/**
 *Submitted for verification at SonicScan.org on 2024-12-18
*/

// SPDX-License-Identifier: GPL-3.0-or-later

// Hydrometer combines powerful liquidity incentives, low slippage, and a vote-locked governance model using $HYDRO and $veHYDRO tokens, ensuring an innovative and decentralized experience for all users.

//https://x.com/Hydrometer_Fi

pragma solidity 0.8.19;

// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

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

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}

interface IPool {
    error DepositsNotEqual();
    error BelowMinimumK();
    error FactoryAlreadySet();
    error InsufficientLiquidity();
    error InsufficientLiquidityMinted();
    error InsufficientLiquidityBurned();
    error InsufficientOutputAmount();
    error InsufficientInputAmount();
    error IsPaused();
    error InvalidTo();
    error K();
    error NotEmergencyCouncil();

    event Fees(address indexed sender, uint256 amount0, uint256 amount1);
    event Mint(address indexed sender, uint256 amount0, uint256 amount1);
    event Burn(address indexed sender, address indexed to, uint256 amount0, uint256 amount1);
    event Swap(
        address indexed sender,
        address indexed to,
        uint256 amount0In,
        uint256 amount1In,
        uint256 amount0Out,
        uint256 amount1Out
    );
    event Sync(uint256 reserve0, uint256 reserve1);
    event Claim(address indexed sender, address indexed recipient, uint256 amount0, uint256 amount1);

    // Struct to capture time period obervations every 30 minutes, used for local oracles
    struct Observation {
        uint256 timestamp;
        uint256 reserve0Cumulative;
        uint256 reserve1Cumulative;
    }

    /// @notice Returns the decimal (dec), reserves (r), stable (st), and tokens (t) of token0 and token1
    function metadata()
        external
        view
        returns (uint256 dec0, uint256 dec1, uint256 r0, uint256 r1, bool st, address t0, address t1);

    /// @notice Claim accumulated but unclaimed fees (claimable0 and claimable1)
    function claimFees() external returns (uint256, uint256);

    /// @notice Returns [token0, token1]
    function tokens() external view returns (address, address);

    /// @notice Address of token in the pool with the lower address value
    function token0() external view returns (address);

    /// @notice Address of token in the poool with the higher address value
    function token1() external view returns (address);

    /// @notice Address of linked PoolFees.sol
    function poolFees() external view returns (address);

    /// @notice Address of PoolFactory that created this contract
    function factory() external view returns (address);

    /// @notice Capture oracle reading every 30 minutes (1800 seconds)
    function periodSize() external view returns (uint256);

    /// @notice Amount of token0 in pool
    function reserve0() external view returns (uint256);

    /// @notice Amount of token1 in pool
    function reserve1() external view returns (uint256);

    /// @notice Timestamp of last update to pool
    function blockTimestampLast() external view returns (uint256);

    /// @notice Cumulative of reserve0 factoring in time elapsed
    function reserve0CumulativeLast() external view returns (uint256);

    /// @notice Cumulative of reserve1 factoring in time elapsed
    function reserve1CumulativeLast() external view returns (uint256);

    /// @notice Accumulated fees of token0 (global)
    function index0() external view returns (uint256);

    /// @notice Accumulated fees of token1 (global)
    function index1() external view returns (uint256);

    /// @notice Get an LP's relative index0 to index0
    function supplyIndex0(address) external view returns (uint256);

    /// @notice Get an LP's relative index1 to index1
    function supplyIndex1(address) external view returns (uint256);

    /// @notice Amount of unclaimed, but claimable tokens from fees of token0 for an LP
    function claimable0(address) external view returns (uint256);

    /// @notice Amount of unclaimed, but claimable tokens from fees of token1 for an LP
    function claimable1(address) external view returns (uint256);

    /// @notice Returns the value of K in the Pool, based on its reserves.
    function getK() external returns (uint256);

    /// @notice Set pool name
    ///         Only callable by Voter.emergencyCouncil()
    /// @param __name String of new name
    function setName(string calldata __name) external;

    /// @notice Set pool symbol
    ///         Only callable by Voter.emergencyCouncil()
    /// @param __symbol String of new symbol
    function setSymbol(string calldata __symbol) external;

    /// @notice Get the number of observations recorded
    function observationLength() external view returns (uint256);

    /// @notice Get the value of the most recent observation
    function lastObservation() external view returns (Observation memory);

    /// @notice True if pool is stable, false if volatile
    function stable() external view returns (bool);

    /// @notice Produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    function currentCumulativePrices()
        external
        view
        returns (uint256 reserve0Cumulative, uint256 reserve1Cumulative, uint256 blockTimestamp);

    /// @notice Provides twap price with user configured granularity, up to the full window size
    /// @param tokenIn .
    /// @param amountIn .
    /// @param granularity .
    /// @return amountOut .
    function quote(address tokenIn, uint256 amountIn, uint256 granularity) external view returns (uint256 amountOut);

    /// @notice Returns a memory set of TWAP prices
    ///         Same as calling sample(tokenIn, amountIn, points, 1)
    /// @param tokenIn .
    /// @param amountIn .
    /// @param points Number of points to return
    /// @return Array of TWAP prices
    function prices(address tokenIn, uint256 amountIn, uint256 points) external view returns (uint256[] memory);

    /// @notice Same as prices with with an additional window argument.
    ///         Window = 2 means 2 * 30min (or 1 hr) between observations
    /// @param tokenIn .
    /// @param amountIn .
    /// @param points .
    /// @param window .
    /// @return Array of TWAP prices
    function sample(
        address tokenIn,
        uint256 amountIn,
        uint256 points,
        uint256 window
    ) external view returns (uint256[] memory);

    /// @notice This low-level function should be called from a contract which performs important safety checks
    /// @param amount0Out   Amount of token0 to send to `to`
    /// @param amount1Out   Amount of token1 to send to `to`
    /// @param to           Address to recieve the swapped output
    /// @param data         Additional calldata for flashloans
    function swap(uint256 amount0Out, uint256 amount1Out, address to, bytes calldata data) external;

    /// @notice This low-level function should be called from a contract which performs important safety checks
    ///         standard uniswap v2 implementation
    /// @param to Address to receive token0 and token1 from burning the pool token
    /// @return amount0 Amount of token0 returned
    /// @return amount1 Amount of token1 returned
    function burn(address to) external returns (uint256 amount0, uint256 amount1);

    /// @notice This low-level function should be called by addLiquidity functions in Router.sol, which performs important safety checks
    ///         standard uniswap v2 implementation
    /// @param to           Address to receive the minted LP token
    /// @return liquidity   Amount of LP token minted
    function mint(address to) external returns (uint256 liquidity);

    /// @notice Update reserves and, on the first call per block, price accumulators
    /// @return _reserve0 .
    /// @return _reserve1 .
    /// @return _blockTimestampLast .
    function getReserves() external view returns (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast);

    /// @notice Get the amount of tokenOut given the amount of tokenIn
    /// @param amountIn Amount of token in
    /// @param tokenIn  Address of token
    /// @return Amount out
    function getAmountOut(uint256 amountIn, address tokenIn) external view returns (uint256);

    /// @notice Force balances to match reserves
    /// @param to Address to receive any skimmed rewards
    function skim(address to) external;

    /// @notice Force reserves to match balances
    function sync() external;

    /// @notice Called on pool creation by PoolFactory
    /// @param _token0 Address of token0
    /// @param _token1 Address of token1
    /// @param _stable True if stable, false if volatile
    function initialize(address _token0, address _token1, bool _stable) external;
}

interface IVoter {
    error AlreadyVotedOrDeposited();
    error DistributeWindow();
    error FactoryPathNotApproved();
    error GaugeAlreadyKilled();
    error GaugeAlreadyRevived();
    error GaugeExists();
    error GaugeDoesNotExist(address _pool);
    error GaugeNotAlive(address _gauge);
    error InactiveManagedNFT();
    error MaximumVotingNumberTooLow();
    error NonZeroVotes();
    error NotAPool();
    error NotApprovedOrOwner();
    error NotGovernor();
    error NotEmergencyCouncil();
    error NotMinter();
    error NotWhitelistedNFT();
    error NotWhitelistedToken();
    error SameValue();
    error SpecialVotingWindow();
    error TooManyPools();
    error UnequalLengths();
    error ZeroBalance();
    error ZeroAddress();

    event GaugeCreated(
        address indexed poolFactory,
        address indexed votingRewardsFactory,
        address indexed gaugeFactory,
        address pool,
        address bribeVotingReward,
        address feeVotingReward,
        address gauge,
        address creator
    );
    event GaugeKilled(address indexed gauge);
    event GaugeRevived(address indexed gauge);
    event Voted(
        address indexed voter,
        address indexed pool,
        uint256 indexed tokenId,
        uint256 weight,
        uint256 totalWeight,
        uint256 timestamp
    );
    event Abstained(
        address indexed voter,
        address indexed pool,
        uint256 indexed tokenId,
        uint256 weight,
        uint256 totalWeight,
        uint256 timestamp
    );
    event NotifyReward(address indexed sender, address indexed reward, uint256 amount);
    event DistributeReward(address indexed sender, address indexed gauge, uint256 amount);
    event WhitelistToken(address indexed whitelister, address indexed token, bool indexed _bool);
    event WhitelistNFT(address indexed whitelister, uint256 indexed tokenId, bool indexed _bool);

    /// @notice Store trusted forwarder address to pass into factories
    function forwarder() external view returns (address);

    /// @notice The ve token that governs these contracts
    function ve() external view returns (address);

    /// @notice Factory registry for valid pool / gauge / rewards factories
    function factoryRegistry() external view returns (address);

    /// @notice Address of Minter.sol
    function minter() external view returns (address);

    /// @notice Standard OZ IGovernor using ve for vote weights.
    function governor() external view returns (address);

    /// @notice Custom Epoch Governor using ve for vote weights.
    function epochGovernor() external view returns (address);

    /// @notice credibly neutral party similar to Curve's Emergency DAO
    function emergencyCouncil() external view returns (address);

    /// @dev Total Voting Weights
    function totalWeight() external view returns (uint256);

    /// @dev Most number of pools one voter can vote for at once
    function maxVotingNum() external view returns (uint256);

    // mappings
    /// @dev Pool => Gauge
    function gauges(address pool) external view returns (address);

    /// @dev Gauge => Pool
    function poolForGauge(address gauge) external view returns (address);

    /// @dev Gauge => Fees Voting Reward
    function gaugeToFees(address gauge) external view returns (address);

    /// @dev Gauge => Bribes Voting Reward
    function gaugeToBribe(address gauge) external view returns (address);

    /// @dev Pool => Weights
    function weights(address pool) external view returns (uint256);

    /// @dev NFT => Pool => Votes
    function votes(uint256 tokenId, address pool) external view returns (uint256);

    /// @dev NFT => Total voting weight of NFT
    function usedWeights(uint256 tokenId) external view returns (uint256);

    /// @dev Nft => Timestamp of last vote (ensures single vote per epoch)
    function lastVoted(uint256 tokenId) external view returns (uint256);

    /// @dev Address => Gauge
    function isGauge(address) external view returns (bool);

    /// @dev Token => Whitelisted status
    function isWhitelistedToken(address token) external view returns (bool);

    /// @dev TokenId => Whitelisted status
    function isWhitelistedNFT(uint256 tokenId) external view returns (bool);

    /// @dev Gauge => Liveness status
    function isAlive(address gauge) external view returns (bool);

    /// @dev Gauge => Amount claimable
    function claimable(address gauge) external view returns (uint256);

    /// @notice Number of pools with a Gauge
    function length() external view returns (uint256);

    /// @notice Called by Minter to distribute weekly emissions rewards for disbursement amongst gauges.
    /// @dev Assumes totalWeight != 0 (Will never be zero as long as users are voting).
    ///      Throws if not called by minter.
    /// @param _amount Amount of rewards to distribute.
    function notifyRewardAmount(uint256 _amount) external;

    /// @dev Utility to distribute to gauges of pools in range _start to _finish.
    /// @param _start   Starting index of gauges to distribute to.
    /// @param _finish  Ending index of gauges to distribute to.
    function distribute(uint256 _start, uint256 _finish) external;

    /// @dev Utility to distribute to gauges of pools in array.
    /// @param _gauges Array of gauges to distribute to.
    function distribute(address[] memory _gauges) external;

    /// @notice Called by users to update voting balances in voting rewards contracts.
    /// @param _tokenId Id of veNFT whose balance you wish to update.
    function poke(uint256 _tokenId) external;

    /// @notice Called by users to vote for pools. Votes distributed proportionally based on weights.
    ///         Can only vote or deposit into a managed NFT once per epoch.
    ///         Can only vote for gauges that have not been killed.
    /// @dev Weights are distributed proportional to the sum of the weights in the array.
    ///      Throws if length of _poolVote and _weights do not match.
    /// @param _tokenId     Id of veNFT you are voting with.
    /// @param _poolVote    Array of pools you are voting for.
    /// @param _weights     Weights of pools.
    function vote(uint256 _tokenId, address[] calldata _poolVote, uint256[] calldata _weights) external;

    /// @notice Called by users to reset voting state. Required if you wish to make changes to
    ///         veNFT state (e.g. merge, split, deposit into managed etc).
    ///         Cannot reset in the same epoch that you voted in.
    ///         Can vote or deposit into a managed NFT again after reset.
    /// @param _tokenId Id of veNFT you are reseting.
    function reset(uint256 _tokenId) external;

    /// @notice Called by users to deposit into a managed NFT.
    ///         Can only vote or deposit into a managed NFT once per epoch.
    ///         Note that NFTs deposited into a managed NFT will be re-locked
    ///         to the maximum lock time on withdrawal.
    /// @dev Throws if not approved or owner.
    ///      Throws if managed NFT is inactive.
    ///      Throws if depositing within privileged window (one hour prior to epoch flip).
    function depositManaged(uint256 _tokenId, uint256 _mTokenId) external;

    /// @notice Called by users to withdraw from a managed NFT.
    ///         Cannot do it in the same epoch that you deposited into a managed NFT.
    ///         Can vote or deposit into a managed NFT again after withdrawing.
    ///         Note that the NFT withdrawn is re-locked to the maximum lock time.
    function withdrawManaged(uint256 _tokenId) external;

    /// @notice Claim emissions from gauges.
    /// @param _gauges Array of gauges to collect emissions from.
    function claimRewards(address[] memory _gauges) external;

    /// @notice Claim bribes for a given NFT.
    /// @dev Utility to help batch bribe claims.
    /// @param _bribes  Array of BribeVotingReward contracts to collect from.
    /// @param _tokens  Array of tokens that are used as bribes.
    /// @param _tokenId Id of veNFT that you wish to claim bribes for.
    function claimBribes(address[] memory _bribes, address[][] memory _tokens, uint256 _tokenId) external;

    /// @notice Claim fees for a given NFT.
    /// @dev Utility to help batch fee claims.
    /// @param _fees    Array of FeesVotingReward contracts to collect from.
    /// @param _tokens  Array of tokens that are used as fees.
    /// @param _tokenId Id of veNFT that you wish to claim fees for.
    function claimFees(address[] memory _fees, address[][] memory _tokens, uint256 _tokenId) external;

    /// @notice Set new governor.
    /// @dev Throws if not called by governor.
    /// @param _governor .
    function setGovernor(address _governor) external;

    /// @notice Set new epoch based governor.
    /// @dev Throws if not called by governor.
    /// @param _epochGovernor .
    function setEpochGovernor(address _epochGovernor) external;

    /// @notice Set new emergency council.
    /// @dev Throws if not called by emergency council.
    /// @param _emergencyCouncil .
    function setEmergencyCouncil(address _emergencyCouncil) external;

    /// @notice Set maximum number of gauges that can be voted for.
    /// @dev Throws if not called by governor.
    ///      Throws if _maxVotingNum is too low.
    ///      Throws if the values are the same.
    /// @param _maxVotingNum .
    function setMaxVotingNum(uint256 _maxVotingNum) external;

    /// @notice Whitelist (or unwhitelist) token for use in bribes.
    /// @dev Throws if not called by governor.
    /// @param _token .
    /// @param _bool .
    function whitelistToken(address _token, bool _bool) external;

    /// @notice Whitelist (or unwhitelist) token id for voting in last hour prior to epoch flip.
    /// @dev Throws if not called by governor.
    ///      Throws if already whitelisted.
    /// @param _tokenId .
    /// @param _bool .
    function whitelistNFT(uint256 _tokenId, bool _bool) external;

    /// @notice Create a new gauge (unpermissioned).
    /// @dev Governor can create a new gauge for a pool with any address.
    /// @param _poolFactory .
    /// @param _pool .
    function createGauge(address _poolFactory, address _pool) external returns (address);

    /// @notice Kills a gauge. The gauge will not receive any new emissions and cannot be deposited into.
    ///         Can still withdraw from gauge.
    /// @dev Throws if not called by emergency council.
    ///      Throws if gauge already killed.
    /// @param _gauge .
    function killGauge(address _gauge) external;

    /// @notice Revives a killed gauge. Gauge will can receive emissions and deposits again.
    /// @dev Throws if not called by emergency council.
    ///      Throws if gauge is not killed.
    /// @param _gauge .
    function reviveGauge(address _gauge) external;

    /// @dev Update claims to emissions for an array of gauges.
    /// @param _gauges Array of gauges to update emissions for.
    function updateFor(address[] memory _gauges) external;

    /// @dev Update claims to emissions for gauges based on their pool id as stored in Voter.
    /// @param _start   Starting index of pools.
    /// @param _end     Ending index of pools.
    function updateFor(uint256 _start, uint256 _end) external;

    /// @dev Update claims to emissions for single gauge
    /// @param _gauge .
    function updateFor(address _gauge) external;
}

interface IPoolCallee {
    function hook(address sender, uint256 amount0, uint256 amount1, bytes calldata data) external;
}

interface IPoolFactory {
    event SetFeeManager(address feeManager);
    event SetPauser(address pauser);
    event SetPauseState(bool state);
    event SetVoter(address voter);
    event PoolCreated(address indexed token0, address indexed token1, bool indexed stable, address pool, uint256);
    event SetCustomFee(address indexed pool, uint256 fee);

    error FeeInvalid();
    error FeeTooHigh();
    error InvalidPool();
    error NotFeeManager();
    error NotPauser();
    error NotVoter();
    error PoolAlreadyExists();
    error SameAddress();
    error ZeroFee();
    error ZeroAddress();

    /// @notice returns the number of pools created from this factory
    function allPoolsLength() external view returns (uint256);

    /// @notice Is a valid pool created by this factory.
    /// @param .
    function isPool(address pool) external view returns (bool);

    /// @notice Return address of pool created by this factory
    /// @param tokenA .
    /// @param tokenB .
    /// @param stable True if stable, false if volatile
    function getPool(address tokenA, address tokenB, bool stable) external view returns (address);

    /// @notice Support for v3-style pools which wraps around getPool(tokenA,tokenB,stable)
    /// @dev fee is converted to stable boolean.
    /// @param tokenA .
    /// @param tokenB .
    /// @param fee  1 if stable, 0 if volatile, else returns address(0)
    function getPool(address tokenA, address tokenB, uint24 fee) external view returns (address);

    /// @dev Only called once to set to Voter.sol - Voter does not have a function
    ///      to call this contract method, so once set it's immutable.
    ///      This also follows convention of setVoterAndDistributor() in VotingEscrow.sol
    /// @param _voter .
    function setVoter(address _voter) external;

    function setPauser(address _pauser) external;

    function setPauseState(bool _state) external;

    function setFeeManager(address _feeManager) external;

    /// @notice Set default fee for stable and volatile pools.
    /// @dev Throws if higher than maximum fee.
    ///      Throws if fee is zero.
    /// @param _stable Stable or volatile pool.
    /// @param _fee .
    function setFee(bool _stable, uint256 _fee) external;

    /// @notice Set overriding fee for a pool from the default
    /// @dev A custom fee of zero means the default fee will be used.
    function setCustomFee(address _pool, uint256 _fee) external;

    /// @notice Returns fee for a pool, as custom fees are possible.
    function getFee(address _pool, bool _stable) external view returns (uint256);

    /// @notice Create a pool given two tokens and if they're stable/volatile
    /// @dev token order does not matter
    /// @param tokenA .
    /// @param tokenB .
    /// @param stable .
    function createPool(address tokenA, address tokenB, bool stable) external returns (address pool);

    /// @notice Support for v3-style pools which wraps around createPool(tokena,tokenB,stable)
    /// @dev fee is converted to stable boolean
    /// @dev token order does not matter
    /// @param tokenA .
    /// @param tokenB .
    /// @param fee 1 if stable, 0 if volatile, else revert
    function createPool(address tokenA, address tokenB, uint24 fee) external returns (address pool);

    function isPaused() external view returns (bool);

    function voter() external view returns (address);

    function implementation() external view returns (address);
}

// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @dev Emitted when `value` tokens are moved from one account (`from`) to
     * another (`to`).
     *
     * Note that `value` may be zero.
     */
    event Transfer(address indexed from, address indexed to, uint256 value);

    /**
     * @dev Emitted when the allowance of a `spender` for an `owner` is set by
     * a call to {approve}. `value` is the new allowance.
     */
    event Approval(address indexed owner, address indexed spender, uint256 value);

    /**
     * @dev Returns the amount of tokens in existence.
     */
    function totalSupply() external view returns (uint256);

    /**
     * @dev Returns the amount of tokens owned by `account`.
     */
    function balanceOf(address account) external view returns (uint256);

    /**
     * @dev Moves `amount` tokens from the caller's account to `to`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address to, uint256 amount) external returns (bool);

    /**
     * @dev Returns the remaining number of tokens that `spender` will be
     * allowed to spend on behalf of `owner` through {transferFrom}. This is
     * zero by default.
     *
     * This value changes when {approve} or {transferFrom} are called.
     */
    function allowance(address owner, address spender) external view returns (uint256);

    /**
     * @dev Sets `amount` as the allowance of `spender` over the caller's tokens.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * IMPORTANT: Beware that changing an allowance with this method brings the risk
     * that someone may use both the old and the new allowance by unfortunate
     * transaction ordering. One possible solution to mitigate this race
     * condition is to first reduce the spender's allowance to 0 and set the
     * desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     *
     * Emits an {Approval} event.
     */
    function approve(address spender, uint256 amount) external returns (bool);

    /**
     * @dev Moves `amount` tokens from `from` to `to` using the
     * allowance mechanism. `amount` is then deducted from the caller's
     * allowance.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(address from, address to, uint256 amount) external returns (bool);
}

// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/utils/SafeERC20.sol)

// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Permit.sol)

/**
 * @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);
}

// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

/**
 * @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
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 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://consensys.net/diligence/blog/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");

        (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 functionCallWithValue(target, data, 0, "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");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, 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) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, 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) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // 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
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}

/**
 * @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'
        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));
        }
    }

    function safePermit(
        IERC20Permit token,
        address owner,
        address spender,
        uint256 value,
        uint256 deadline,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        uint256 nonceBefore = token.nonces(owner);
        token.permit(owner, spender, value, deadline, v, r, s);
        uint256 nonceAfter = token.nonces(owner);
        require(nonceAfter == nonceBefore + 1, "SafeERC20: permit did not succeed");
    }

    /**
     * @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
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

/// @title PoolFees
/// @notice Contract used as 1:1 pool relationship to split out fees.
/// @notice Ensures curve does not need to be modified for LP shares.
contract PoolFees {
    using SafeERC20 for IERC20;
    address internal immutable pool; // The pool it is bonded to
    address internal immutable token0; // token0 of pool, saved localy and statically for gas optimization
    address internal immutable token1; // Token1 of pool, saved localy and statically for gas optimization

    error NotPool();

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

    /// @notice Allow the pool to transfer fees to users
    function claimFeesFor(address _recipient, uint256 _amount0, uint256 _amount1) external {
        if (msg.sender != pool) revert NotPool();
        if (_amount0 > 0) IERC20(token0).safeTransfer(_recipient, _amount0);
        if (_amount1 > 0) IERC20(token1).safeTransfer(_recipient, _amount1);
    }
}

// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/ERC20.sol)

// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.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);
}

// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

/**
 * @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) {
        return msg.data;
    }
}

/**
 * @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.openzeppelin.com/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * The default value of {decimals} is 18. To change this, you should override
 * this function so it returns a different value.
 *
 * We have followed general OpenZeppelin Contracts guidelines: functions revert
 * instead 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}.
     *
     * 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 default value returned by this function, unless
     * it's 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:
     *
     * - `to` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address to, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _transfer(owner, to, 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}.
     *
     * NOTE: If `amount` is the maximum `uint256`, the allowance is not updated on
     * `transferFrom`. This is semantically equivalent to an infinite approval.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        address owner = _msgSender();
        _approve(owner, 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}.
     *
     * NOTE: Does not update the allowance if the current allowance
     * is the maximum `uint256`.
     *
     * Requirements:
     *
     * - `from` and `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     * - the caller must have allowance for ``from``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address from, address to, uint256 amount) public virtual override returns (bool) {
        address spender = _msgSender();
        _spendAllowance(from, spender, amount);
        _transfer(from, to, 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) {
        address owner = _msgSender();
        _approve(owner, spender, allowance(owner, 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) {
        address owner = _msgSender();
        uint256 currentAllowance = allowance(owner, spender);
        require(currentAllowance >= subtractedValue, "ERC20: decreased allowance below zero");
        unchecked {
            _approve(owner, spender, currentAllowance - subtractedValue);
        }

        return true;
    }

    /**
     * @dev Moves `amount` of tokens from `from` to `to`.
     *
     * This 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:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `from` must have a balance of at least `amount`.
     */
    function _transfer(address from, address to, uint256 amount) internal virtual {
        require(from != address(0), "ERC20: transfer from the zero address");
        require(to != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(from, to, amount);

        uint256 fromBalance = _balances[from];
        require(fromBalance >= amount, "ERC20: transfer amount exceeds balance");
        unchecked {
            _balances[from] = fromBalance - amount;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, 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:
     *
     * - `account` 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;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(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");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

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

        _afterTokenTransfer(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 Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(address owner, address spender, uint256 amount) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - 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 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 {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been 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 _afterTokenTransfer(address from, address to, uint256 amount) internal virtual {}
}

// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/extensions/ERC20Permit.sol)

// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/ECDSA.sol)

// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        return (signer, RecoverError.NoError);
    }

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

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

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

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

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

// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

// OpenZeppelin Contracts (last updated v4.7.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, `uint256`._
 * _Available since v4.9 for `string`, `bytes`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }
}

type ShortString is bytes32;

/**
 * @dev This library provides functions to convert short memory strings
 * into a `ShortString` type that can be used as an immutable variable.
 * Strings of arbitrary length can be optimized if they are short enough by
 * the addition of a storage variable used as fallback.
 *
 * Usage example:
 *
 * ```solidity
 * contract Named {
 *     using ShortStrings for *;
 *
 *     ShortString private immutable _name;
 *     string private _nameFallback;
 *
 *     constructor(string memory contractName) {
 *         _name = contractName.toShortStringWithFallback(_nameFallback);
 *     }
 *
 *     function name() external view returns (string memory) {
 *         return _name.toStringWithFallback(_nameFallback);
 *     }
 * }
 * ```
 */
library ShortStrings {
    error StringTooLong(string str);

    /**
     * @dev Encode a string of at most 31 chars into a `ShortString`.
     *
     * This will trigger a `StringTooLong` error is the input string is too long.
     */
    function toShortString(string memory str) internal pure returns (ShortString) {
        bytes memory bstr = bytes(str);
        if (bstr.length > 31) {
            revert StringTooLong(str);
        }
        return ShortString.wrap(bytes32(uint256(bytes32(bstr)) | bstr.length));
    }

    /**
     * @dev Decode a `ShortString` back to a "normal" string.
     */
    function toString(ShortString sstr) internal pure returns (string memory) {
        uint256 len = length(sstr);
        // using `new string(len)` would work locally but is not memory safe.
        string memory str = new string(32);
        /// @solidity memory-safe-assembly
        assembly {
            mstore(str, len)
            mstore(add(str, 0x20), sstr)
        }
        return str;
    }

    /**
     * @dev Return the length of a `ShortString`.
     */
    function length(ShortString sstr) internal pure returns (uint256) {
        return uint256(ShortString.unwrap(sstr)) & 0xFF;
    }

    /**
     * @dev Encode a string into a `ShortString`, or write it to storage if it is too long.
     */
    function toShortStringWithFallback(string memory value, string storage store) internal returns (ShortString) {
        if (bytes(value).length < 32) {
            return toShortString(value);
        } else {
            StorageSlot.getStringSlot(store).value = value;
            return ShortString.wrap(0);
        }
    }

    /**
     * @dev Decode a string that was encoded to `ShortString` or written to storage using {setWithFallback}.
     */
    function toStringWithFallback(ShortString value, string storage store) internal pure returns (string memory) {
        if (length(value) > 0) {
            return toString(value);
        } else {
            return store;
        }
    }
}

interface IERC5267 {
    /**
     * @dev MAY be emitted to signal that the domain could have changed.
     */
    event EIP712DomainChanged();

    /**
     * @dev returns the fields and values that describe the domain separator used by this contract for EIP-712
     * signature.
     */
    function eip712Domain()
        external
        view
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        );
}

/**
 * @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].
 *
 * NOTE: In the upgradeable version of this contract, the cached values will correspond to the address, and the domain
 * separator of the implementation contract. This will cause the `_domainSeparatorV4` function to always rebuild the
 * separator from the immutable values, which is cheaper than accessing a cached version in cold storage.
 *
 * _Available since v3.4._
 *
 * @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
 */
abstract contract EIP712 is IERC5267 {
    using ShortStrings for *;

    bytes32 private constant _TYPE_HASH =
        keccak256("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)");

    /* 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 _cachedDomainSeparator;
    uint256 private immutable _cachedChainId;
    address private immutable _cachedThis;

    ShortString private immutable _name;
    ShortString private immutable _version;
    string private _nameFallback;
    string private _versionFallback;

    bytes32 private immutable _hashedName;
    bytes32 private immutable _hashedVersion;

    /* 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) {
        _name = name.toShortStringWithFallback(_nameFallback);
        _version = version.toShortStringWithFallback(_versionFallback);
        _hashedName = keccak256(bytes(name));
        _hashedVersion = keccak256(bytes(version));

        _cachedChainId = block.chainid;
        _cachedDomainSeparator = _buildDomainSeparator();
        _cachedThis = address(this);
    }

    /**
     * @dev Returns the domain separator for the current chain.
     */
    function _domainSeparatorV4() internal view returns (bytes32) {
        if (address(this) == _cachedThis && block.chainid == _cachedChainId) {
            return _cachedDomainSeparator;
        } else {
            return _buildDomainSeparator();
        }
    }

    function _buildDomainSeparator() private view returns (bytes32) {
        return keccak256(abi.encode(_TYPE_HASH, _hashedName, _hashedVersion, 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);
    }

    /**
     * @dev See {EIP-5267}.
     */
    function eip712Domain()
        public
        view
        virtual
        override
        returns (
            bytes1 fields,
            string memory name,
            string memory version,
            uint256 chainId,
            address verifyingContract,
            bytes32 salt,
            uint256[] memory extensions
        )
    {
        return (
            hex"0f", // 01111
            _name.toStringWithFallback(_nameFallback),
            _version.toStringWithFallback(_versionFallback),
            block.chainid,
            address(this),
            bytes32(0),
            new uint256[](0)
        );
    }
}

// OpenZeppelin Contracts v4.4.1 (utils/Counters.sol)

/**
 * @title Counters
 * @author Matt Condon (@shrugs)
 * @dev Provides counters that can only be incremented, decremented or reset. 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;
        }
    }

    function reset(Counter storage counter) internal {
        counter._value = 0;
    }
}

/**
 * @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 constant _PERMIT_TYPEHASH =
        keccak256("Permit(address owner,address spender,uint256 value,uint256 nonce,uint256 deadline)");
    /**
     * @dev In previous versions `_PERMIT_TYPEHASH` was declared as `immutable`.
     * However, to ensure consistency with the upgradeable transpiler, we will continue
     * to reserve a slot.
     * @custom:oz-renamed-from _PERMIT_TYPEHASH
     */
    // solhint-disable-next-line var-name-mixedcase
    bytes32 private _PERMIT_TYPEHASH_DEPRECATED_SLOT;

    /**
     * @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 {
        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();
    }
}

// OpenZeppelin Contracts (last updated v4.8.0) (security/ReentrancyGuard.sol)

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
abstract contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor() {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and making it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        _nonReentrantBefore();
        _;
        _nonReentrantAfter();
    }

    function _nonReentrantBefore() private {
        // On the first call to nonReentrant, _status will be _NOT_ENTERED
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _status = _ENTERED;
    }

    function _nonReentrantAfter() private {
        // By storing the original value once again, a refund is triggered (see
        // https://eips.ethereum.org/EIPS/eip-2200)
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Returns true if the reentrancy guard is currently set to "entered", which indicates there is a
     * `nonReentrant` function in the call stack.
     */
    function _reentrancyGuardEntered() internal view returns (bool) {
        return _status == _ENTERED;
    }
}

/// @title Pool
/// @author velodrome.finance, @figs999, @pegahcarter
/// @notice Protocol token pool, either stable or volatile
contract Pool is IPool, ERC20Permit, ReentrancyGuard {
    using SafeERC20 for IERC20;

    string private _name;
    string private _symbol;
    address private _voter;

    /// @inheritdoc IPool
    bool public stable;

    uint256 internal constant MINIMUM_LIQUIDITY = 10 ** 3;
    uint256 internal constant MINIMUM_K = 10 ** 10;

    /// @inheritdoc IPool
    address public token0;
    /// @inheritdoc IPool
    address public token1;
    /// @inheritdoc IPool
    address public poolFees;
    /// @inheritdoc IPool
    address public factory;

    /// @inheritdoc IPool
    uint256 public constant periodSize = 1800;

    Observation[] public observations;

    uint256 internal decimals0;
    uint256 internal decimals1;

    /// @inheritdoc IPool
    uint256 public reserve0;
    /// @inheritdoc IPool
    uint256 public reserve1;
    /// @inheritdoc IPool
    uint256 public blockTimestampLast;

    /// @inheritdoc IPool
    uint256 public reserve0CumulativeLast;
    /// @inheritdoc IPool
    uint256 public reserve1CumulativeLast;

    /// @inheritdoc IPool
    uint256 public index0 = 0;
    /// @inheritdoc IPool
    uint256 public index1 = 0;

    /// @inheritdoc IPool
    mapping(address => uint256) public supplyIndex0;
    /// @inheritdoc IPool
    mapping(address => uint256) public supplyIndex1;

    /// @inheritdoc IPool
    mapping(address => uint256) public claimable0;
    /// @inheritdoc IPool
    mapping(address => uint256) public claimable1;

    constructor() ERC20("", "") ERC20Permit("") {}

    /// @inheritdoc IPool
    function initialize(address _token0, address _token1, bool _stable) external {
        if (factory != address(0)) revert FactoryAlreadySet();
        factory = _msgSender();
        _voter = IPoolFactory(factory).voter();
        (token0, token1, stable) = (_token0, _token1, _stable);
        poolFees = address(new PoolFees(_token0, _token1));
        string memory symbol0 = ERC20(_token0).symbol();
        string memory symbol1 = ERC20(_token1).symbol();
        if (_stable) {
            _name = string(abi.encodePacked("Stable AMM - ", symbol0, "/", symbol1));
            _symbol = string(abi.encodePacked("sAMM-", symbol0, "/", symbol1));
        } else {
            _name = string(abi.encodePacked("Volatile AMM - ", symbol0, "/", symbol1));
            _symbol = string(abi.encodePacked("vAMM-", symbol0, "/", symbol1));
        }

        decimals0 = 10 ** ERC20(_token0).decimals();
        decimals1 = 10 ** ERC20(_token1).decimals();

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

    /// @inheritdoc IPool
    function setName(string calldata __name) external {
        if (msg.sender != IVoter(_voter).emergencyCouncil()) revert NotEmergencyCouncil();
        _name = __name;
    }

    /// @inheritdoc IPool
    function setSymbol(string calldata __symbol) external {
        if (msg.sender != IVoter(_voter).emergencyCouncil()) revert NotEmergencyCouncil();
        _symbol = __symbol;
    }

    /// @inheritdoc IPool
    function observationLength() external view returns (uint256) {
        return observations.length;
    }

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

    /// @inheritdoc IPool
    function metadata()
        external
        view
        returns (uint256 dec0, uint256 dec1, uint256 r0, uint256 r1, bool st, address t0, address t1)
    {
        return (decimals0, decimals1, reserve0, reserve1, stable, token0, token1);
    }

    /// @inheritdoc IPool
    function tokens() external view returns (address, address) {
        return (token0, token1);
    }

    /// @inheritdoc IPool
    function getK() external nonReentrant returns (uint256) {
        return _k(reserve0, reserve1);
    }

    /// @inheritdoc IPool
    function claimFees() external returns (uint256 claimed0, uint256 claimed1) {
        address sender = _msgSender();
        _updateFor(sender);

        claimed0 = claimable0[sender];
        claimed1 = claimable1[sender];

        if (claimed0 > 0 || claimed1 > 0) {
            claimable0[sender] = 0;
            claimable1[sender] = 0;

            PoolFees(poolFees).claimFeesFor(sender, claimed0, claimed1);

            emit Claim(sender, sender, claimed0, claimed1);
        }
    }

    /// @dev Accrue fees on token0
    function _update0(uint256 amount) internal {
        // Only update on this pool if there is a fee
        if (amount == 0) return;
        IERC20(token0).safeTransfer(poolFees, amount); // transfer the fees out to PoolFees
        uint256 _ratio = (amount * 1e18) / totalSupply(); // 1e18 adjustment is removed during claim
        if (_ratio > 0) {
            index0 += _ratio;
        }
        emit Fees(_msgSender(), amount, 0);
    }

    /// @dev Accrue fees on token1
    function _update1(uint256 amount) internal {
        // Only update on this pool if there is a fee
        if (amount == 0) return;
        IERC20(token1).safeTransfer(poolFees, amount);
        uint256 _ratio = (amount * 1e18) / totalSupply();
        if (_ratio > 0) {
            index1 += _ratio;
        }
        emit Fees(_msgSender(), 0, amount);
    }

    /// @dev This function MUST be called on any balance changes, otherwise can be used to infinitely claim fees
    ///      Fees are segregated from core funds, so fees can never put liquidity at risk.
    function _updateFor(address recipient) internal {
        uint256 _supplied = balanceOf(recipient); // get LP balance of `recipient`
        if (_supplied > 0) {
            uint256 _supplyIndex0 = supplyIndex0[recipient]; // get last adjusted index0 for recipient
            uint256 _supplyIndex1 = supplyIndex1[recipient];
            uint256 _index0 = index0; // get global index0 for accumulated fees
            uint256 _index1 = index1;
            supplyIndex0[recipient] = _index0; // update user current position to global position
            supplyIndex1[recipient] = _index1;
            uint256 _delta0 = _index0 - _supplyIndex0; // see if there is any difference that need to be accrued
            uint256 _delta1 = _index1 - _supplyIndex1;
            if (_delta0 > 0) {
                uint256 _share = (_supplied * _delta0) / 1e18; // add accrued difference for each supplied token
                claimable0[recipient] += _share;
            }
            if (_delta1 > 0) {
                uint256 _share = (_supplied * _delta1) / 1e18;
                claimable1[recipient] += _share;
            }
        } else {
            supplyIndex0[recipient] = index0; // new users are set to the default global state
            supplyIndex1[recipient] = index1;
        }
    }

    /// @inheritdoc IPool
    function getReserves() public view returns (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast) {
        _reserve0 = reserve0;
        _reserve1 = reserve1;
        _blockTimestampLast = blockTimestampLast;
    }

    /// @dev update reserves and, on the first call per block, price accumulators
    function _update(uint256 balance0, uint256 balance1, uint256 _reserve0, uint256 _reserve1) internal {
        uint256 blockTimestamp = block.timestamp;
        uint256 timeElapsed = blockTimestamp - blockTimestampLast;
        if (timeElapsed > 0 && _reserve0 != 0 && _reserve1 != 0) {
            reserve0CumulativeLast += _reserve0 * timeElapsed;
            reserve1CumulativeLast += _reserve1 * timeElapsed;
        }

        Observation memory _point = lastObservation();
        timeElapsed = blockTimestamp - _point.timestamp; // compare the last observation with current timestamp, if greater than 30 minutes, record a new event
        if (timeElapsed > periodSize) {
            observations.push(Observation(blockTimestamp, reserve0CumulativeLast, reserve1CumulativeLast));
        }
        reserve0 = balance0;
        reserve1 = balance1;
        blockTimestampLast = blockTimestamp;
        emit Sync(reserve0, reserve1);
    }

    /// @inheritdoc IPool
    function currentCumulativePrices()
        public
        view
        returns (uint256 reserve0Cumulative, uint256 reserve1Cumulative, uint256 blockTimestamp)
    {
        blockTimestamp = block.timestamp;
        reserve0Cumulative = reserve0CumulativeLast;
        reserve1Cumulative = reserve1CumulativeLast;

        // if time has elapsed since the last update on the pool, mock the accumulated price values
        (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast) = getReserves();
        if (_blockTimestampLast != blockTimestamp) {
            // subtraction overflow is desired
            uint256 timeElapsed = blockTimestamp - _blockTimestampLast;
            reserve0Cumulative += _reserve0 * timeElapsed;
            reserve1Cumulative += _reserve1 * timeElapsed;
        }
    }

    /// @inheritdoc IPool
    function quote(address tokenIn, uint256 amountIn, uint256 granularity) external view returns (uint256 amountOut) {
        uint256[] memory _prices = sample(tokenIn, amountIn, granularity, 1);
        uint256 priceAverageCumulative;
        uint256 _length = _prices.length;
        for (uint256 i = 0; i < _length; i++) {
            priceAverageCumulative += _prices[i];
        }
        return priceAverageCumulative / granularity;
    }

    /// @inheritdoc IPool
    function prices(address tokenIn, uint256 amountIn, uint256 points) external view returns (uint256[] memory) {
        return sample(tokenIn, amountIn, points, 1);
    }

    /// @inheritdoc IPool
    function sample(
        address tokenIn,
        uint256 amountIn,
        uint256 points,
        uint256 window
    ) public view returns (uint256[] memory) {
        uint256[] memory _prices = new uint256[](points);

        uint256 length = observations.length - 1;
        uint256 i = length - (points * window);
        uint256 nextIndex = 0;
        uint256 index = 0;

        for (; i < length; i += window) {
            nextIndex = i + window;
            uint256 timeElapsed = observations[nextIndex].timestamp - observations[i].timestamp;
            uint256 _reserve0 = (observations[nextIndex].reserve0Cumulative - observations[i].reserve0Cumulative) /
                timeElapsed;
            uint256 _reserve1 = (observations[nextIndex].reserve1Cumulative - observations[i].reserve1Cumulative) /
                timeElapsed;
            _prices[index] = _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
            // index < length; length cannot overflow
            unchecked {
                index = index + 1;
            }
        }
        return _prices;
    }

    /// @inheritdoc IPool
    function mint(address to) external nonReentrant returns (uint256 liquidity) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        uint256 _balance0 = IERC20(token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(token1).balanceOf(address(this));
        uint256 _amount0 = _balance0 - _reserve0;
        uint256 _amount1 = _balance1 - _reserve1;

        uint256 _totalSupply = totalSupply(); // gas savings, must be defined here since totalSupply can update in _mintFee
        if (_totalSupply == 0) {
            liquidity = Math.sqrt(_amount0 * _amount1) - MINIMUM_LIQUIDITY;
            _mint(address(1), MINIMUM_LIQUIDITY); // permanently lock the first MINIMUM_LIQUIDITY tokens - cannot be address(0)
            if (stable) {
                if ((_amount0 * 1e18) / decimals0 != (_amount1 * 1e18) / decimals1) revert DepositsNotEqual();
                if (_k(_amount0, _amount1) <= MINIMUM_K) revert BelowMinimumK();
            }
        } else {
            liquidity = Math.min((_amount0 * _totalSupply) / _reserve0, (_amount1 * _totalSupply) / _reserve1);
        }
        if (liquidity == 0) revert InsufficientLiquidityMinted();
        _mint(to, liquidity);

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Mint(_msgSender(), _amount0, _amount1);
    }

    /// @inheritdoc IPool
    function burn(address to) external nonReentrant returns (uint256 amount0, uint256 amount1) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        (address _token0, address _token1) = (token0, token1);
        uint256 _balance0 = IERC20(_token0).balanceOf(address(this));
        uint256 _balance1 = IERC20(_token1).balanceOf(address(this));
        uint256 _liquidity = balanceOf(address(this));

        uint256 _totalSupply = totalSupply(); // gas savings, must be defined here since totalSupply can update in _mintFee
        amount0 = (_liquidity * _balance0) / _totalSupply; // using balances ensures pro-rata distribution
        amount1 = (_liquidity * _balance1) / _totalSupply; // using balances ensures pro-rata distribution
        if (amount0 == 0 || amount1 == 0) revert InsufficientLiquidityBurned();
        _burn(address(this), _liquidity);
        IERC20(_token0).safeTransfer(to, amount0);
        IERC20(_token1).safeTransfer(to, amount1);
        _balance0 = IERC20(_token0).balanceOf(address(this));
        _balance1 = IERC20(_token1).balanceOf(address(this));

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Burn(_msgSender(), to, amount0, amount1);
    }

    /// @inheritdoc IPool
    function swap(uint256 amount0Out, uint256 amount1Out, address to, bytes calldata data) external nonReentrant {
        if (IPoolFactory(factory).isPaused()) revert IsPaused();
        if (amount0Out == 0 && amount1Out == 0) revert InsufficientOutputAmount();
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        if (amount0Out >= _reserve0 || amount1Out >= _reserve1) revert InsufficientLiquidity();

        uint256 _balance0;
        uint256 _balance1;
        {
            // scope for _token{0,1}, avoids stack too deep errors
            (address _token0, address _token1) = (token0, token1);
            if (to == _token0 || to == _token1) revert InvalidTo();
            if (amount0Out > 0) IERC20(_token0).safeTransfer(to, amount0Out); // optimistically transfer tokens
            if (amount1Out > 0) IERC20(_token1).safeTransfer(to, amount1Out); // optimistically transfer tokens
            if (data.length > 0) IPoolCallee(to).hook(_msgSender(), amount0Out, amount1Out, data); // callback, used for flash loans
            _balance0 = IERC20(_token0).balanceOf(address(this));
            _balance1 = IERC20(_token1).balanceOf(address(this));
        }
        uint256 amount0In = _balance0 > _reserve0 - amount0Out ? _balance0 - (_reserve0 - amount0Out) : 0;
        uint256 amount1In = _balance1 > _reserve1 - amount1Out ? _balance1 - (_reserve1 - amount1Out) : 0;
        if (amount0In == 0 && amount1In == 0) revert InsufficientInputAmount();
        {
            // scope for reserve{0,1}Adjusted, avoids stack too deep errors
            (address _token0, address _token1) = (token0, token1);
            if (amount0In > 0) _update0((amount0In * IPoolFactory(factory).getFee(address(this), stable)) / 10000); // accrue fees for token0 and move them out of pool
            if (amount1In > 0) _update1((amount1In * IPoolFactory(factory).getFee(address(this), stable)) / 10000); // accrue fees for token1 and move them out of pool
            _balance0 = IERC20(_token0).balanceOf(address(this)); // since we removed tokens, we need to reconfirm balances, can also simply use previous balance - amountIn/ 10000, but doing balanceOf again as safety check
            _balance1 = IERC20(_token1).balanceOf(address(this));
            // The curve, either x3y+y3x for stable pools, or x*y for volatile pools
            if (_k(_balance0, _balance1) < _k(_reserve0, _reserve1)) revert K();
        }

        _update(_balance0, _balance1, _reserve0, _reserve1);
        emit Swap(_msgSender(), to, amount0In, amount1In, amount0Out, amount1Out);
    }

    /// @inheritdoc IPool
    function skim(address to) external nonReentrant {
        (address _token0, address _token1) = (token0, token1);
        IERC20(_token0).safeTransfer(to, IERC20(_token0).balanceOf(address(this)) - (reserve0));
        IERC20(_token1).safeTransfer(to, IERC20(_token1).balanceOf(address(this)) - (reserve1));
    }

    /// @inheritdoc IPool
    function sync() external nonReentrant {
        _update(IERC20(token0).balanceOf(address(this)), IERC20(token1).balanceOf(address(this)), reserve0, reserve1);
    }

    function _f(uint256 x0, uint256 y) internal pure returns (uint256) {
        uint256 _a = (x0 * y) / 1e18;
        uint256 _b = ((x0 * x0) / 1e18 + (y * y) / 1e18);
        return (_a * _b) / 1e18;
    }

    function _d(uint256 x0, uint256 y) internal pure returns (uint256) {
        return (3 * x0 * ((y * y) / 1e18)) / 1e18 + ((((x0 * x0) / 1e18) * x0) / 1e18);
    }

    function _get_y(uint256 x0, uint256 xy, uint256 y) internal view returns (uint256) {
        for (uint256 i = 0; i < 255; i++) {
            uint256 k = _f(x0, y);
            if (k < xy) {
                // there are two cases where dy == 0
                // case 1: The y is converged and we find the correct answer
                // case 2: _d(x0, y) is too large compare to (xy - k) and the rounding error
                //         screwed us.
                //         In this case, we need to increase y by 1
                uint256 dy = ((xy - k) * 1e18) / _d(x0, y);
                if (dy == 0) {
                    if (k == xy) {
                        // We found the correct answer. Return y
                        return y;
                    }
                    if (_k(x0, y + 1) > xy) {
                        // If _k(x0, y + 1) > xy, then we are close to the correct answer.
                        // There's no closer answer than y + 1
                        return y + 1;
                    }
                    dy = 1;
                }
                y = y + dy;
            } else {
                uint256 dy = ((k - xy) * 1e18) / _d(x0, y);
                if (dy == 0) {
                    if (k == xy || _f(x0, y - 1) < xy) {
                        // Likewise, if k == xy, we found the correct answer.
                        // If _f(x0, y - 1) < xy, then we are close to the correct answer.
                        // There's no closer answer than "y"
                        // It's worth mentioning that we need to find y where f(x0, y) >= xy
                        // As a result, we can't return y - 1 even it's closer to the correct answer
                        return y;
                    }
                    dy = 1;
                }
                y = y - dy;
            }
        }
        revert("!y");
    }

    /// @inheritdoc IPool
    function getAmountOut(uint256 amountIn, address tokenIn) external view returns (uint256) {
        (uint256 _reserve0, uint256 _reserve1) = (reserve0, reserve1);
        amountIn -= (amountIn * IPoolFactory(factory).getFee(address(this), stable)) / 10000; // remove fee from amount received
        return _getAmountOut(amountIn, tokenIn, _reserve0, _reserve1);
    }

    function _getAmountOut(
        uint256 amountIn,
        address tokenIn,
        uint256 _reserve0,
        uint256 _reserve1
    ) internal view returns (uint256) {
        if (stable) {
            uint256 xy = _k(_reserve0, _reserve1);
            _reserve0 = (_reserve0 * 1e18) / decimals0;
            _reserve1 = (_reserve1 * 1e18) / decimals1;
            (uint256 reserveA, uint256 reserveB) = tokenIn == token0 ? (_reserve0, _reserve1) : (_reserve1, _reserve0);
            amountIn = tokenIn == token0 ? (amountIn * 1e18) / decimals0 : (amountIn * 1e18) / decimals1;
            uint256 y = reserveB - _get_y(amountIn + reserveA, xy, reserveB);
            return (y * (tokenIn == token0 ? decimals1 : decimals0)) / 1e18;
        } else {
            (uint256 reserveA, uint256 reserveB) = tokenIn == token0 ? (_reserve0, _reserve1) : (_reserve1, _reserve0);
            return (amountIn * reserveB) / (reserveA + amountIn);
        }
    }

    function _k(uint256 x, uint256 y) internal view returns (uint256) {
        if (stable) {
            uint256 _x = (x * 1e18) / decimals0;
            uint256 _y = (y * 1e18) / decimals1;
            uint256 _a = (_x * _y) / 1e18;
            uint256 _b = ((_x * _x) / 1e18 + (_y * _y) / 1e18);
            return (_a * _b) / 1e18; // x3y+y3x >= k
        } else {
            return x * y; // xy >= k
        }
    }

    /*
    @dev OZ inheritance overrides
    These are needed as _name and _symbol are set privately before
    logic is executed within the constructor to set _name and _symbol.
    */
    function name() public view override returns (string memory) {
        return _name;
    }

    function symbol() public view override returns (string memory) {
        return _symbol;
    }

    function _beforeTokenTransfer(address from, address to, uint256) internal override {
        _updateFor(from);
        _updateFor(to);
    }
}

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