
        int24 tickSpacing
    ) private {
        Ticks memory _cushion;
        (_cushion.lower, _cushion.upper) = (elastic.lower, active.lower);
        if (_cushion.lower == _cushion.upper) _cushion.lower -= tickSpacing;
        _uniswapEnter(_cushion, _liquidityForAmount1(_cushion, balance1));
        cushion = _cushion;
    }

    function _placeCushionUpper(
        Ticks memory active,
        uint256 balance0,
        int24 tickSpacing
    ) private {
        Ticks memory _cushion;
        (_cushion.lower, _cushion.upper) = (active.upper, elastic.upper);
        if (_cushion.lower == _cushion.upper) _cushion.upper += tickSpacing;
        _uniswapEnter(_cushion, _liquidityForAmount0(_cushion, balance0));
        cushion = _cushion;
    }

    function _placeExcessLower(
        Ticks memory active,
        uint256 balance1,
        int24 tickSpacing
    ) private {
        Ticks memory _excess;
        (_excess.lower, _excess.upper) = (active.lower - tickSpacing, active.lower);
        _uniswapEnter(_excess, _liquidityForAmount1(_excess, balance1));
        excess = _excess;
    }

    function _placeExcessUpper(
        Ticks memory active,
        uint256 balance0,
        int24 tickSpacing
    ) private {
        Ticks memory _excess;
        (_excess.lower, _excess.upper) = (active.upper, active.upper + tickSpacing);
        _uniswapEnter(_excess, _liquidityForAmount0(_excess, balance0));
        excess = _excess;
    }

    function _coerceTicksToSpacing(Ticks memory ticks) private view returns (Ticks memory ticksCoerced) {
        ticksCoerced.lower =
            ticks.lower -
            (ticks.lower < 0 ? TICK_SPACING + (ticks.lower % TICK_SPACING) : ticks.lower % TICK_SPACING);
        ticksCoerced.upper =
            ticks.upper +
            (ticks.upper < 0 ? -ticks.upper % TICK_SPACING : TICK_SPACING - (ticks.upper % TICK_SPACING));
        assert(ticksCoerced.lower <= ticks.lower);
        assert(ticksCoerced.upper >= ticks.upper);
    }
}

// File: @openzeppelin/contracts/utils/Address.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        // solhint-disable-next-line no-inline-assembly
        assembly { size := extcodesize(account) }
        return size > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (bool success, ) = recipient.call{ value: amount }("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

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

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

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

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

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.call{ value: value }(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data, string memory errorMessage) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

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

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data, string memory errorMessage) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(bool success, bytes memory returndata, string memory errorMessage) private pure returns(bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: @uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import './pool/IUniswapV3PoolImmutables.sol';
import './pool/IUniswapV3PoolState.sol';
import './pool/IUniswapV3PoolDerivedState.sol';
import './pool/IUniswapV3PoolActions.sol';
import './pool/IUniswapV3PoolOwnerActions.sol';
import './pool/IUniswapV3PoolEvents.sol';

/// @title The interface for a Uniswap V3 Pool
/// @notice A Uniswap pool facilitates swapping and automated market making between any two assets that strictly conform
/// to the ERC20 specification
/// @dev The pool interface is broken up into many smaller pieces
interface IUniswapV3Pool is
    IUniswapV3PoolImmutables,
    IUniswapV3PoolState,
    IUniswapV3PoolDerivedState,
    IUniswapV3PoolActions,
    IUniswapV3PoolOwnerActions,
    IUniswapV3PoolEvents
{

}

// File: contracts/libraries/FullMath.sol



// SPDX-License-Identifier: MIT
pragma solidity >=0.4.0;

/// @title Contains 512-bit math functions
/// @notice Facilitates multiplication and division that can have overflow of an intermediate value without any loss of precision
/// @dev Handles "phantom overflow" i.e., allows multiplication and division where an intermediate value overflows 256 bits
library FullMath {
    /// @notice Calculates floor(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv
    function mulDiv(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = a * b
            // Compute the product mod 2**256 and mod 2**256 - 1
            // then 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(a, b, not(0))
                prod0 := mul(a, b)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division
            if (prod1 == 0) {
                require(denominator > 0);
                assembly {
                    result := div(prod0, denominator)
                }
                return result;
            }

            // Make sure the result is less than 2**256.
            // Also prevents denominator == 0
            require(denominator > prod1);

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

            // Make division exact by subtracting the remainder from [prod1 prod0]
            // Compute remainder using mulmod
            uint256 remainder;
            assembly {
                remainder := mulmod(a, b, denominator)
            }
            // Subtract 256 bit number from 512 bit number
            assembly {
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator
            // Compute largest power of two divisor of denominator.
            // Always >= 1.
            // https://ethereum.stackexchange.com/a/96646
            uint256 twos = denominator & (~denominator + 1);
            // Divide denominator by power of two
            assembly {
                denominator := div(denominator, twos)
            }

            // Divide [prod1 prod0] by the factors of two
            assembly {
                prod0 := div(prod0, twos)
            }
            // Shift in bits from prod1 into prod0. For this we need
            // to flip `twos` such that it is 2**256 / twos.
            // If twos is zero, then it becomes one
            assembly {
                twos := add(div(sub(0, twos), twos), 1)
            }
            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
            // correct for four bits. That is, denominator * inv = 1 mod 2**4
            uint256 inv = (3 * denominator) ^ 2;
            // Now use 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.
            inv *= 2 - denominator * inv; // inverse mod 2**8
            inv *= 2 - denominator * inv; // inverse mod 2**16
            inv *= 2 - denominator * inv; // inverse mod 2**32
            inv *= 2 - denominator * inv; // inverse mod 2**64
            inv *= 2 - denominator * inv; // inverse mod 2**128
            inv *= 2 - denominator * inv; // 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 precoditions 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 * inv;
            return result;
        }
    }

    /// @notice Calculates ceil(a×b÷denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
    /// @param a The multiplicand
    /// @param b The multiplier
    /// @param denominator The divisor
    /// @return result The 256-bit result
    function mulDivRoundingUp(
        uint256 a,
        uint256 b,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        result = mulDiv(a, b, denominator);
        if (mulmod(a, b, denominator) > 0) {
            require(result < type(uint256).max);
            result++;
        }
    }

    /// @dev https://medium.com/wicketh/mathemagic-full-multiply-27650fec525d
    function mul512(uint256 a, uint256 b) internal pure returns (uint256 r0, uint256 r1) {
        assembly {
            let mm := mulmod(a, b, not(0))
            r0 := mul(a, b)
            r1 := sub(sub(mm, r0), lt(mm, r0))
        }
    }

    /// @dev Like `mul512`, but multiply a number by itself
    function square512(uint256 a) internal pure returns (uint256 r0, uint256 r1) {
        assembly {
            let mm := mulmod(a, a, not(0))
            r0 := mul(a, a)
            r1 := sub(sub(mm, r0), lt(mm, r0))
        }
    }

    /// @dev https://github.com/hifi-finance/prb-math/blob/main/contracts/PRBMathCommon.sol
    function log2floor(uint256 x) internal pure returns (uint256 msb) {
        unchecked {
            if (x >= 2**128) {
                x >>= 128;
                msb += 128;
            }
            if (x >= 2**64) {
                x >>= 64;
                msb += 64;
            }
            if (x >= 2**32) {
                x >>= 32;
                msb += 32;
            }
            if (x >= 2**16) {
                x >>= 16;
                msb += 16;
            }
            if (x >= 2**8) {
                x >>= 8;
                msb += 8;
            }
            if (x >= 2**4) {
                x >>= 4;
                msb += 4;
            }
            if (x >= 2**2) {
                x >>= 2;
                msb += 2;
            }
            if (x >= 2**1) {
                // No need to shift x any more.
                msb += 1;
            }
        }
    }

    /// @dev https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogDeBruijn
    function log2ceil(uint256 x) internal pure returns (uint256 y) {
        assembly {
            let arg := x
            x := sub(x, 1)
            x := or(x, div(x, 0x02))
            x := or(x, div(x, 0x04))
            x := or(x, div(x, 0x10))
            x := or(x, div(x, 0x100))
            x := or(x, div(x, 0x10000))
            x := or(x, div(x, 0x100000000))
            x := or(x, div(x, 0x10000000000000000))
            x := or(x, div(x, 0x100000000000000000000000000000000))
            x := add(x, 1)
            let m := mload(0x40)
            mstore(m, 0xf8f9cbfae6cc78fbefe7cdc3a1793dfcf4f0e8bbd8cec470b6a28a7a5a3e1efd)
            mstore(add(m, 0x20), 0xf5ecf1b3e9debc68e1d9cfabc5997135bfb7a7a3938b7b606b5b4b3f2f1f0ffe)
            mstore(add(m, 0x40), 0xf6e4ed9ff2d6b458eadcdf97bd91692de2d4da8fd2d0ac50c6ae9a8272523616)
            mstore(add(m, 0x60), 0xc8c0b887b0a8a4489c948c7f847c6125746c645c544c444038302820181008ff)
            mstore(add(m, 0x80), 0xf7cae577eec2a03cf3bad76fb589591debb2dd67e0aa9834bea6925f6a4a2e0e)
            mstore(add(m, 0xa0), 0xe39ed557db96902cd38ed14fad815115c786af479b7e83247363534337271707)
            mstore(add(m, 0xc0), 0xc976c13bb96e881cb166a933a55e490d9d56952b8d4e801485467d2362422606)
            mstore(add(m, 0xe0), 0x753a6d1b65325d0c552a4d1345224105391a310b29122104190a110309020100)
            mstore(0x40, add(m, 0x100))
            let magic := 0x818283848586878898a8b8c8d8e8f929395969799a9b9d9e9faaeb6bedeeff
            let shift := 0x100000000000000000000000000000000000000000000000000000000000000
            let a := div(mul(x, magic), shift)
            y := div(mload(add(m, sub(255, a))), shift)
            y := add(y, mul(256, gt(arg, 0x8000000000000000000000000000000000000000000000000000000000000000)))
        }
    }
}

// File: contracts/libraries/LiquidityAmounts.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

import "./FixedPoint96.sol";
import "./FullMath.sol";

/// @title Liquidity amount functions
/// @notice Provides functions for computing liquidity amounts from token amounts and prices
library LiquidityAmounts {
    /// @notice Downcasts uint256 to uint128
    /// @param x The uint258 to be downcasted
    /// @return y The passed value, downcasted to uint128
    function toUint128(uint256 x) private pure returns (uint128 y) {
        require((y = uint128(x)) == x);
    }

    /// @notice Computes the amount of liquidity received for a given amount of token0 and price range
    /// @dev Calculates amount0 * (sqrt(upper) * sqrt(lower)) / (sqrt(upper) - sqrt(lower))
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount0 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount0(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        uint256 intermediate = FullMath.mulDiv(sqrtRatioAX96, sqrtRatioBX96, FixedPoint96.Q96);
        return toUint128(FullMath.mulDiv(amount0, intermediate, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the amount of liquidity received for a given amount of token1 and price range
    /// @dev Calculates amount1 / (sqrt(upper) - sqrt(lower)).
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount1 The amount1 being sent in
    /// @return liquidity The amount of returned liquidity
    function getLiquidityForAmount1(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);
        return toUint128(FullMath.mulDiv(amount1, FixedPoint96.Q96, sqrtRatioBX96 - sqrtRatioAX96));
    }

    /// @notice Computes the maximum amount of liquidity received for a given amount of token0, token1, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param amount0 The amount of token0 being sent in
    /// @param amount1 The amount of token1 being sent in
    /// @return liquidity The maximum amount of liquidity received
    function getLiquidityForAmounts(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128 liquidity) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            liquidity = getLiquidityForAmount0(sqrtRatioAX96, sqrtRatioBX96, amount0);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            uint128 liquidity0 = getLiquidityForAmount0(sqrtRatioX96, sqrtRatioBX96, amount0);
            uint128 liquidity1 = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioX96, amount1);

            liquidity = liquidity0 < liquidity1 ? liquidity0 : liquidity1;
        } else {
            liquidity = getLiquidityForAmount1(sqrtRatioAX96, sqrtRatioBX96, amount1);
        }
    }

    /// @notice Computes the amount of token0 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    function getAmount0ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return
            FullMath.mulDiv(
                uint256(liquidity) << FixedPoint96.RESOLUTION,
                sqrtRatioBX96 - sqrtRatioAX96,
                sqrtRatioBX96
            ) / sqrtRatioAX96;
    }

    /// @notice Computes the amount of token1 for a given amount of liquidity and a price range
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount1 The amount of token1
    function getAmount1ForLiquidity(
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        return FullMath.mulDiv(liquidity, sqrtRatioBX96 - sqrtRatioAX96, FixedPoint96.Q96);
    }

    /// @notice Computes the token0 and token1 value for a given amount of liquidity, the current
    /// pool prices and the prices at the tick boundaries
    /// @param sqrtRatioX96 A sqrt price representing the current pool prices
    /// @param sqrtRatioAX96 A sqrt price representing the first tick boundary
    /// @param sqrtRatioBX96 A sqrt price representing the second tick boundary
    /// @param liquidity The liquidity being valued
    /// @return amount0 The amount of token0
    /// @return amount1 The amount of token1
    function getAmountsForLiquidity(
        uint160 sqrtRatioX96,
        uint160 sqrtRatioAX96,
        uint160 sqrtRatioBX96,
        uint128 liquidity
    ) internal pure returns (uint256 amount0, uint256 amount1) {
        if (sqrtRatioAX96 > sqrtRatioBX96) (sqrtRatioAX96, sqrtRatioBX96) = (sqrtRatioBX96, sqrtRatioAX96);

        if (sqrtRatioX96 <= sqrtRatioAX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        } else if (sqrtRatioX96 < sqrtRatioBX96) {
            amount0 = getAmount0ForLiquidity(sqrtRatioX96, sqrtRatioBX96, liquidity);
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioX96, liquidity);
        } else {
            amount1 = getAmount1ForLiquidity(sqrtRatioAX96, sqrtRatioBX96, liquidity);
        }
    }
}

// File: contracts/libraries/Math.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

library Math {
    // babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
    function sqrt(uint256 y) internal pure returns (uint256 z) {
        unchecked {
            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/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Math library for computing sqrt prices from ticks and vice versa
/// @notice Computes sqrt price for ticks of size 1.0001, i.e. sqrt(1.0001^tick) as fixed point Q64.96 numbers. Supports
/// prices between 2**-128 and 2**128
library TickMath {
    /// @dev The minimum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**-128
    int24 internal constant MIN_TICK = -887272;
    /// @dev The maximum tick that may be passed to #getSqrtRatioAtTick computed from log base 1.0001 of 2**128
    int24 internal constant MAX_TICK = -MIN_TICK;

    /// @dev The minimum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MIN_TICK)
    uint160 internal constant MIN_SQRT_RATIO = 4295128739;
    /// @dev The maximum value that can be returned from #getSqrtRatioAtTick. Equivalent to getSqrtRatioAtTick(MAX_TICK)
    uint160 internal constant MAX_SQRT_RATIO = 1461446703485210103287273052203988822378723970342;

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
        uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
        require(absTick <= uint256(uint24(MAX_TICK)), "T");

        uint256 ratio = absTick & 0x1 != 0 ? 0xfffcb933bd6fad37aa2d162d1a594001 : 0x100000000000000000000000000000000;
        if (absTick & 0x2 != 0) ratio = (ratio * 0xfff97272373d413259a46990580e213a) >> 128;
        if (absTick & 0x4 != 0) ratio = (ratio * 0xfff2e50f5f656932ef12357cf3c7fdcc) >> 128;
        if (absTick & 0x8 != 0) ratio = (ratio * 0xffe5caca7e10e4e61c3624eaa0941cd0) >> 128;
        if (absTick & 0x10 != 0) ratio = (ratio * 0xffcb9843d60f6159c9db58835c926644) >> 128;
        if (absTick & 0x20 != 0) ratio = (ratio * 0xff973b41fa98c081472e6896dfb254c0) >> 128;
        if (absTick & 0x40 != 0) ratio = (ratio * 0xff2ea16466c96a3843ec78b326b52861) >> 128;
        if (absTick & 0x80 != 0) ratio = (ratio * 0xfe5dee046a99a2a811c461f1969c3053) >> 128;
        if (absTick & 0x100 != 0) ratio = (ratio * 0xfcbe86c7900a88aedcffc83b479aa3a4) >> 128;
        if (absTick & 0x200 != 0) ratio = (ratio * 0xf987a7253ac413176f2b074cf7815e54) >> 128;
        if (absTick & 0x400 != 0) ratio = (ratio * 0xf3392b0822b70005940c7a398e4b70f3) >> 128;
        if (absTick & 0x800 != 0) ratio = (ratio * 0xe7159475a2c29b7443b29c7fa6e889d9) >> 128;
        if (absTick & 0x1000 != 0) ratio = (ratio * 0xd097f3bdfd2022b8845ad8f792aa5825) >> 128;
        if (absTick & 0x2000 != 0) ratio = (ratio * 0xa9f746462d870fdf8a65dc1f90e061e5) >> 128;
        if (absTick & 0x4000 != 0) ratio = (ratio * 0x70d869a156d2a1b890bb3df62baf32f7) >> 128;
        if (absTick & 0x8000 != 0) ratio = (ratio * 0x31be135f97d08fd981231505542fcfa6) >> 128;
        if (absTick & 0x10000 != 0) ratio = (ratio * 0x9aa508b5b7a84e1c677de54f3e99bc9) >> 128;
        if (absTick & 0x20000 != 0) ratio = (ratio * 0x5d6af8dedb81196699c329225ee604) >> 128;
        if (absTick & 0x40000 != 0) ratio = (ratio * 0x2216e584f5fa1ea926041bedfe98) >> 128;
        if (absTick & 0x80000 != 0) ratio = (ratio * 0x48a170391f7dc42444e8fa2) >> 128;

        if (tick > 0) ratio = type(uint256).max / ratio;

        // this divides by 1<<32 rounding up to go from a Q128.128 to a Q128.96.
        // we then downcast because we know the result always fits within 160 bits due to our tick input constraint
        // we round up in the division so getTickAtSqrtRatio of the output price is always consistent
        sqrtPriceX96 = uint160((ratio >> 32) + (ratio % (1 << 32) == 0 ? 0 : 1));
    }

    /// @notice Calculates the greatest tick value such that getRatioAtTick(tick) <= ratio
    /// @dev Throws in case sqrtPriceX96 < MIN_SQRT_RATIO, as MIN_SQRT_RATIO is the lowest value getRatioAtTick may
    /// ever return.
    /// @param sqrtPriceX96 The sqrt ratio for which to compute the tick as a Q64.96
    /// @return tick The greatest tick for which the ratio is less than or equal to the input ratio
    function getTickAtSqrtRatio(uint160 sqrtPriceX96) internal pure returns (int24 tick) {
        // second inequality must be < because the price can never reach the price at the max tick
        require(sqrtPriceX96 >= MIN_SQRT_RATIO && sqrtPriceX96 < MAX_SQRT_RATIO, "R");
        uint256 ratio = uint256(sqrtPriceX96) << 32;

        uint256 r = ratio;
        uint256 msb = 0;

        assembly {
            let f := shl(7, gt(r, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(6, gt(r, 0xFFFFFFFFFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(5, gt(r, 0xFFFFFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(4, gt(r, 0xFFFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(3, gt(r, 0xFF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(2, gt(r, 0xF))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := shl(1, gt(r, 0x3))
            msb := or(msb, f)
            r := shr(f, r)
        }
        assembly {
            let f := gt(r, 0x1)
            msb := or(msb, f)
        }

        if (msb >= 128) r = ratio >> (msb - 127);
        else r = ratio << (127 - msb);

        int256 log_2 = (int256(msb) - 128) << 64;

        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(63, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(62, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(61, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(60, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(59, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(58, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(57, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(56, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(55, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(54, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(53, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(52, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(51, f))
            r := shr(f, r)
        }
        assembly {
            r := shr(127, mul(r, r))
            let f := shr(128, r)
            log_2 := or(log_2, shl(50, f))
        }

        int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

        int24 tickLow = int24((log_sqrt10001 - 3402992956809132418596140100660247210) >> 128);
        int24 tickHi = int24((log_sqrt10001 + 291339464771989622907027621153398088495) >> 128);

        tick = tickLow == tickHi ? tickLow : getSqrtRatioAtTick(tickHi) <= sqrtPriceX96 ? tickHi : tickLow;
    }
}

// File: contracts/interfaces/IAloePredictions.sol



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

import "./IAloePredictionsActions.sol";
import "./IAloePredictionsDerivedState.sol";
import "./IAloePredictionsEvents.sol";
import "./IAloePredictionsState.sol";

/// @title Aloe predictions market interface
/// @dev The interface is broken up into many smaller pieces
interface IAloePredictions is
    IAloePredictionsActions,
    IAloePredictionsDerivedState,
    IAloePredictionsEvents,
    IAloePredictionsState
{

}

// File: contracts/interfaces/IAloePredictionsImmutables.sol



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

interface IAloePredictionsImmutables {
    /// @dev The maximum number of proposals that should be aggregated
    function NUM_PROPOSALS_TO_AGGREGATE() external view returns (uint8);

    /// @dev The number of standard deviations to +/- from the mean when computing ground truth bounds
    function GROUND_TRUTH_STDDEV_SCALE() external view returns (uint256);

    /// @dev The minimum length of an epoch, in seconds. Epochs may be longer if no one calls `advance`
    function EPOCH_LENGTH_SECONDS() external view returns (uint32);

    /// @dev The ALOE token used for staking
    function ALOE() external view returns (address);

    /// @dev The Uniswap pair for which predictions should be made
    function UNI_POOL() external view returns (address);

    /// @dev The incentive vault to use for staking extras and `advance()` reward
    function INCENTIVE_VAULT() external view returns (address);
}

// File: contracts/AloePoolERC20.sol



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

import "@openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol";

contract AloePoolERC20 is ERC20Permit {
    constructor() ERC20Permit("Aloe V1") ERC20("Aloe V1", "ALOE-V1") {}
}

// File: contracts/UniswapMinter.sol



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

import "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";

import "@uniswap/v3-core/contracts/interfaces/callback/IUniswapV3MintCallback.sol";
import "@uniswap/v3-core/contracts/interfaces/IUniswapV3Pool.sol";

import "./libraries/LiquidityAmounts.sol";
import "./libraries/TickMath.sol";

import "./structs/Ticks.sol";

contract UniswapMinter is IUniswapV3MintCallback {
    using SafeERC20 for IERC20;

    IUniswapV3Pool public immutable UNI_POOL;

    uint24 public immutable UNI_FEE;

    int24 public immutable TICK_SPACING;

    IERC20 public immutable TOKEN0;

    IERC20 public immutable TOKEN1;

    uint256 internal lastMintedAmount0;

    uint256 internal lastMintedAmount1;

    constructor(IUniswapV3Pool uniPool) {
        UNI_POOL = uniPool;
        UNI_FEE = uniPool.fee();
        TICK_SPACING = uniPool.tickSpacing();
        TOKEN0 = IERC20(uniPool.token0());
        TOKEN1 = IERC20(uniPool.token1());
    }

    /// @dev Do zero-burns to poke the Uniswap pools so earned fees are updated
    function _uniswapPoke(Ticks memory ticks) internal {
        (uint128 liquidity, , , , ) = _position(ticks);
        if (liquidity == 0) return;
        UNI_POOL.burn(ticks.lower, ticks.upper, 0);
    }

    /// @dev Deposits liquidity in a range on the Uniswap pool.
    function _uniswapEnter(Ticks memory ticks, uint128 liquidity) internal {
        if (liquidity == 0) return;
        UNI_POOL.mint(address(this), ticks.lower, ticks.upper, liquidity, "");
    }

    /// @dev Withdraws liquidity from a range and collects all fees in the process.
    function _uniswapExit(Ticks memory ticks, uint128 liquidity)
        internal
        returns (
            uint256 burned0,
            uint256 burned1,
            uint256 earned0,
            uint256 earned1
        )
    {
        if (liquidity != 0) {
            (burned0, burned1) = UNI_POOL.burn(ticks.lower, ticks.upper, liquidity);
        }

        // Collect all owed tokens including earned fees
        (uint256 collected0, uint256 collected1) =
            UNI_POOL.collect(address(this), ticks.lower, ticks.upper, type(uint128).max, type(uint128).max);

        earned0 = collected0 - burned0;
        earned1 = collected1 - burned1;
    }

    /**
     * @notice Amounts of TOKEN0 and TOKEN1 held in vault's position. Includes
     * owed fees, except those accrued since last poke.
     */
    function _collectableAmountsAsOfLastPoke(Ticks memory ticks) public view returns (uint256, uint256) {
        (uint128 liquidity, , , uint128 earnable0, uint128 earnable1) = _position(ticks);
        (uint160 sqrtPriceX96, , , , , , ) = UNI_POOL.slot0();
        (uint256 burnable0, uint256 burnable1) = _amountsForLiquidity(ticks, liquidity, sqrtPriceX96);

        return (burnable0 + earnable0, burnable1 + earnable1);
    }

    /// @dev Wrapper around `IUniswapV3Pool.positions()`.
    function _position(Ticks memory ticks)
        internal
        view
        returns (
            uint128, // liquidity
            uint256, // feeGrowthInside0LastX128
            uint256, // feeGrowthInside1LastX128
            uint128, // tokensOwed0
            uint128 // tokensOwed1
        )
    {
        return UNI_POOL.positions(keccak256(abi.encodePacked(address(this), ticks.lower, ticks.upper)));
    }

    /// @dev Wrapper around `LiquidityAmounts.getAmountsForLiquidity()`.
    function _amountsForLiquidity(Ticks memory ticks, uint128 liquidity, uint160 sqrtPriceX96) internal pure returns (uint256, uint256) {
        return
            LiquidityAmounts.getAmountsForLiquidity(
                sqrtPriceX96,
                TickMath.getSqrtRatioAtTick(ticks.lower),
                TickMath.getSqrtRatioAtTick(ticks.upper),
                liquidity
            );
    }

    /// @dev Wrapper around `LiquidityAmounts.getLiquidityForAmounts()`.
    function _liquidityForAmounts(
        Ticks memory ticks,
        uint160 sqrtPriceX96,
        uint256 amount0,
        uint256 amount1
    ) internal pure returns (uint128) {
        return
            LiquidityAmounts.getLiquidityForAmounts(
                sqrtPriceX96,
                TickMath.getSqrtRatioAtTick(ticks.lower),
                TickMath.getSqrtRatioAtTick(ticks.upper),
                amount0,
                amount1
            );
    }

    /// @dev Wrapper around `LiquidityAmounts.getLiquidityForAmount0()`.
    function _liquidityForAmount0(Ticks memory ticks, uint256 amount0) internal pure returns (uint128) {
        return
            LiquidityAmounts.getLiquidityForAmount0(
                TickMath.getSqrtRatioAtTick(ticks.lower),
                TickMath.getSqrtRatioAtTick(ticks.upper),
                amount0
            );
    }

    /// @dev Wrapper around `LiquidityAmounts.getLiquidityForAmount1()`.
    function _liquidityForAmount1(Ticks memory ticks, uint256 amount1) internal pure returns (uint128) {
        return
            LiquidityAmounts.getLiquidityForAmount1(
                TickMath.getSqrtRatioAtTick(ticks.lower),
                TickMath.getSqrtRatioAtTick(ticks.upper),
                amount1
            );
    }

    /// @dev Callback for Uniswap V3 pool.
    function uniswapV3MintCallback(
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external override {
        require(msg.sender == address(UNI_POOL), "Fake callback");
        if (amount0 != 0) TOKEN0.safeTransfer(msg.sender, amount0);
        if (amount1 != 0) TOKEN1.safeTransfer(msg.sender, amount1);

        lastMintedAmount0 = amount0;
        lastMintedAmount1 = amount1;
    }
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolImmutables.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that never changes
/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values
interface IUniswapV3PoolImmutables {
    /// @notice The contract that deployed the pool, which must adhere to the IUniswapV3Factory interface
    /// @return The contract address
    function factory() external view returns (address);

    /// @notice The first of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token0() external view returns (address);

    /// @notice The second of the two tokens of the pool, sorted by address
    /// @return The token contract address
    function token1() external view returns (address);

    /// @notice The pool's fee in hundredths of a bip, i.e. 1e-6
    /// @return The fee
    function fee() external view returns (uint24);

    /// @notice The pool tick spacing
    /// @dev Ticks can only be used at multiples of this value, minimum of 1 and always positive
    /// e.g.: a tickSpacing of 3 means ticks can be initialized every 3rd tick, i.e., ..., -6, -3, 0, 3, 6, ...
    /// This value is an int24 to avoid casting even though it is always positive.
    /// @return The tick spacing
    function tickSpacing() external view returns (int24);

    /// @notice The maximum amount of position liquidity that can use any tick in the range
    /// @dev This parameter is enforced per tick to prevent liquidity from overflowing a uint128 at any point, and
    /// also prevents out-of-range liquidity from being used to prevent adding in-range liquidity to a pool
    /// @return The max amount of liquidity per tick
    function maxLiquidityPerTick() external view returns (uint128);
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that can change
/// @notice These methods compose the pool's state, and can change with any frequency including multiple times
/// per transaction
interface IUniswapV3PoolState {
    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas
    /// when accessed externally.
    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value
    /// tick The current tick of the pool, i.e. according to the last tick transition that was run.
    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick
    /// boundary.
    /// observationIndex The index of the last oracle observation that was written,
    /// observationCardinality The current maximum number of observations stored in the pool,
    /// observationCardinalityNext The next maximum number of observations, to be updated when the observation.
    /// feeProtocol The protocol fee for both tokens of the pool.
    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0
    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0()
        external
        view
        returns (
            uint160 sqrtPriceX96,
            int24 tick,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext,
            uint8 feeProtocol,
            bool unlocked
        );

    /// @notice The fee growth as a Q128.128 fees of token0 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal0X128() external view returns (uint256);

    /// @notice The fee growth as a Q128.128 fees of token1 collected per unit of liquidity for the entire life of the pool
    /// @dev This value can overflow the uint256
    function feeGrowthGlobal1X128() external view returns (uint256);

    /// @notice The amounts of token0 and token1 that are owed to the protocol
    /// @dev Protocol fees will never exceed uint128 max in either token
    function protocolFees() external view returns (uint128 token0, uint128 token1);

    /// @notice The currently in range liquidity available to the pool
    /// @dev This value has no relationship to the total liquidity across all ticks
    function liquidity() external view returns (uint128);

    /// @notice Look up information about a specific tick in the pool
    /// @param tick The tick to look up
    /// @return liquidityGross the total amount of position liquidity that uses the pool either as tick lower or
    /// tick upper,
    /// liquidityNet how much liquidity changes when the pool price crosses the tick,
    /// feeGrowthOutside0X128 the fee growth on the other side of the tick from the current tick in token0,
    /// feeGrowthOutside1X128 the fee growth on the other side of the tick from the current tick in token1,
    /// tickCumulativeOutside the cumulative tick value on the other side of the tick from the current tick
    /// secondsPerLiquidityOutsideX128 the seconds spent per liquidity on the other side of the tick from the current tick,
    /// secondsOutside the seconds spent on the other side of the tick from the current tick,
    /// initialized Set to true if the tick is initialized, i.e. liquidityGross is greater than 0, otherwise equal to false.
    /// Outside values can only be used if the tick is initialized, i.e. if liquidityGross is greater than 0.
    /// In addition, these values are only relative and must be used only in comparison to previous snapshots for
    /// a specific position.
    function ticks(int24 tick)
        external
        view
        returns (
            uint128 liquidityGross,
            int128 liquidityNet,
            uint256 feeGrowthOutside0X128,
            uint256 feeGrowthOutside1X128,
            int56 tickCumulativeOutside,
            uint160 secondsPerLiquidityOutsideX128,
            uint32 secondsOutside,
            bool initialized
        );

    /// @notice Returns 256 packed tick initialized boolean values. See TickBitmap for more information
    function tickBitmap(int16 wordPosition) external view returns (uint256);

    /// @notice Returns the information about a position by the position's key
    /// @param key The position's key is a hash of a preimage composed by the owner, tickLower and tickUpper
    /// @return _liquidity The amount of liquidity in the position,
    /// Returns feeGrowthInside0LastX128 fee growth of token0 inside the tick range as of the last mint/burn/poke,
    /// Returns feeGrowthInside1LastX128 fee growth of token1 inside the tick range as of the last mint/burn/poke,
    /// Returns tokensOwed0 the computed amount of token0 owed to the position as of the last mint/burn/poke,
    /// Returns tokensOwed1 the computed amount of token1 owed to the position as of the last mint/burn/poke
    function positions(bytes32 key)
        external
        view
        returns (
            uint128 _liquidity,
            uint256 feeGrowthInside0LastX128,
            uint256 feeGrowthInside1LastX128,
            uint128 tokensOwed0,
            uint128 tokensOwed1
        );

    /// @notice Returns data about a specific observation index
    /// @param index The element of the observations array to fetch
    /// @dev You most likely want to use #observe() instead of this method to get an observation as of some amount of time
    /// ago, rather than at a specific index in the array.
    /// @return blockTimestamp The timestamp of the observation,
    /// Returns tickCumulative the tick multiplied by seconds elapsed for the life of the pool as of the observation timestamp,
    /// Returns secondsPerLiquidityCumulativeX128 the seconds per in range liquidity for the life of the pool as of the observation timestamp,
    /// Returns initialized whether the observation has been initialized and the values are safe to use
    function observations(uint256 index)
        external
        view
        returns (
            uint32 blockTimestamp,
            int56 tickCumulative,
            uint160 secondsPerLiquidityCumulativeX128,
            bool initialized
        );
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolDerivedState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Pool state that is not stored
/// @notice Contains view functions to provide information about the pool that is computed rather than stored on the
/// blockchain. The functions here may have variable gas costs.
interface IUniswapV3PoolDerivedState {
    /// @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
    /// @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
    /// the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
    /// you must call it with secondsAgos = [3600, 0].
    /// @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
    /// log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
    /// @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
    /// @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
    /// @return secondsPerLiquidityCumulativeX128s Cumulative seconds per liquidity-in-range value as of each `secondsAgos` from the current block
    /// timestamp
    function observe(uint32[] calldata secondsAgos)
        external
        view
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);

    /// @notice Returns a snapshot of the tick cumulative, seconds per liquidity and seconds inside a tick range
    /// @dev Snapshots must only be compared to other snapshots, taken over a period for which a position existed.
    /// I.e., snapshots cannot be compared if a position is not held for the entire period between when the first
    /// snapshot is taken and the second snapshot is taken.
    /// @param tickLower The lower tick of the range
    /// @param tickUpper The upper tick of the range
    /// @return tickCumulativeInside The snapshot of the tick accumulator for the range
    /// @return secondsPerLiquidityInsideX128 The snapshot of seconds per liquidity for the range
    /// @return secondsInside The snapshot of seconds per liquidity for the range
    function snapshotCumulativesInside(int24 tickLower, int24 tickUpper)
        external
        view
        returns (
            int56 tickCumulativeInside,
            uint160 secondsPerLiquidityInsideX128,
            uint32 secondsInside
        );
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface IUniswapV3PoolActions {
    /// @notice Sets the initial price for the pool
    /// @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value
    /// @param sqrtPriceX96 the initial sqrt price of the pool as a Q64.96
    function initialize(uint160 sqrtPriceX96) external;

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @dev The caller of this method receives a callback in the form of IUniswapV3MintCallback#uniswapV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
    /// on tickLower, tickUpper, the amount of liquidity, and the current price.
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    /// @param data Any data that should be passed through to the callback
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Collects tokens owed to a position
    /// @dev Does not recompute fees earned, which must be done either via mint or burn of any amount of liquidity.
    /// Collect must be called by the position owner. To withdraw only token0 or only token1, amount0Requested or
    /// amount1Requested may be set to zero. To withdraw all tokens owed, caller may pass any value greater than the
    /// actual tokens owed, e.g. type(uint128).max. Tokens owed may be from accumulated swap fees or burned liquidity.
    /// @param recipient The address which should receive the fees collected
    /// @param tickLower The lower tick of the position for which to collect fees
    /// @param tickUpper The upper tick of the position for which to collect fees
    /// @param amount0Requested How much token0 should be withdrawn from the fees owed
    /// @param amount1Requested How much token1 should be withdrawn from the fees owed
    /// @return amount0 The amount of fees collected in token0
    /// @return amount1 The amount of fees collected in token1
    function collect(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);

    /// @notice Burn liquidity from the sender and account tokens owed for the liquidity to the position
    /// @dev Can be used to trigger a recalculation of fees owed to a position by calling with an amount of 0
    /// @dev Fees must be collected separately via a call to #collect
    /// @param tickLower The lower tick of the position for which to burn liquidity
    /// @param tickUpper The upper tick of the position for which to burn liquidity
    /// @param amount How much liquidity to burn
    /// @return amount0 The amount of token0 sent to the recipient
    /// @return amount1 The amount of token1 sent to the recipient
    function burn(
        int24 tickLower,
        int24 tickUpper,
        uint128 amount
    ) external returns (uint256 amount0, uint256 amount1);

    /// @notice Swap token0 for token1, or token1 for token0
    /// @dev The caller of this method receives a callback in the form of IUniswapV3SwapCallback#uniswapV3SwapCallback
    /// @param recipient The address to receive the output of the swap
    /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0
    /// @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
    /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
    /// value after the swap. If one for zero, the price cannot be greater than this value after the swap
    /// @param data Any data to be passed through to the callback
    /// @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
    /// @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Receive token0 and/or token1 and pay it back, plus a fee, in the callback
    /// @dev The caller of this method receives a callback in the form of IUniswapV3FlashCallback#uniswapV3FlashCallback
    /// @dev Can be used to donate underlying tokens pro-rata to currently in-range liquidity providers by calling
    /// with 0 amount{0,1} and sending the donation amount(s) from the callback
    /// @param recipient The address which will receive the token0 and token1 amounts
    /// @param amount0 The amount of token0 to send
    /// @param amount1 The amount of token1 to send
    /// @param data Any data to be passed through to the callback
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external;

    /// @notice Increase the maximum number of price and liquidity observations that this pool will store
    /// @dev This method is no-op if the pool already has an observationCardinalityNext greater than or equal to
    /// the input observationCardinalityNext.
    /// @param observationCardinalityNext The desired minimum number of observations for the pool to store
    function increaseObservationCardinalityNext(uint16 observationCardinalityNext) external;
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolOwnerActions.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Permissioned pool actions
/// @notice Contains pool methods that may only be called by the factory owner
interface IUniswapV3PoolOwnerActions {
    /// @notice Set the denominator of the protocol's % share of the fees
    /// @param feeProtocol0 new protocol fee for token0 of the pool
    /// @param feeProtocol1 new protocol fee for token1 of the pool
    function setFeeProtocol(uint8 feeProtocol0, uint8 feeProtocol1) external;

    /// @notice Collect the protocol fee accrued to the pool
    /// @param recipient The address to which collected protocol fees should be sent
    /// @param amount0Requested The maximum amount of token0 to send, can be 0 to collect fees in only token1
    /// @param amount1Requested The maximum amount of token1 to send, can be 0 to collect fees in only token0
    /// @return amount0 The protocol fee collected in token0
    /// @return amount1 The protocol fee collected in token1
    function collectProtocol(
        address recipient,
        uint128 amount0Requested,
        uint128 amount1Requested
    ) external returns (uint128 amount0, uint128 amount1);
}

// File: @uniswap/v3-core/contracts/interfaces/pool/IUniswapV3PoolEvents.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Events emitted by a pool
/// @notice Contains all events emitted by the pool
interface IUniswapV3PoolEvents {
    /// @notice Emitted exactly once by a pool when #initialize is first called on the pool
    /// @dev Mint/Burn/Swap cannot be emitted by the pool before Initialize
    /// @param sqrtPriceX96 The initial sqrt price of the pool, as a Q64.96
    /// @param tick The initial tick of the pool, i.e. log base 1.0001 of the starting price of the pool
    event Initialize(uint160 sqrtPriceX96, int24 tick);

    /// @notice Emitted when liquidity is minted for a given position
    /// @param sender The address that minted the liquidity
    /// @param owner The owner of the position and recipient of any minted liquidity
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity minted to the position range
    /// @param amount0 How much token0 was required for the minted liquidity
    /// @param amount1 How much token1 was required for the minted liquidity
    event Mint(
        address sender,
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted when fees are collected by the owner of a position
    /// @dev Collect events may be emitted with zero amount0 and amount1 when the caller chooses not to collect fees
    /// @param owner The owner of the position for which fees are collected
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount0 The amount of token0 fees collected
    /// @param amount1 The amount of token1 fees collected
    event Collect(
        address indexed owner,
        address recipient,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount0,
        uint128 amount1
    );

    /// @notice Emitted when a position's liquidity is removed
    /// @dev Does not withdraw any fees earned by the liquidity position, which must be withdrawn via #collect
    /// @param owner The owner of the position for which liquidity is removed
    /// @param tickLower The lower tick of the position
    /// @param tickUpper The upper tick of the position
    /// @param amount The amount of liquidity to remove
    /// @param amount0 The amount of token0 withdrawn
    /// @param amount1 The amount of token1 withdrawn
    event Burn(
        address indexed owner,
        int24 indexed tickLower,
        int24 indexed tickUpper,
        uint128 amount,
        uint256 amount0,
        uint256 amount1
    );

    /// @notice Emitted by the pool for any swaps between token0 and token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the output of the swap
    /// @param amount0 The delta of the token0 balance of the pool
    /// @param amount1 The delta of the token1 balance of the pool
    /// @param sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96
    /// @param liquidity The liquidity of the pool after the swap
    /// @param tick The log base 1.0001 of price of the pool after the swap
    event Swap(
        address indexed sender,
        address indexed recipient,
        int256 amount0,
        int256 amount1,
        uint160 sqrtPriceX96,
        uint128 liquidity,
        int24 tick
    );

    /// @notice Emitted by the pool for any flashes of token0/token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the tokens from flash
    /// @param amount0 The amount of token0 that was flashed
    /// @param amount1 The amount of token1 that was flashed
    /// @param paid0 The amount of token0 paid for the flash, which can exceed the amount0 plus the fee
    /// @param paid1 The amount of token1 paid for the flash, which can exceed the amount1 plus the fee
    event Flash(
        address indexed sender,
        address indexed recipient,
        uint256 amount0,
        uint256 amount1,
        uint256 paid0,
        uint256 paid1
    );

    /// @notice Emitted by the pool for increases to the number of observations that can be stored
    /// @dev observationCardinalityNext is not the observation cardinality until an observation is written at the index
    /// just before a mint/swap/burn.
    /// @param observationCardinalityNextOld The previous value of the next observation cardinality
    /// @param observationCardinalityNextNew The updated value of the next observation cardinality
    event IncreaseObservationCardinalityNext(
        uint16 observationCardinalityNextOld,
        uint16 observationCardinalityNextNew
    );

    /// @notice Emitted when the protocol fee is changed by the pool
    /// @param feeProtocol0Old The previous value of the token0 protocol fee
    /// @param feeProtocol1Old The previous value of the token1 protocol fee
    /// @param feeProtocol0New The updated value of the token0 protocol fee
    /// @param feeProtocol1New The updated value of the token1 protocol fee
    event SetFeeProtocol(uint8 feeProtocol0Old, uint8 feeProtocol1Old, uint8 feeProtocol0New, uint8 feeProtocol1New);

    /// @notice Emitted when the collected protocol fees are withdrawn by the factory owner
    /// @param sender The address that collects the protocol fees
    /// @param recipient The address that receives the collected protocol fees
    /// @param amount0 The amount of token0 protocol fees that is withdrawn
    /// @param amount0 The amount of token1 protocol fees that is withdrawn
    event CollectProtocol(address indexed sender, address indexed recipient, uint128 amount0, uint128 amount1);
}

// File: contracts/libraries/FixedPoint96.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.4.0;

/// @title FixedPoint96
/// @notice A library for handling binary fixed point numbers, see https://en.wikipedia.org/wiki/Q_(number_format)
/// @dev Used in SqrtPriceMath.sol
library FixedPoint96 {
    uint8 internal constant RESOLUTION = 96;
    uint256 internal constant Q96 = 0x1000000000000000000000000;
}

// File: contracts/interfaces/IAloePredictionsActions.sol



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

interface IAloePredictionsActions {
    /// @notice Advances the epoch no more than once per hour
    function advance() external;

    /**
     * @notice Allows users to submit proposals in `epoch`. These proposals specify aggregate position
     * in `epoch + 1` and adjusted stakes become claimable in `epoch + 2`
     * @param lower The Q128.48 price at the lower bound, unless `shouldInvertPrices`, in which case
     * this should be `1 / (priceAtUpperBound * 2 ** 16)`
     * @param upper The Q128.48 price at the upper bound, unless `shouldInvertPrices`, in which case
     * this should be `1 / (priceAtLowerBound * 2 ** 16)`
     * @param stake The amount of ALOE to stake on this proposal. Once submitted, you can't unsubmit!
     * @return key The unique ID of this proposal, used to update bounds and claim reward
     */
    function submitProposal(
        uint176 lower,
        uint176 upper,
        uint80 stake
    ) external returns (uint40 key);

    /**
     * @notice Allows users to update bounds of a proposal they submitted previously. This only
     * works if the epoch hasn't increased since submission
     * @param key The key of the proposal that should be updated
     * @param lower The Q128.48 price at the lower bound, unless `shouldInvertPrices`, in which case
     * this should be `1 / (priceAtUpperBound * 2 ** 16)`
     * @param upper The Q128.48 price at the upper bound, unless `shouldInvertPrices`, in which case
     * this should be `1 / (priceAtLowerBound * 2 ** 16)`
     */
    function updateProposal(
        uint40 key,
        uint176 lower,
        uint176 upper
    ) external;

    /**
     * @notice Allows users to reclaim ALOE that they staked in previous epochs, as long as
     * the epoch has ground truth information
     * @dev ALOE is sent to `proposal.source` not `msg.sender`, so anyone can trigger a claim
     * for anyone else
     * @param key The key of the proposal that should be judged and rewarded
     * @param extras An array of tokens for which extra incentives should be claimed
     */
    function claimReward(uint40 key, address[] calldata extras) external;
}

// File: contracts/interfaces/IAloePredictionsDerivedState.sol



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

import "../structs/Bounds.sol";

interface IAloePredictionsDerivedState {
    /**
     * @notice Statistics for the most recent crowdsourced probability density function, evaluated about current price
     * @return areInverted Whether the reported values are for inverted prices
     * @return mean Result of `computeMean()`
     * @return sigmaL The sqrt of the lower semivariance
     * @return sigmaU The sqrt of the upper semivariance
     */
    function current()
        external
        view
        returns (
            bool areInverted,
            uint176 mean,
            uint128 sigmaL,
            uint128 sigmaU
        );

    /// @notice The earliest time at which the epoch can end
    function epochExpectedEndTime() external view returns (uint32);

    /**
     * @notice Aggregates proposals in the previous `epoch`. Only the top `NUM_PROPOSALS_TO_AGGREGATE`, ordered by
     * stake, will be considered.
     * @return mean The mean of the crowdsourced probability density function (1st Raw Moment)
     */
    function computeMean() external view returns (uint176 mean);

    /**
     * @notice Aggregates proposals in the previous `epoch`. Only the top `NUM_PROPOSALS_TO_AGGREGATE`, ordered by
     * stake, will be considered.
     * @return lower The lower semivariance of the crowdsourced probability density function (2nd Central Moment, Lower)
     * @return upper The upper semivariance of the crowdsourced probability density function (2nd Central Moment, Upper)
     */
    function computeSemivariancesAbout(uint176 center) external view returns (uint256 lower, uint256 upper);

    /**
     * @notice Fetches Uniswap prices over 10 discrete intervals in the past hour. Computes mean and standard
     * deviation of these samples, and returns "ground truth" bounds that should enclose ~95% of trading activity
     * @return bounds The "ground truth" price range that will be used when computing rewards
     * @return shouldInvertPricesNext Whether proposals in the next epoch should be submitted with inverted bounds
     */
    function fetchGroundTruth() external view returns (Bounds memory bounds, bool shouldInvertPricesNext);

    /**
     * @notice Builds a memory array that can be passed to Uniswap V3's `observe` function to specify
     * intervals over which mean prices should be fetched
     * @return secondsAgos From how long ago each cumulative tick and liquidity value should be returned
     */
    function selectedOracleTimetable() external pure returns (uint32[] memory secondsAgos);
}

// File: contracts/interfaces/IAloePredictionsEvents.sol



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

interface IAloePredictionsEvents {
    event ProposalSubmitted(
        address indexed source,
        uint24 indexed epoch,
        uint40 key,
        uint176 lower,
        uint176 upper,
        uint80 stake
    );

    event ProposalUpdated(address indexed source, uint24 indexed epoch, uint40 key, uint176 lower, uint176 upper);

    event FetchedGroundTruth(uint176 lower, uint176 upper, bool didInvertPrices);

    event Advanced(uint24 epoch, uint32 epochStartTime);

    event ClaimedReward(address indexed recipient, uint24 indexed epoch, uint40 key, uint80 amount);
}

// File: contracts/interfaces/IAloePredictionsState.sol



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

import "../structs/EpochSummary.sol";
import "../structs/Proposal.sol";

interface IAloePredictionsState {
    /// @dev A mapping containing every proposal. These get deleted when claimed
    function proposals(uint40 key)
        external
        view
        returns (
            address source,
            uint24 submissionEpoch,
            uint176 lower,
            uint176 upper,
            uint80 stake
        );

    /// @dev The unique ID that will be assigned to the next submitted proposal
    function nextProposalKey() external view returns (uint40);

    /// @dev The current epoch. May increase up to once per hour. Never decreases
    function epoch() external view returns (uint24);

    /// @dev The time at which the current epoch started
    function epochStartTime() external view returns (uint32);

    /// @dev Whether new proposals should be submitted with inverted prices
    function shouldInvertPrices() external view returns (bool);

    /// @dev Whether proposals in `epoch - 1` were submitted with inverted prices
    function didInvertPrices() external view returns (bool);
}

// File: contracts/structs/Bounds.sol



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

struct Bounds {
    // Q128.48 price at tickLower of a Uniswap position
    uint176 lower;
    // Q128.48 price at tickUpper of a Uniswap position
    uint176 upper;
}

// File: contracts/structs/EpochSummary.sol



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

import "./Accumulators.sol";
import "./Bounds.sol";

struct EpochSummary {
    Bounds groundTruth;
    Accumulators accumulators;
}

// File: contracts/structs/Proposal.sol



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

struct Proposal {
    // The address that submitted the proposal
    address source;
    // The epoch in which the proposal was submitted
    uint24 epoch;
    // Q128.48 price at tickLower of proposed Uniswap position
    uint176 lower;
    // Q128.48 price at tickUpper of proposed Uniswap position
    uint176 upper;
    // The amount of ALOE held; fits in uint80 because max supply is 1000000 with 18 decimals
    uint80 stake;
}

// File: contracts/structs/Accumulators.sol



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

import "../libraries/UINT512.sol";

struct Accumulators {
    // The number of (proposals added - proposals removed) during the epoch
    uint40 proposalCount;
    // The total amount of ALOE staked; fits in uint80 because max supply is 1000000 with 18 decimals
    uint80 stakeTotal;
    // For the remaining properties, read comments as if `stake`, `lower`, and `upper` are NumPy arrays.
    // Each index represents a proposal, e.g. proposal 0 would be `(stake[0], lower[0], upper[0])`

    // `(stake * (upper - lower)).sum()`
    uint256 stake0thMomentRaw;
    // `lower.sum()`
    uint256 sumOfLowerBounds;
    // `(stake * lower).sum()`
    uint256 sumOfLowerBoundsWeighted;
    // `upper.sum()`
    uint256 sumOfUpperBounds;
    // `(stake * upper).sum()`
    uint256 sumOfUpperBoundsWeighted;
    // `(np.square(lower) + np.square(upper)).sum()`
    UINT512 sumOfSquaredBounds;
    // `(stake * (np.square(lower) + np.square(upper))).sum()`
    UINT512 sumOfSquaredBoundsWeighted;
}

// File: contracts/libraries/UINT512.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity ^0.8.0;

import "./FullMath.sol";

struct UINT512 {
    // Least significant bits
    uint256 LS;
    // Most significant bits
    uint256 MS;
}

library UINT512Math {
    /// @dev Adds an (LS, MS) pair in place. Assumes result fits in uint512
    function iadd(
        UINT512 storage self,
        uint256 LS,
        uint256 MS
    ) internal {
        unchecked {
            if (self.LS > type(uint256).max - LS) {
                self.LS = addmod(self.LS, LS, type(uint256).max);
                self.MS += 1 + MS;
            } else {
                self.LS += LS;
                self.MS += MS;
            }
        }
    }

    /// @dev Adds an (LS, MS) pair to self. Assumes result fits in uint512
    function add(
        UINT512 memory self,
        uint256 LS,
        uint256 MS
    ) internal pure returns (uint256, uint256) {
        unchecked {
            return
                (self.LS > type(uint256).max - LS)
                    ? (addmod(self.LS, LS, type(uint256).max), self.MS + MS + 1)
                    : (self.LS + LS, self.MS + MS);
        }
    }

    /// @dev Subtracts an (LS, MS) pair in place. Assumes result > 0
    function isub(
        UINT512 storage self,
        uint256 LS,
        uint256 MS
    ) internal {
        unchecked {
            if (self.LS < LS) {
                self.LS = type(uint256).max + self.LS - LS;
                self.MS -= 1 + MS;
            } else {
                self.LS -= LS;
                self.MS -= MS;
            }
        }
    }

    /// @dev Subtracts an (LS, MS) pair from self. Assumes result > 0
    function sub(
        UINT512 memory self,
        uint256 LS,
        uint256 MS
    ) internal pure returns (uint256, uint256) {
        unchecked {
            return (self.LS < LS) ? (type(uint256).max + self.LS - LS, self.MS - MS - 1) : (self.LS - LS, self.MS - MS);
        }
    }

    /// @dev Multiplies self by single uint256, s. Assumes result fits in uint512
    function muls(UINT512 memory self, uint256 s) internal pure returns (uint256, uint256) {
        unchecked {
            self.MS *= s;
            (self.LS, s) = FullMath.mul512(self.LS, s);
            return (self.LS, self.MS + s);
        }
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-ERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./draft-IERC20Permit.sol";
import "../ERC20.sol";
import "../../../utils/cryptography/draft-EIP712.sol";
import "../../../utils/cryptography/ECDSA.sol";
import "../../../utils/Counters.sol";

/**
 * @dev Implementation of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on `{IERC20-approve}`, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 *
 * _Available since v3.4._
 */
abstract contract ERC20Permit is ERC20, IERC20Permit, EIP712 {
    using Counters for Counters.Counter;

    mapping (address => Counters.Counter) private _nonces;

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private immutable _PERMIT_TYPEHASH = keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");

    /**
     * @dev Initializes the {EIP712} domain separator using the `name` parameter, and setting `version` to `"1"`.
     *
     * It's a good idea to use the same `name` that is defined as the ERC20 token name.
     */
    constructor(string memory name) EIP712(name, "1") {
    }

    /**
     * @dev See {IERC20Permit-permit}.
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) public virtual override {
        // solhint-disable-next-line not-rely-on-time
        require(block.timestamp <= deadline, "ERC20Permit: expired deadline");

        bytes32 structHash = keccak256(
            abi.encode(
                _PERMIT_TYPEHASH,
                owner,
                spender,
                value,
                _useNonce(owner),
                deadline
            )
        );

        bytes32 hash = _hashTypedDataV4(structHash);

        address signer = ECDSA.recover(hash, v, r, s);
        require(signer == owner, "ERC20Permit: invalid signature");

        _approve(owner, spender, value);
    }

    /**
     * @dev See {IERC20Permit-nonces}.
     */
    function nonces(address owner) public view virtual override returns (uint256) {
        return _nonces[owner].current();
    }

    /**
     * @dev See {IERC20Permit-DOMAIN_SEPARATOR}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view override returns (bytes32) {
        return _domainSeparatorV4();
    }

    /**
     * @dev "Consume a nonce": return the current value and increment.
     *
     * _Available since v4.1._
     */
    function _useNonce(address owner) internal virtual returns (uint256 current) {
        Counters.Counter storage nonce = _nonces[owner];
        current = nonce.current();
        nonce.increment();
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/draft-IERC20Permit.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC20 Permit extension allowing approvals to be made via signatures, as defined in
 * https://eips.ethereum.org/EIPS/eip-2612[EIP-2612].
 *
 * Adds the {permit} method, which can be used to change an account's ERC20 allowance (see {IERC20-allowance}) by
 * presenting a message signed by the account. By not relying on {IERC20-approve}, the token holder account doesn't
 * need to send a transaction, and thus is not required to hold Ether at all.
 */
interface IERC20Permit {
    /**
     * @dev Sets `value` as the allowance of `spender` over ``owner``'s tokens,
     * given ``owner``'s signed approval.
     *
     * IMPORTANT: The same issues {IERC20-approve} has related to transaction
     * ordering also apply here.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `deadline` must be a timestamp in the future.
     * - `v`, `r` and `s` must be a valid `secp256k1` signature from `owner`
     * over the EIP712-formatted function arguments.
     * - the signature must use ``owner``'s current nonce (see {nonces}).
     *
     * For more information on the signature format, see the
     * https://eips.ethereum.org/EIPS/eip-2612#specification[relevant EIP
     * section].
     */
    function permit(address owner, address spender, uint256 value, uint256 deadline, uint8 v, bytes32 r, bytes32 s) external;

    /**
     * @dev Returns the current nonce for `owner`. This value must be
     * included whenever a signature is generated for {permit}.
     *
     * Every successful call to {permit} increases ``owner``'s nonce by one. This
     * prevents a signature from being used multiple times.
     */
    function nonces(address owner) external view returns (uint256);

    /**
     * @dev Returns the domain separator used in the encoding of the signature for {permit}, as defined by {EIP712}.
     */
    // solhint-disable-next-line func-name-mixedcase
    function DOMAIN_SEPARATOR() external view returns (bytes32);
}

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



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./IERC20.sol";
import "./extensions/IERC20Metadata.sol";
import "../../utils/Context.sol";

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin guidelines: functions revert instead
 * of returning `false` on failure. This behavior is nonetheless conventional
 * and does not conflict with the expectations of ERC20 applications.
 *
 * Additionally, an {Approval} event is emitted on calls to {transferFrom}.
 * This allows applications to reconstruct the allowance for all accounts just
 * by listening to said events. Other implementations of the EIP may not emit
 * these events, as it isn't required by the specification.
 *
 * Finally, the non-standard {decreaseAllowance} and {increaseAllowance}
 * functions have been added to mitigate the well-known issues around setting
 * allowances. See {IERC20-approve}.
 */
contract ERC20 is Context, IERC20, IERC20Metadata {
    mapping (address => uint256) private _balances;

    mapping (address => mapping (address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;

    /**
     * @dev Sets the values for {name} and {symbol}.
     *
     * The defaut value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor (string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev Returns the name of the token.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5,05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

    /**
     * @dev See {IERC20-totalSupply}.
     */
    function totalSupply() public view virtual override returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev See {IERC20-balanceOf}.
     */
    function balanceOf(address account) public view virtual override returns (uint256) {
        return _balances[account];
    }

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, amount);
        return true;
    }

    /**
     * @dev See {IERC20-allowance}.
     */
    function allowance(address owner, address spender) public view virtual override returns (uint256) {
        return _allowances[owner][spender];
    }

    /**
     * @dev See {IERC20-approve}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), spender, amount);
        return true;
    }

    /**
     * @dev See {IERC20-transferFrom}.
     *
     * Emits an {Approval} event indicating the updated allowance. This is not
     * required by the EIP. See the note at the beginning of {ERC20}.
     *
     * Requirements:
     *
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address sender, address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);

        uint256 currentAllowance = _allowances[sender][_msgSender()];
        require(currentAllowance >= amount, "ERC20: transfer amount exceeds allowance");
        _approve(sender, _msgSender(), currentAllowance - amount);

        return true;
    }

    /**
     * @dev Atomically increases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function increaseAllowance(address spender, uint256 addedValue) public virtual returns (bool) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender] + addedValue);
        return true;
    }

    /**
     * @dev Atomically decreases the allowance granted to `spender` by the caller.
     *
     * This is an alternative to {approve} that can be used as a mitigation for
     * problems described in {IERC20-approve}.
     *
     * Emits an {Approval} event indicating the updated allowance.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     * - `spender` must have allowance for the caller of at least
     * `subtractedValue`.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public virtual returns (bool) {
        uint256 currentAllowance = _allowances[_msgSender()][spender];
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        _approve(_msgSender(), spender, currentAllowance - subtractedValue);

        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is internal function is equivalent to {transfer}, and can be used to
     * e.g. implement automatic token fees, slashing mechanisms, etc.
     *
     * Emits a {Transfer} event.
     *
     * Requirements:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(address sender, address recipient, uint256 amount) internal virtual {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(sender, recipient, amount);

        uint256 senderBalance = _balances[sender];
        require(senderBalance >= amount, "ERC20: transfer amount exceeds balance");
        _balances[sender] = senderBalance - amount;
        _balances[recipient] += amount;

        emit Transfer(sender, recipient, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        _balances[account] += amount;
        emit Transfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        _balances[account] = accountBalance - amount;
        _totalSupply -= amount;

        emit Transfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(address owner, address spender, uint256 amount) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be to transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(address from, address to, uint256 amount) internal virtual { }
}

// File: @openzeppelin/contracts/utils/cryptography/draft-EIP712.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "./ECDSA.sol";

/**
 * @dev https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.
 *
 * The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
 * thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
 * they need in their contracts using a combination of `abi.encode` and `keccak256`.
 *
 * This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
 * scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
 * ({_hashTypedDataV4}).
 *
 * The implementation of the domain separator was designed to be as efficient as possible while still properly updating
 * the chain id to protect against replay attacks on an eventual fork of the chain.
 *
 * NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
 * https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].
 *
 * _Available since v3.4._
 */
abstract contract EIP712 {
    /* solhint-disable var-name-mixedcase */
    // Cache the domain separator as an immutable value, but also store the chain id that it corresponds to, in order to
    // invalidate the cached domain separator if the chain id changes.
    bytes32 private immutable _CACHED_DOMAIN_SEPARATOR;
    uint256 private immutable _CACHED_CHAIN_ID;

    bytes32 private immutable _HASHED_NAME;
    bytes32 private immutable _HASHED_VERSION;
    bytes32 private immutable _TYPE_HASH;
    /* solhint-enable var-name-mixedcase */

    /**
     * @dev Initializes the domain separator and parameter caches.
     *
     * The meaning of `name` and `version` is specified in
     * https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:
     *
     * - `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
     * - `version`: the current major version of the signing domain.
     *
     * NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
     * contract upgrade].
     */
    constructor(string memory name, string memory version) {
        bytes32 hashedName = keccak256(bytes(name));
        bytes32 hashedVersion = keccak256(bytes(version));
        bytes32 typeHash = keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");
        _HASHED_NAME = hashedName;
        _HASHED_VERSION = hashedVersion;
        _CACHED_CHAIN_ID = block.chainid;
        _CACHED_DOMAIN_SEPARATOR = _buildDomainSeparator(typeHash, hashedName, hashedVersion);
        _TYPE_HASH = typeHash;
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (block.chainid == _CACHED_CHAIN_ID) {
            return _CACHED_DOMAIN_SEPARATOR;
        } else {
            return _buildDomainSeparator(_TYPE_HASH, _HASHED_NAME, _HASHED_VERSION);
        }
    }

    function _buildDomainSeparator(bytes32 typeHash, bytes32 name, bytes32 version) private view returns (bytes32) {
        return keccak256(
            abi.encode(
                typeHash,
                name,
                version,
                block.chainid,
                address(this)
            )
        );
    }

    /**
     * @dev Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
     * function returns the hash of the fully encoded EIP712 message for this domain.
     *
     * This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:
     *
     * ```solidity
     * bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
     *     keccak256("Mail(address to,string contents)"),
     *     mailTo,
     *     keccak256(bytes(mailContents))
     * )));
     * address signer = ECDSA.recover(digest, signature);
     * ```
     */
    function _hashTypedDataV4(bytes32 structHash) internal view virtual returns (bytes32) {
        return ECDSA.toTypedDataHash(_domainSeparatorV4(), structHash);
    }
}

// File: @openzeppelin/contracts/utils/cryptography/ECDSA.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        // Divide the signature in r, s and v variables
        bytes32 r;
        bytes32 s;
        uint8 v;

        // Check the signature length
        // - case 65: r,s,v signature (standard)
        // - case 64: r,vs signature (cf https://eips.ethereum.org/EIPS/eip-2098) _Available since v4.1._
        if (signature.length == 65) {
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            // solhint-disable-next-line no-inline-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
        } else if (signature.length == 64) {
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            // solhint-disable-next-line no-inline-assembly
            assembly {
                let vs := mload(add(signature, 0x40))
                r := mload(add(signature, 0x20))
                s := and(vs, 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff)
                v := add(shr(255, vs), 27)
            }
        } else {
            revert("ECDSA: invalid signature length");
        }

        return recover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (281): 0 < s < secp256k1n ÷ 2 + 1, and for v in (282): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        require(uint256(s) <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, "ECDSA: invalid signature 's' value");
        require(v == 27 || v == 28, "ECDSA: invalid signature 'v' value");

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        require(signer != address(0), "ECDSA: invalid signature");

        return signer;
    }

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

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

// File: @openzeppelin/contracts/utils/Counters.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented or decremented by one. This can be used e.g. to track the number
 * of elements in a mapping, issuing ERC721 ids, or counting request ids.
 *
 * Include with `using Counters for Counters.Counter;`
 */
library Counters {
    struct Counter {
        // This variable should never be directly accessed by users of the library: interactions must be restricted to
        // the library's function. As of Solidity v0.5.2, this cannot be enforced, though there is a proposal to add
        // this feature: see https://github.com/ethereum/solidity/issues/4637
        uint256 _value; // default: 0
    }

    function current(Counter storage counter) internal view returns (uint256) {
        return counter._value;
    }

    function increment(Counter storage counter) internal {
        unchecked {
            counter._value += 1;
        }
    }

    function decrement(Counter storage counter) internal {
        uint256 value = counter._value;
        require(value > 0, "Counter: decrement overflow");
        unchecked {
            counter._value = value - 1;
        }
    }
}

// File: @openzeppelin/contracts/token/ERC20/extensions/IERC20Metadata.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/*
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }
}

// File: @uniswap/v3-core/contracts/interfaces/callback/IUniswapV3MintCallback.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0;

/// @title Callback for IUniswapV3PoolActions#mint
/// @notice Any contract that calls IUniswapV3PoolActions#mint must implement this interface
interface IUniswapV3MintCallback {
    /// @notice Called to `msg.sender` after minting liquidity to a position from IUniswapV3Pool#mint.
    /// @dev In the implementation you must pay the pool tokens owed for the minted liquidity.
    /// The caller of this method must be checked to be a UniswapV3Pool deployed by the canonical UniswapV3Factory.
    /// @param amount0Owed The amount of token0 due to the pool for the minted liquidity
    /// @param amount1Owed The amount of token1 due to the pool for the minted liquidity
    /// @param data Any data passed through by the caller via the IUniswapV3PoolActions#mint call
    function uniswapV3MintCallback(
        uint256 amount0Owed,
        uint256 amount1Owed,
        bytes calldata data
    ) external;
}

// File: contracts/structs/Ticks.sol



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

struct Ticks {
    // Lower tick of a Uniswap position
    int24 lower;
    // Upper tick of a Uniswap position
    int24 upper;
}