// File: @pancakeswap/v3-core/contracts/interfaces/callback/IPancakeV3SwapCallback.sol



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

/// @title Callback for IPancakeV3PoolActions#swap
/// @notice Any contract that calls IPancakeV3PoolActions#swap must implement this interface
interface IPancakeV3SwapCallback {
    /// @notice Called to `msg.sender` after executing a swap via IPancakeV3Pool#swap.
    /// @dev In the implementation you must pay the pool tokens owed for the swap.
    /// The caller of this method must be checked to be a PancakeV3Pool deployed by the canonical PancakeV3Factory.
    /// amount0Delta and amount1Delta can both be 0 if no tokens were swapped.
    /// @param amount0Delta The amount of token0 that was sent (negative) or must be received (positive) by the pool by
    /// the end of the swap. If positive, the callback must send that amount of token0 to the pool.
    /// @param amount1Delta The amount of token1 that was sent (negative) or must be received (positive) by the pool by
    /// the end of the swap. If positive, the callback must send that amount of token1 to the pool.
    /// @param data Any data passed through by the caller via the IPancakeV3PoolActions#swap call
    function pancakeV3SwapCallback(
        int256 amount0Delta,
        int256 amount1Delta,
        bytes calldata data
    ) external;
}

// File: @pancakeswap/v3-core/contracts/interfaces/IPancakeV3Pool.sol



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

import './pool/IPancakeV3PoolImmutables.sol';
import './pool/IPancakeV3PoolState.sol';
import './pool/IPancakeV3PoolDerivedState.sol';
import './pool/IPancakeV3PoolActions.sol';
import './pool/IPancakeV3PoolOwnerActions.sol';
import './pool/IPancakeV3PoolEvents.sol';

/// @title The interface for a PancakeSwap V3 Pool
/// @notice A PancakeSwap pool facilitates swapping and automated market making between any two assets that strictly conform
/// to the ERC20 specification
/// @dev The pool interface is broken up into many smaller pieces
interface IPancakeV3Pool is
    IPancakeV3PoolImmutables,
    IPancakeV3PoolState,
    IPancakeV3PoolDerivedState,
    IPancakeV3PoolActions,
    IPancakeV3PoolOwnerActions,
    IPancakeV3PoolEvents
{

}

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolActions.sol



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

/// @title Permissionless pool actions
/// @notice Contains pool methods that can be called by anyone
interface IPancakeV3PoolActions {
    /// @notice Sets the initial price for the pool
    /// @dev Price is represented as a sqrt(amountToken1/amountToken0) Q64.96 value
    /// @param sqrtPriceX96 the initial sqrt price of the pool as a Q64.96
    function initialize(uint160 sqrtPriceX96) external;

    /// @notice Adds liquidity for the given recipient/tickLower/tickUpper position
    /// @dev The caller of this method receives a callback in the form of IPancakeV3MintCallback#pancakeV3MintCallback
    /// in which they must pay any token0 or token1 owed for the liquidity. The amount of token0/token1 due depends
    /// on tickLower, tickUpper, the amount of liquidity, and the current price.
    /// @param recipient The address for which the liquidity will be created
    /// @param tickLower The lower tick of the position in which to add liquidity
    /// @param tickUpper The upper tick of the position in which to add liquidity
    /// @param amount The amount of liquidity to mint
    /// @param data Any data that should be passed through to the callback
    /// @return amount0 The amount of token0 that was paid to mint the given amount of liquidity. Matches the value in the callback
    /// @return amount1 The amount of token1 that was paid to mint the given amount of liquidity. Matches the value in the callback
    function mint(
        address recipient,
        int24 tickLower,
        int24 tickUpper,
        uint128 amount,
        bytes calldata data
    ) external returns (uint256 amount0, uint256 amount1);

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

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

    /// @notice Swap token0 for token1, or token1 for token0
    /// @dev The caller of this method receives a callback in the form of IPancakeV3SwapCallback#pancakeV3SwapCallback
    /// @param recipient The address to receive the output of the swap
    /// @param zeroForOne The direction of the swap, true for token0 to token1, false for token1 to token0
    /// @param amountSpecified The amount of the swap, which implicitly configures the swap as exact input (positive), or exact output (negative)
    /// @param sqrtPriceLimitX96 The Q64.96 sqrt price limit. If zero for one, the price cannot be less than this
    /// value after the swap. If one for zero, the price cannot be greater than this value after the swap
    /// @param data Any data to be passed through to the callback
    /// @return amount0 The delta of the balance of token0 of the pool, exact when negative, minimum when positive
    /// @return amount1 The delta of the balance of token1 of the pool, exact when negative, minimum when positive
    function swap(
        address recipient,
        bool zeroForOne,
        int256 amountSpecified,
        uint160 sqrtPriceLimitX96,
        bytes calldata data
    ) external returns (int256 amount0, int256 amount1);

    /// @notice Receive token0 and/or token1 and pay it back, plus a fee, in the callback
    /// @dev The caller of this method receives a callback in the form of IPancakeV3FlashCallback#pancakeV3FlashCallback
    /// @dev Can be used to donate underlying tokens pro-rata to currently in-range liquidity providers by calling
    /// with 0 amount{0,1} and sending the donation amount(s) from the callback
    /// @param recipient The address which will receive the token0 and token1 amounts
    /// @param amount0 The amount of token0 to send
    /// @param amount1 The amount of token1 to send
    /// @param data Any data to be passed through to the callback
    function flash(
        address recipient,
        uint256 amount0,
        uint256 amount1,
        bytes calldata data
    ) external;

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

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolDerivedState.sol



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

/// @title Pool state that is not stored
/// @notice Contains view functions to provide information about the pool that is computed rather than stored on the
/// blockchain. The functions here may have variable gas costs.
interface IPancakeV3PoolDerivedState {
    /// @notice Returns the cumulative tick and liquidity as of each timestamp `secondsAgo` from the current block timestamp
    /// @dev To get a time weighted average tick or liquidity-in-range, you must call this with two values, one representing
    /// the beginning of the period and another for the end of the period. E.g., to get the last hour time-weighted average tick,
    /// you must call it with secondsAgos = [3600, 0].
    /// @dev The time weighted average tick represents the geometric time weighted average price of the pool, in
    /// log base sqrt(1.0001) of token1 / token0. The TickMath library can be used to go from a tick value to a ratio.
    /// @param secondsAgos From how long ago each cumulative tick and liquidity value should be returned
    /// @return tickCumulatives Cumulative tick values as of each `secondsAgos` from the current block timestamp
    /// @return secondsPerLiquidityCumulativeX128s Cumulative seconds per liquidity-in-range value as of each `secondsAgos` from the current block
    /// timestamp
    function observe(uint32[] calldata secondsAgos)
        external
        view
        returns (int56[] memory tickCumulatives, uint160[] memory secondsPerLiquidityCumulativeX128s);

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

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolEvents.sol



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

/// @title Events emitted by a pool
/// @notice Contains all events emitted by the pool
interface IPancakeV3PoolEvents {
    /// @notice Emitted exactly once by a pool when #initialize is first called on the pool
    /// @dev Mint/Burn/Swap cannot be emitted by the pool before Initialize
    /// @param sqrtPriceX96 The initial sqrt price of the pool, as a Q64.96
    /// @param tick The initial tick of the pool, i.e. log base 1.0001 of the starting price of the pool
    event Initialize(uint160 sqrtPriceX96, int24 tick);

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

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

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

    /// @notice Emitted by the pool for any swaps between token0 and token1
    /// @param sender The address that initiated the swap call, and that received the callback
    /// @param recipient The address that received the output of the swap
    /// @param amount0 The delta of the token0 balance of the pool
    /// @param amount1 The delta of the token1 balance of the pool
    /// @param sqrtPriceX96 The sqrt(price) of the pool after the swap, as a Q64.96
    /// @param liquidity The liquidity of the pool after the swap
    /// @param tick The log base 1.0001 of price of the pool after the swap
    /// @param protocolFeesToken0 The protocol fee of token0 in the swap
    /// @param protocolFeesToken1 The protocol fee of token1 in the swap
    event Swap(
        address indexed sender,
        address indexed recipient,
        int256 amount0,
        int256 amount1,
        uint160 sqrtPriceX96,
        uint128 liquidity,
        int24 tick,
        uint128 protocolFeesToken0,
        uint128 protocolFeesToken1
    );

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

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

    /// @notice Emitted when the protocol fee is changed by the pool
    /// @param feeProtocol0Old The previous value of the token0 protocol fee
    /// @param feeProtocol1Old The previous value of the token1 protocol fee
    /// @param feeProtocol0New The updated value of the token0 protocol fee
    /// @param feeProtocol1New The updated value of the token1 protocol fee
    event SetFeeProtocol(
        uint32 feeProtocol0Old,
        uint32 feeProtocol1Old,
        uint32 feeProtocol0New,
        uint32 feeProtocol1New
    );

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

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolImmutables.sol



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

/// @title Pool state that never changes
/// @notice These parameters are fixed for a pool forever, i.e., the methods will always return the same values
interface IPancakeV3PoolImmutables {
    /// @notice The contract that deployed the pool, which must adhere to the IPancakeV3Factory interface
    /// @return The contract address
    function factory() external view returns (address);

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

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

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

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

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

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolOwnerActions.sol



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

/// @title Permissioned pool actions
/// @notice Contains pool methods that may only be called by the factory owner
interface IPancakeV3PoolOwnerActions {
    /// @notice Set the denominator of the protocol's % share of the fees
    /// @param feeProtocol0 new protocol fee for token0 of the pool
    /// @param feeProtocol1 new protocol fee for token1 of the pool
    function setFeeProtocol(uint32 feeProtocol0, uint32 feeProtocol1) external;

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

    /// @notice Set the LM pool to enable liquidity mining
    function setLmPool(address lmPool) external;
}

// File: @pancakeswap/v3-core/contracts/interfaces/pool/IPancakeV3PoolState.sol



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

/// @title Pool state that can change
/// @notice These methods compose the pool's state, and can change with any frequency including multiple times
/// per transaction
interface IPancakeV3PoolState {
    /// @notice The 0th storage slot in the pool stores many values, and is exposed as a single method to save gas
    /// when accessed externally.
    /// @return sqrtPriceX96 The current price of the pool as a sqrt(token1/token0) Q64.96 value
    /// tick The current tick of the pool, i.e. according to the last tick transition that was run.
    /// This value may not always be equal to SqrtTickMath.getTickAtSqrtRatio(sqrtPriceX96) if the price is on a tick
    /// boundary.
    /// observationIndex The index of the last oracle observation that was written,
    /// observationCardinality The current maximum number of observations stored in the pool,
    /// observationCardinalityNext The next maximum number of observations, to be updated when the observation.
    /// feeProtocol The protocol fee for both tokens of the pool.
    /// Encoded as two 4 bit values, where the protocol fee of token1 is shifted 4 bits and the protocol fee of token0
    /// is the lower 4 bits. Used as the denominator of a fraction of the swap fee, e.g. 4 means 1/4th of the swap fee.
    /// unlocked Whether the pool is currently locked to reentrancy
    function slot0()
        external
        view
        returns (
            uint160 sqrtPriceX96,
            int24 tick,
            uint16 observationIndex,
            uint16 observationCardinality,
            uint16 observationCardinalityNext,
            uint32 feeProtocol,
            bool unlocked
        );

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

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

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

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

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

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

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

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

// File: @pancakeswap/v3-core/contracts/libraries/BitMath.sol



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

/// @title BitMath
/// @dev This library provides functionality for computing bit properties of an unsigned integer
library BitMath {
    /// @notice Returns the index of the most significant bit of the number,
    ///     where the least significant bit is at index 0 and the most significant bit is at index 255
    /// @dev The function satisfies the property:
    ///     x >= 2**mostSignificantBit(x) and x < 2**(mostSignificantBit(x)+1)
    /// @param x the value for which to compute the most significant bit, must be greater than 0
    /// @return r the index of the most significant bit
    function mostSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0);

        if (x >= 0x100000000000000000000000000000000) {
            x >>= 128;
            r += 128;
        }
        if (x >= 0x10000000000000000) {
            x >>= 64;
            r += 64;
        }
        if (x >= 0x100000000) {
            x >>= 32;
            r += 32;
        }
        if (x >= 0x10000) {
            x >>= 16;
            r += 16;
        }
        if (x >= 0x100) {
            x >>= 8;
            r += 8;
        }
        if (x >= 0x10) {
            x >>= 4;
            r += 4;
        }
        if (x >= 0x4) {
            x >>= 2;
            r += 2;
        }
        if (x >= 0x2) r += 1;
    }

    /// @notice Returns the index of the least significant bit of the number,
    ///     where the least significant bit is at index 0 and the most significant bit is at index 255
    /// @dev The function satisfies the property:
    ///     (x & 2**leastSignificantBit(x)) != 0 and (x & (2**(leastSignificantBit(x)) - 1)) == 0)
    /// @param x the value for which to compute the least significant bit, must be greater than 0
    /// @return r the index of the least significant bit
    function leastSignificantBit(uint256 x) internal pure returns (uint8 r) {
        require(x > 0);

        r = 255;
        if (x & type(uint128).max > 0) {
            r -= 128;
        } else {
            x >>= 128;
        }
        if (x & type(uint64).max > 0) {
            r -= 64;
        } else {
            x >>= 64;
        }
        if (x & type(uint32).max > 0) {
            r -= 32;
        } else {
            x >>= 32;
        }
        if (x & type(uint16).max > 0) {
            r -= 16;
        } else {
            x >>= 16;
        }
        if (x & type(uint8).max > 0) {
            r -= 8;
        } else {
            x >>= 8;
        }
        if (x & 0xf > 0) {
            r -= 4;
        } else {
            x >>= 4;
        }
        if (x & 0x3 > 0) {
            r -= 2;
        } else {
            x >>= 2;
        }
        if (x & 0x1 > 0) r -= 1;
    }
}

// File: @pancakeswap/v3-core/contracts/libraries/LowGasSafeMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.0;

/// @title Optimized overflow and underflow safe math operations
/// @notice Contains methods for doing math operations that revert on overflow or underflow for minimal gas cost
library LowGasSafeMath {
    /// @notice Returns x + y, reverts if sum overflows uint256
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x);
    }

    /// @notice Returns x - y, reverts if underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x - y) <= x);
    }

    /// @notice Returns x * y, reverts if overflows
    /// @param x The multiplicand
    /// @param y The multiplier
    /// @return z The product of x and y
    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(x == 0 || (z = x * y) / x == y);
    }

    /// @notice Returns x + y, reverts if overflows or underflows
    /// @param x The augend
    /// @param y The addend
    /// @return z The sum of x and y
    function add(int256 x, int256 y) internal pure returns (int256 z) {
        require((z = x + y) >= x == (y >= 0));
    }

    /// @notice Returns x - y, reverts if overflows or underflows
    /// @param x The minuend
    /// @param y The subtrahend
    /// @return z The difference of x and y
    function sub(int256 x, int256 y) internal pure returns (int256 z) {
        require((z = x - y) <= x == (y >= 0));
    }
}

// File: @pancakeswap/v3-core/contracts/libraries/SafeCast.sol



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

/// @title Safe casting methods
/// @notice Contains methods for safely casting between types
library SafeCast {
    /// @notice Cast a uint256 to a uint160, revert on overflow
    /// @param y The uint256 to be downcasted
    /// @return z The downcasted integer, now type uint160
    function toUint160(uint256 y) internal pure returns (uint160 z) {
        require((z = uint160(y)) == y);
    }

    /// @notice Cast a int256 to a int128, revert on overflow or underflow
    /// @param y The int256 to be downcasted
    /// @return z The downcasted integer, now type int128
    function toInt128(int256 y) internal pure returns (int128 z) {
        require((z = int128(y)) == y);
    }

    /// @notice Cast a uint256 to a int256, revert on overflow
    /// @param y The uint256 to be casted
    /// @return z The casted integer, now type int256
    function toInt256(uint256 y) internal pure returns (int256 z) {
        require(y < 2**255);
        z = int256(y);
    }
}

// File: @pancakeswap/v3-core/contracts/libraries/TickBitmap.sol



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

import './BitMath.sol';

/// @title Packed tick initialized state library
/// @notice Stores a packed mapping of tick index to its initialized state
/// @dev The mapping uses int16 for keys since ticks are represented as int24 and there are 256 (2^8) values per word.
library TickBitmap {
    /// @notice Computes the position in the mapping where the initialized bit for a tick lives
    /// @param tick The tick for which to compute the position
    /// @return wordPos The key in the mapping containing the word in which the bit is stored
    /// @return bitPos The bit position in the word where the flag is stored
    function position(int24 tick) private pure returns (int16 wordPos, uint8 bitPos) {
        wordPos = int16(tick >> 8);
        bitPos = uint8(tick % 256);
    }

    /// @notice Flips the initialized state for a given tick from false to true, or vice versa
    /// @param self The mapping in which to flip the tick
    /// @param tick The tick to flip
    /// @param tickSpacing The spacing between usable ticks
    function flipTick(
        mapping(int16 => uint256) storage self,
        int24 tick,
        int24 tickSpacing
    ) internal {
        require(tick % tickSpacing == 0); // ensure that the tick is spaced
        (int16 wordPos, uint8 bitPos) = position(tick / tickSpacing);
        uint256 mask = 1 << bitPos;
        self[wordPos] ^= mask;
    }

    /// @notice Returns the next initialized tick contained in the same word (or adjacent word) as the tick that is either
    /// to the left (less than or equal to) or right (greater than) of the given tick
    /// @param self The mapping in which to compute the next initialized tick
    /// @param tick The starting tick
    /// @param tickSpacing The spacing between usable ticks
    /// @param lte Whether to search for the next initialized tick to the left (less than or equal to the starting tick)
    /// @return next The next initialized or uninitialized tick up to 256 ticks away from the current tick
    /// @return initialized Whether the next tick is initialized, as the function only searches within up to 256 ticks
    function nextInitializedTickWithinOneWord(
        mapping(int16 => uint256) storage self,
        int24 tick,
        int24 tickSpacing,
        bool lte
    ) internal view returns (int24 next, bool initialized) {
        int24 compressed = tick / tickSpacing;
        if (tick < 0 && tick % tickSpacing != 0) compressed--; // round towards negative infinity

        if (lte) {
            (int16 wordPos, uint8 bitPos) = position(compressed);
            // all the 1s at or to the right of the current bitPos
            uint256 mask = (1 << bitPos) - 1 + (1 << bitPos);
            uint256 masked = self[wordPos] & mask;

            // if there are no initialized ticks to the right of or at the current tick, return rightmost in the word
            initialized = masked != 0;
            // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
            next = initialized
                ? (compressed - int24(bitPos - BitMath.mostSignificantBit(masked))) * tickSpacing
                : (compressed - int24(bitPos)) * tickSpacing;
        } else {
            // start from the word of the next tick, since the current tick state doesn't matter
            (int16 wordPos, uint8 bitPos) = position(compressed + 1);
            // all the 1s at or to the left of the bitPos
            uint256 mask = ~((1 << bitPos) - 1);
            uint256 masked = self[wordPos] & mask;

            // if there are no initialized ticks to the left of the current tick, return leftmost in the word
            initialized = masked != 0;
            // overflow/underflow is possible, but prevented externally by limiting both tickSpacing and tick
            next = initialized
                ? (compressed + 1 + int24(BitMath.leastSignificantBit(masked) - bitPos)) * tickSpacing
                : (compressed + 1 + int24(type(uint8).max - bitPos)) * tickSpacing;
        }
    }
}

// File: @pancakeswap/v3-core/contracts/libraries/TickMath.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.5.0 <0.8.0;

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

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

    /// @notice Calculates sqrt(1.0001^tick) * 2^96
    /// @dev Throws if |tick| > max tick
    /// @param tick The input tick for the above formula
    /// @return sqrtPriceX96 A Fixed point Q64.96 number representing the sqrt of the ratio of the two assets (token1/token0)
    /// at the given tick
    function getSqrtRatioAtTick(int24 tick) internal pure returns (uint160 sqrtPriceX96) {
        uint256 absTick = tick < 0 ? uint256(-int256(tick)) : uint256(int256(tick));
        require(absTick <= uint256(MAX_TICK), 'T');

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

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

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

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

        uint256 r = ratio;
        uint256 msb = 0;

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

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

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

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

        int256 log_sqrt10001 = log_2 * 255738958999603826347141; // 128.128 number

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

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

// File: @pancakeswap/v3-periphery/contracts/base/PeripheryImmutableState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '../interfaces/IPeripheryImmutableState.sol';

/// @title Immutable state
/// @notice Immutable state used by periphery contracts
abstract contract PeripheryImmutableState is IPeripheryImmutableState {
    /// @inheritdoc IPeripheryImmutableState
    address public immutable override deployer;
    /// @inheritdoc IPeripheryImmutableState
    address public immutable override factory;
    /// @inheritdoc IPeripheryImmutableState
    address public immutable override WETH9;

    constructor(address _deployer, address _factory, address _WETH9) {
        deployer = _deployer;
        factory = _factory;
        WETH9 = _WETH9;
    }
}

// File: @pancakeswap/v3-periphery/contracts/interfaces/IPeripheryImmutableState.sol



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

/// @title Immutable state
/// @notice Functions that return immutable state of the router
interface IPeripheryImmutableState {
    /// @return Returns the address of the PancakeSwap V3 deployer
    function deployer() external view returns (address);

    /// @return Returns the address of the PancakeSwap V3 factory
    function factory() external view returns (address);

    /// @return Returns the address of WETH9
    function WETH9() external view returns (address);
}

// File: @pancakeswap/v3-periphery/contracts/libraries/BytesLib.sol



// SPDX-License-Identifier: GPL-2.0-or-later
/*
 * @title Solidity Bytes Arrays Utils
 * @author Gonçalo Sá <goncalo.sa@consensys.net>
 *
 * @dev Bytes tightly packed arrays utility library for ethereum contracts written in Solidity.
 *      The library lets you concatenate, slice and type cast bytes arrays both in memory and storage.
 */
pragma solidity >=0.5.0 <0.8.0;

library BytesLib {
    function slice(
        bytes memory _bytes,
        uint256 _start,
        uint256 _length
    ) internal pure returns (bytes memory) {
        require(_length + 31 >= _length, 'slice_overflow');
        require(_start + _length >= _start, 'slice_overflow');
        require(_bytes.length >= _start + _length, 'slice_outOfBounds');

        bytes memory tempBytes;

        assembly {
            switch iszero(_length)
                case 0 {
                    // Get a location of some free memory and store it in tempBytes as
                    // Solidity does for memory variables.
                    tempBytes := mload(0x40)

                    // The first word of the slice result is potentially a partial
                    // word read from the original array. To read it, we calculate
                    // the length of that partial word and start copying that many
                    // bytes into the array. The first word we copy will start with
                    // data we don't care about, but the last `lengthmod` bytes will
                    // land at the beginning of the contents of the new array. When
                    // we're done copying, we overwrite the full first word with
                    // the actual length of the slice.
                    let lengthmod := and(_length, 31)

                    // The multiplication in the next line is necessary
                    // because when slicing multiples of 32 bytes (lengthmod == 0)
                    // the following copy loop was copying the origin's length
                    // and then ending prematurely not copying everything it should.
                    let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                    let end := add(mc, _length)

                    for {
                        // The multiplication in the next line has the same exact purpose
                        // as the one above.
                        let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                    } lt(mc, end) {
                        mc := add(mc, 0x20)
                        cc := add(cc, 0x20)
                    } {
                        mstore(mc, mload(cc))
                    }

                    mstore(tempBytes, _length)

                    //update free-memory pointer
                    //allocating the array padded to 32 bytes like the compiler does now
                    mstore(0x40, and(add(mc, 31), not(31)))
                }
                //if we want a zero-length slice let's just return a zero-length array
                default {
                    tempBytes := mload(0x40)
                    //zero out the 32 bytes slice we are about to return
                    //we need to do it because Solidity does not garbage collect
                    mstore(tempBytes, 0)

                    mstore(0x40, add(tempBytes, 0x20))
                }
        }

        return tempBytes;
    }

    function toAddress(bytes memory _bytes, uint256 _start) internal pure returns (address) {
        require(_start + 20 >= _start, 'toAddress_overflow');
        require(_bytes.length >= _start + 20, 'toAddress_outOfBounds');
        address tempAddress;

        assembly {
            tempAddress := div(mload(add(add(_bytes, 0x20), _start)), 0x1000000000000000000000000)
        }

        return tempAddress;
    }

    function toUint24(bytes memory _bytes, uint256 _start) internal pure returns (uint24) {
        require(_start + 3 >= _start, 'toUint24_overflow');
        require(_bytes.length >= _start + 3, 'toUint24_outOfBounds');
        uint24 tempUint;

        assembly {
            tempUint := mload(add(add(_bytes, 0x3), _start))
        }

        return tempUint;
    }
}

// File: @pancakeswap/v3-periphery/contracts/libraries/Path.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.6.0;

import './BytesLib.sol';

/// @title Functions for manipulating path data for multihop swaps
library Path {
    using BytesLib for bytes;

    /// @dev The length of the bytes encoded address
    uint256 private constant ADDR_SIZE = 20;
    /// @dev The length of the bytes encoded fee
    uint256 private constant FEE_SIZE = 3;

    /// @dev The offset of a single token address and pool fee
    uint256 private constant NEXT_OFFSET = ADDR_SIZE + FEE_SIZE;
    /// @dev The offset of an encoded pool key
    uint256 private constant POP_OFFSET = NEXT_OFFSET + ADDR_SIZE;
    /// @dev The minimum length of an encoding that contains 2 or more pools
    uint256 private constant MULTIPLE_POOLS_MIN_LENGTH = POP_OFFSET + NEXT_OFFSET;

    /// @notice Returns true iff the path contains two or more pools
    /// @param path The encoded swap path
    /// @return True if path contains two or more pools, otherwise false
    function hasMultiplePools(bytes memory path) internal pure returns (bool) {
        return path.length >= MULTIPLE_POOLS_MIN_LENGTH;
    }

    /// @notice Returns the number of pools in the path
    /// @param path The encoded swap path
    /// @return The number of pools in the path
    function numPools(bytes memory path) internal pure returns (uint256) {
        // Ignore the first token address. From then on every fee and token offset indicates a pool.
        return ((path.length - ADDR_SIZE) / NEXT_OFFSET);
    }

    /// @notice Decodes the first pool in path
    /// @param path The bytes encoded swap path
    /// @return tokenA The first token of the given pool
    /// @return tokenB The second token of the given pool
    /// @return fee The fee level of the pool
    function decodeFirstPool(bytes memory path)
        internal
        pure
        returns (
            address tokenA,
            address tokenB,
            uint24 fee
        )
    {
        tokenA = path.toAddress(0);
        fee = path.toUint24(ADDR_SIZE);
        tokenB = path.toAddress(NEXT_OFFSET);
    }

    /// @notice Gets the segment corresponding to the first pool in the path
    /// @param path The bytes encoded swap path
    /// @return The segment containing all data necessary to target the first pool in the path
    function getFirstPool(bytes memory path) internal pure returns (bytes memory) {
        return path.slice(0, POP_OFFSET);
    }

    /// @notice Skips a token + fee element from the buffer and returns the remainder
    /// @param path The swap path
    /// @return The remaining token + fee elements in the path
    function skipToken(bytes memory path) internal pure returns (bytes memory) {
        return path.slice(NEXT_OFFSET, path.length - NEXT_OFFSET);
    }
}

// File: @uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol



pragma solidity >=0.5.0;

interface IUniswapV2Pair {
    event Approval(address indexed owner, address indexed spender, uint value);
    event Transfer(address indexed from, address indexed to, uint value);

    function name() external pure returns (string memory);
    function symbol() external pure returns (string memory);
    function decimals() external pure returns (uint8);
    function totalSupply() external view returns (uint);
    function balanceOf(address owner) external view returns (uint);
    function allowance(address owner, address spender) external view returns (uint);

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

    function DOMAIN_SEPARATOR() external view returns (bytes32);
    function PERMIT_TYPEHASH() external pure returns (bytes32);
    function nonces(address owner) external view returns (uint);

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

    event Mint(address indexed sender, uint amount0, uint amount1);
    event Burn(address indexed sender, uint amount0, uint amount1, address indexed to);
    event Swap(
        address indexed sender,
        uint amount0In,
        uint amount1In,
        uint amount0Out,
        uint amount1Out,
        address indexed to
    );
    event Sync(uint112 reserve0, uint112 reserve1);

    function MINIMUM_LIQUIDITY() external pure returns (uint);
    function factory() external view returns (address);
    function token0() external view returns (address);
    function token1() external view returns (address);
    function getReserves() external view returns (uint112 reserve0, uint112 reserve1, uint32 blockTimestampLast);
    function price0CumulativeLast() external view returns (uint);
    function price1CumulativeLast() external view returns (uint);
    function kLast() external view returns (uint);

    function mint(address to) external returns (uint liquidity);
    function burn(address to) external returns (uint amount0, uint amount1);
    function swap(uint amount0Out, uint amount1Out, address to, bytes calldata data) external;
    function skim(address to) external;
    function sync() external;

    function initialize(address, address) external;
}

// File: contracts/base/ImmutableState.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;

import '../interfaces/IImmutableState.sol';

/// @title Immutable state
/// @notice Immutable state used by the swap router
abstract contract ImmutableState is IImmutableState {
    /// @inheritdoc IImmutableState
    address public immutable override factoryV2;
    /// @inheritdoc IImmutableState
    address public immutable override positionManager;

    constructor(address _factoryV2, address _positionManager) {
        factoryV2 = _factoryV2;
        positionManager = _positionManager;
    }
}

// File: contracts/interfaces/IImmutableState.sol



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

/// @title Immutable state
/// @notice Functions that return immutable state of the router
interface IImmutableState {
    /// @return Returns the address of the PancakeSwap V2 factory
    function factoryV2() external view returns (address);

    /// @return Returns the address of PancakeSwap V3 NFT position manager
    function positionManager() external view returns (address);
}

// File: contracts/interfaces/IMixedRouteQuoterV1.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.7.5;
pragma abicoder v2;

/// @title MixedRouteQuoterV1 Interface
/// @notice Supports quoting the calculated amounts for exact input swaps. Is specialized for routes containing a mix of Stable, V2 and V3 liquidity.
/// @notice For each pool also tells you the number of initialized ticks crossed and the sqrt price of the pool after the swap.
/// @dev These functions are not marked view because they rely on calling non-view functions and reverting
/// to compute the result. They are also not gas efficient and should not be called on-chain.
interface IMixedRouteQuoterV1 {
    /// @notice Returns the amount out received for a given exact input swap without executing the swap
    /// @param path The path of the swap, i.e. each token pair and the pool fee
    /// @param flag 0 for V3, 1 for V2, 2 for 2pool, 3 for 3pool
    /// @param amountIn The amount of the first token to swap
    /// @return amountOut The amount of the last token that would be received
    /// @return v3SqrtPriceX96AfterList List of the sqrt price after the swap for each v3 pool in the path, 0 for v2 or stable pools
    /// @return v3InitializedTicksCrossedList List of the initialized ticks that the swap crossed for each v3 pool in the path, 0 for v2 or stable pools
    /// @return v3SwapGasEstimate The estimate of the gas that the v3 swaps in the path consume
    function quoteExactInput(bytes memory path, uint256[] memory flag, uint256 amountIn)
        external
        returns (
            uint256 amountOut,
            uint160[] memory v3SqrtPriceX96AfterList,
            uint32[] memory v3InitializedTicksCrossedList,
            uint256 v3SwapGasEstimate
        );

    struct QuoteExactInputSingleV3Params {
        address tokenIn;
        address tokenOut;
        uint256 amountIn;
        uint24 fee;
        uint160 sqrtPriceLimitX96;
    }

    struct QuoteExactInputSingleV2Params {
        address tokenIn;
        address tokenOut;
        uint256 amountIn;
    }

    struct QuoteExactInputSingleStableParams {
        address tokenIn;
        address tokenOut;
        uint256 amountIn;
        uint256 flag;
    }

    /// @notice Returns the amount out received for a given exact input but for a swap of a single pool
    /// @param params The params for the quote, encoded as `QuoteExactInputSingleParams`
    /// tokenIn The token being swapped in
    /// tokenOut The token being swapped out
    /// fee The fee of the token pool to consider for the pair
    /// amountIn The desired input amount
    /// sqrtPriceLimitX96 The price limit of the pool that cannot be exceeded by the swap
    /// @return amountOut The amount of `tokenOut` that would be received
    /// @return sqrtPriceX96After The sqrt price of the pool after the swap
    /// @return initializedTicksCrossed The number of initialized ticks that the swap crossed
    /// @return gasEstimate The estimate of the gas that the swap consumes
    function quoteExactInputSingleV3(QuoteExactInputSingleV3Params memory params)
        external
        returns (
            uint256 amountOut,
            uint160 sqrtPriceX96After,
            uint32 initializedTicksCrossed,
            uint256 gasEstimate
        );

    /// @notice Returns the amount out received for a given exact input but for a swap of a single V2 pool
    /// @param params The params for the quote, encoded as `QuoteExactInputSingleV2Params`
    /// tokenIn The token being swapped in
    /// tokenOut The token being swapped out
    /// amountIn The desired input amount
    /// @return amountOut The amount of `tokenOut` that would be received
    function quoteExactInputSingleV2(QuoteExactInputSingleV2Params memory params) external returns (uint256 amountOut);

    /// @notice Returns the amount out received for a given exact input but for a swap of a single Stable pool
    /// @param params The params for the quote, encoded as `QuoteExactInputSingleStableParams`
    /// tokenIn The token being swapped in
    /// tokenOut The token being swapped out
    /// amountIn The desired input amount
    /// flag The token amount in a single Stable pool. 2 for 2pool, 3 for 3pool
    /// @return amountOut The amount of `tokenOut` that would be received
    function quoteExactInputSingleStable(QuoteExactInputSingleStableParams memory params) external returns (uint256 amountOut);

    /// @dev ExactOutput swaps are not supported by this new Quoter which is specialized for supporting routes
    ///      crossing Stable, V2 liquidity pairs and V3 pools.
    /// @deprecated quoteExactOutputSingle and exactOutput. Use QuoterV2 instead.
}

// File: contracts/interfaces/IStableSwap.sol



// SPDX-License-Identifier: MIT
pragma solidity =0.7.6;
pragma abicoder v2;

interface IStableSwap {
    // solium-disable-next-line mixedcase
    function get_dy(
        uint256 i,
        uint256 j,
        uint256 dx
    ) external view returns (uint256 dy);

    // solium-disable-next-line mixedcase
    function exchange(
        uint256 i,
        uint256 j,
        uint256 dx,
        uint256 minDy
    ) external payable;

    // solium-disable-next-line mixedcase
    function coins(uint256 i) external view returns (address);

    // solium-disable-next-line mixedcase
    function balances(uint256 i) external view returns (uint256);

    // solium-disable-next-line mixedcase
    function A() external view returns (uint256);

    // solium-disable-next-line mixedcase
    function fee() external view returns (uint256);
}

// File: contracts/interfaces/IStableSwapFactory.sol



// SPDX-License-Identifier: MIT
pragma solidity =0.7.6;
pragma abicoder v2;

interface IStableSwapFactory {
    struct StableSwapPairInfo {
        address swapContract;
        address token0;
        address token1;
        address LPContract;
    }

    struct StableSwapThreePoolPairInfo {
        address swapContract;
        address token0;
        address token1;
        address token2;
        address LPContract;
    }

    // solium-disable-next-line mixedcase
    function pairLength() external view returns (uint256);

    function getPairInfo(address _tokenA, address _tokenB) 
        external 
        view 
        returns (StableSwapPairInfo memory info);

    function getThreePoolPairInfo(address _tokenA, address _tokenB)
        external
        view
        returns (StableSwapThreePoolPairInfo memory info);
        
}

// File: contracts/interfaces/IStableSwapInfo.sol



// SPDX-License-Identifier: MIT
pragma solidity =0.7.6;
pragma abicoder v2;

interface IStableSwapInfo {
    function get_dx(
        address _swap,
        uint256 i,
        uint256 j,
        uint256 dy,
        uint256 max_dx
    ) external view returns (uint256);
}

// File: contracts/lens/MixedRouteQuoterV1.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;
pragma abicoder v2;

import '@pancakeswap/v3-periphery/contracts/base/PeripheryImmutableState.sol';
import '@pancakeswap/v3-core/contracts/libraries/SafeCast.sol';
import '@pancakeswap/v3-core/contracts/libraries/TickMath.sol';
import '@pancakeswap/v3-core/contracts/libraries/TickBitmap.sol';
import '@pancakeswap/v3-core/contracts/interfaces/IPancakeV3Pool.sol';
import '@pancakeswap/v3-core/contracts/interfaces/callback/IPancakeV3SwapCallback.sol';
import '@pancakeswap/v3-periphery/contracts/libraries/Path.sol';
import '@uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol';

import '../base/ImmutableState.sol';
import '../interfaces/IMixedRouteQuoterV1.sol';
import '../interfaces/IStableSwap.sol';
import '../libraries/PoolTicksCounter.sol';
import '../libraries/SmartRouterHelper.sol';

/// @title Provides on chain quotes for V3, V2, Stable and MixedRoute exact input swaps
/// @notice Allows getting the expected amount out for a given swap without executing the swap
/// @notice Does not support exact output swaps since using the contract balance between exactOut swaps is not supported
/// @dev These functions are not gas efficient and should _not_ be called on chain. Instead, optimistically execute
/// the swap and check the amounts in the callback.
contract MixedRouteQuoterV1 is IMixedRouteQuoterV1, IPancakeV3SwapCallback, PeripheryImmutableState {
    using Path for bytes;
    using SafeCast for uint256;
    using PoolTicksCounter for IPancakeV3Pool;

    address public immutable factoryV2;
    address public immutable factoryStable;

    /**
    /// @dev Value to bit mask with path fee to determine if V2 or V3 route
    // max V3 fee:           000011110100001001000000 (24 bits)
    // mask:       1 << 23 = 100000000000000000000000 = decimal value 8388608
    uint24 private constant flagBitmask = 8388608;

    /// @dev Transient storage variable used to check a safety condition in exact output swaps.
    uint256 private amountOutCached;
    */

    constructor(
        address _deployer,
        address _factory,
        address _factoryV2,
        address _factoryStable,
        address _WETH9
    ) PeripheryImmutableState(_deployer, _factory, _WETH9) {
        factoryV2 = _factoryV2;
        factoryStable = _factoryStable;
    }



    /************************************************** V3 **************************************************/

    /// @inheritdoc IPancakeV3SwapCallback
    function pancakeV3SwapCallback(
        int256 amount0Delta,
        int256 amount1Delta,
        bytes memory path
    ) external view override {
        require(amount0Delta > 0 || amount1Delta > 0); // swaps entirely within 0-liquidity regions are not supported
        (address tokenIn, address tokenOut, uint24 fee) = path.decodeFirstPool();
        SmartRouterHelper.verifyCallback(deployer, tokenIn, tokenOut, fee);

        (bool isExactInput, uint256 amountReceived) =
            amount0Delta > 0
                ? (tokenIn < tokenOut, uint256(-amount1Delta))
                : (tokenOut < tokenIn, uint256(-amount0Delta));

        IPancakeV3Pool pool = SmartRouterHelper.getPool(deployer, tokenIn, tokenOut, fee);
        (uint160 v3SqrtPriceX96After, int24 tickAfter, , , , , ) = pool.slot0();

        if (isExactInput) {
            assembly {
                let ptr := mload(0x40)
                mstore(ptr, amountReceived)
                mstore(add(ptr, 0x20), v3SqrtPriceX96After)
                mstore(add(ptr, 0x40), tickAfter)
                revert(ptr, 0x60)
            }
        } else {
            /// since we don't support exactOutput, revert here
            revert('Exact output quote not supported');
        }
    }

    /// @dev Parses a revert reason that should contain the numeric quote
    function parseRevertReason(bytes memory reason)
        private
        pure
        returns (
            uint256 amount,
            uint160 sqrtPriceX96After,
            int24 tickAfter
        )
    {
        if (reason.length != 0x60) {
            if (reason.length < 0x44) revert('Unexpected error');
            assembly {
                reason := add(reason, 0x04)
            }
            revert(abi.decode(reason, (string)));
        }
        return abi.decode(reason, (uint256, uint160, int24));
    }

    function handleV3Revert(
        bytes memory reason,
        IPancakeV3Pool pool,
        uint256 gasEstimate
    )
        private
        view
        returns (
            uint256 amount,
            uint160 sqrtPriceX96After,
            uint32 initializedTicksCrossed,
            uint256
        )
    {
        int24 tickBefore;
        int24 tickAfter;
        (, tickBefore, , , , , ) = pool.slot0();
        (amount, sqrtPriceX96After, tickAfter) = parseRevertReason(reason);

        initializedTicksCrossed = pool.countInitializedTicksCrossed(tickBefore, tickAfter);

        return (amount, sqrtPriceX96After, initializedTicksCrossed, gasEstimate);
    }

    /// @dev Fetch an exactIn quote for a V3 Pool on chain
    function quoteExactInputSingleV3(QuoteExactInputSingleV3Params memory params)
        public
        override
        returns (
            uint256 amountOut,
            uint160 sqrtPriceX96After,
            uint32 initializedTicksCrossed,
            uint256 gasEstimate
        )
    {
        bool zeroForOne = params.tokenIn < params.tokenOut;
        IPancakeV3Pool pool = SmartRouterHelper.getPool(deployer, params.tokenIn, params.tokenOut, params.fee);

        uint256 gasBefore = gasleft();
        try
            pool.swap(
                address(this), // address(0) might cause issues with some tokens
                zeroForOne,
                params.amountIn.toInt256(),
                params.sqrtPriceLimitX96 == 0
                    ? (zeroForOne ? TickMath.MIN_SQRT_RATIO + 1 : TickMath.MAX_SQRT_RATIO - 1)
                    : params.sqrtPriceLimitX96,
                abi.encodePacked(params.tokenIn, params.fee, params.tokenOut)
            )
        {} catch (bytes memory reason) {
            gasEstimate = gasBefore - gasleft();
            return handleV3Revert(reason, pool, gasEstimate);
        }
    }



    /************************************************** V2 **************************************************/

    /// @dev Fetch an exactIn quote for a V2 pair on chain
    function quoteExactInputSingleV2(QuoteExactInputSingleV2Params memory params)
        public
        view
        override
        returns (uint256 amountOut)
    {
        (uint256 reserveIn, uint256 reserveOut) = SmartRouterHelper.getReserves(factoryV2, params.tokenIn, params.tokenOut);
        amountOut = SmartRouterHelper.getAmountOut(params.amountIn, reserveIn, reserveOut);
    }



    /************************************************** Stable **************************************************/

    /// @dev Fetch an exactIn quote for a Stable pair on chain
    function quoteExactInputSingleStable(QuoteExactInputSingleStableParams memory params)
        public
        view
        override
        returns (uint256 amountOut)
    {
        (uint256 i, uint256 j, address swapContract) = SmartRouterHelper.getStableInfo(factoryStable, params.tokenIn, params.tokenOut, params.flag);
        amountOut = IStableSwap(swapContract).get_dy(i, j, params.amountIn);
    }



    /************************************************** Mixed **************************************************/

    /// @dev Get the quote for an exactIn swap between an array of Stable, V2 and/or V3 pools
    /// @param flag 0 for V3, 1 for V2, 2 for 2pool, 3 for 3pool
    function quoteExactInput(
        bytes memory path,
        uint256[] memory flag, 
        uint256 amountIn
    )
        public
        override
        returns (
            uint256 amountOut,
            uint160[] memory v3SqrtPriceX96AfterList,
            uint32[] memory v3InitializedTicksCrossedList,
            uint256 v3SwapGasEstimate
        )
    {
        v3SqrtPriceX96AfterList = new uint160[](path.numPools());
        v3InitializedTicksCrossedList = new uint32[](path.numPools());

        uint256 i = 0;
        while (true) {
            (address tokenIn, address tokenOut, uint24 fee) = path.decodeFirstPool();

            if (flag[i] == 1) {
                amountIn = quoteExactInputSingleV2(
                    QuoteExactInputSingleV2Params({
                        tokenIn: tokenIn, 
                        tokenOut: tokenOut, 
                        amountIn: amountIn
                    })
                );
            } else if (flag[i] == 0) {
                /// the outputs of prior swaps become the inputs to subsequent ones
                (
                    uint256 _amountOut,
                    uint160 _sqrtPriceX96After,
                    uint32 _initializedTicksCrossed,
                    uint256 _gasEstimate
                ) =
                    quoteExactInputSingleV3(
                        QuoteExactInputSingleV3Params({
                            tokenIn: tokenIn,
                            tokenOut: tokenOut,
                            fee: fee,
                            amountIn: amountIn,
                            sqrtPriceLimitX96: 0
                        })
                    );
                v3SqrtPriceX96AfterList[i] = _sqrtPriceX96After;
                v3InitializedTicksCrossedList[i] = _initializedTicksCrossed;
                v3SwapGasEstimate += _gasEstimate;
                amountIn = _amountOut;
            } else {
                amountIn = quoteExactInputSingleStable(
                    QuoteExactInputSingleStableParams({
                        tokenIn: tokenIn, 
                        tokenOut: tokenOut, 
                        amountIn: amountIn, 
                        flag: flag[i]
                    })
                );
            }

            i++;

            /// decide whether to continue or terminate
            if (path.hasMultiplePools()) {
                path = path.skipToken();
            } else {
                return (amountIn, v3SqrtPriceX96AfterList, v3InitializedTicksCrossedList, v3SwapGasEstimate);
            }
        }
    }
}

// File: contracts/libraries/PoolTicksCounter.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity >=0.6.0;

import '@pancakeswap/v3-core/contracts/interfaces/IPancakeV3Pool.sol';

library PoolTicksCounter {
    /// @dev This function counts the number of initialized ticks that would incur a gas cost between tickBefore and tickAfter.
    /// When tickBefore and/or tickAfter themselves are initialized, the logic over whether we should count them depends on the
    /// direction of the swap. If we are swapping upwards (tickAfter > tickBefore) we don't want to count tickBefore but we do
    /// want to count tickAfter. The opposite is true if we are swapping downwards.
    function countInitializedTicksCrossed(
        IPancakeV3Pool self,
        int24 tickBefore,
        int24 tickAfter
    ) internal view returns (uint32 initializedTicksCrossed) {
        int16 wordPosLower;
        int16 wordPosHigher;
        uint8 bitPosLower;
        uint8 bitPosHigher;
        bool tickBeforeInitialized;
        bool tickAfterInitialized;

        {
            // Get the key and offset in the tick bitmap of the active tick before and after the swap.
            int16 wordPos = int16((tickBefore / self.tickSpacing()) >> 8);
            uint8 bitPos = uint8((tickBefore / self.tickSpacing()) % 256);

            int16 wordPosAfter = int16((tickAfter / self.tickSpacing()) >> 8);
            uint8 bitPosAfter = uint8((tickAfter / self.tickSpacing()) % 256);

            // In the case where tickAfter is initialized, we only want to count it if we are swapping downwards.
            // If the initializable tick after the swap is initialized, our original tickAfter is a
            // multiple of tick spacing, and we are swapping downwards we know that tickAfter is initialized
            // and we shouldn't count it.
            tickAfterInitialized =
                ((self.tickBitmap(wordPosAfter) & (1 << bitPosAfter)) > 0) &&
                ((tickAfter % self.tickSpacing()) == 0) &&
                (tickBefore > tickAfter);

            // In the case where tickBefore is initialized, we only want to count it if we are swapping upwards.
            // Use the same logic as above to decide whether we should count tickBefore or not.
            tickBeforeInitialized =
                ((self.tickBitmap(wordPos) & (1 << bitPos)) > 0) &&
                ((tickBefore % self.tickSpacing()) == 0) &&
                (tickBefore < tickAfter);

            if (wordPos < wordPosAfter || (wordPos == wordPosAfter && bitPos <= bitPosAfter)) {
                wordPosLower = wordPos;
                bitPosLower = bitPos;
                wordPosHigher = wordPosAfter;
                bitPosHigher = bitPosAfter;
            } else {
                wordPosLower = wordPosAfter;
                bitPosLower = bitPosAfter;
                wordPosHigher = wordPos;
                bitPosHigher = bitPos;
            }
        }

        // Count the number of initialized ticks crossed by iterating through the tick bitmap.
        // Our first mask should include the lower tick and everything to its left.
        uint256 mask = type(uint256).max << bitPosLower;
        while (wordPosLower <= wordPosHigher) {
            // If we're on the final tick bitmap page, ensure we only count up to our
            // ending tick.
            if (wordPosLower == wordPosHigher) {
                mask = mask & (type(uint256).max >> (255 - bitPosHigher));
            }

            uint256 masked = self.tickBitmap(wordPosLower) & mask;
            initializedTicksCrossed += countOneBits(masked);
            wordPosLower++;
            // Reset our mask so we consider all bits on the next iteration.
            mask = type(uint256).max;
        }

        if (tickAfterInitialized) {
            initializedTicksCrossed -= 1;
        }

        if (tickBeforeInitialized) {
            initializedTicksCrossed -= 1;
        }

        return initializedTicksCrossed;
    }

    function countOneBits(uint256 x) private pure returns (uint16) {
        uint16 bits = 0;
        while (x != 0) {
            bits++;
            x &= (x - 1);
        }
        return bits;
    }
}

// File: contracts/libraries/SmartRouterHelper.sol



// SPDX-License-Identifier: GPL-2.0-or-later
pragma solidity =0.7.6;
pragma abicoder v2;

import '../interfaces/IStableSwapFactory.sol';
import '../interfaces/IStableSwapInfo.sol';
import '@uniswap/v2-core/contracts/interfaces/IUniswapV2Pair.sol';
import '@pancakeswap/v3-core/contracts/libraries/LowGasSafeMath.sol';
import '@pancakeswap/v3-core/contracts/interfaces/IPancakeV3Pool.sol';

library SmartRouterHelper {
    using LowGasSafeMath for uint256;

    /************************************************** Stable **************************************************/

    // get the pool info in stable swap
    function getStableInfo(
        address stableSwapFactory,
        address input,
        address output,
        uint256 flag
    ) public view returns (uint256 i, uint256 j, address swapContract) {
        if (flag == 2) {
            IStableSwapFactory.StableSwapPairInfo memory info = IStableSwapFactory(stableSwapFactory).getPairInfo(input, output);
            i = input == info.token0 ? 0 : 1;
            j = (i == 0) ? 1 : 0;
            swapContract = info.swapContract;
        } else if (flag == 3) {
            IStableSwapFactory.StableSwapThreePoolPairInfo memory info = IStableSwapFactory(stableSwapFactory).getThreePoolPairInfo(input, output);

            if (input == info.token0) i = 0;
            else if (input == info.token1) i = 1;
            else if (input == info.token2) i = 2;

            if (output == info.token0) j = 0;
            else if (output == info.token1) j = 1;
            else if (output == info.token2) j = 2;

            swapContract = info.swapContract;
        }

        require(swapContract != address(0), "getStableInfo: invalid pool address");
    }

    function getStableAmountsIn(
        address stableSwapFactory,
        address stableSwapInfo,
        address[] memory path,
        uint256[] memory flag,
        uint256 amountOut
    ) public view returns (uint256[] memory amounts) {
        uint256 length = path.length;
        require(length >= 2, "getStableAmountsIn: incorrect length");

        amounts = new uint256[](length);
        amounts[length - 1] = amountOut;

        for (uint256 i = length - 1; i > 0; i--) {
            uint256 last = i - 1;
            (uint256 k, uint256 j, address swapContract) = getStableInfo(stableSwapFactory, path[last], path[i], flag[last]);
            amounts[last] = IStableSwapInfo(stableSwapInfo).get_dx(swapContract, k, j, amounts[i], type(uint256).max);
        }
    }



    /************************************************** V2 **************************************************/

    // bytes32 internal constant V2_INIT_CODE_HASH = 0xd0d4c4cd0848c93cb4fd1f498d7013ee6bfb25783ea21593d5834f5d250ece66; // BSC TESTNET
    // bytes32 internal constant V2_INIT_CODE_HASH = 0x00fb7f630766e6a796048ea87d01acd3068e8ff67d078148a3fa3f4a84f69bd5; // BSC
    // bytes32 internal constant V2_INIT_CODE_HASH = 0x57224589c67f3f30a6b0d7a1b54cf3153ab84563bc609ef41dfb34f8b2974d2d; // ETH, GOERLI
    bytes32 internal constant V2_INIT_CODE_HASH = 0x57224589c67f3f30a6b0d7a1b54cf3153ab84563bc609ef41dfb34f8b2974d2d;

    // returns sorted token addresses, used to handle return values from pairs sorted in this order
    function sortTokens(address tokenA, address tokenB) public pure returns (address token0, address token1) {
        require(tokenA != tokenB);
        (token0, token1) = tokenA < tokenB ? (tokenA, tokenB) : (tokenB, tokenA);
        require(token0 != address(0));
    }

    // calculates the CREATE2 address for a pair without making any external calls
    function pairFor(
        address factory,
        address tokenA,
        address tokenB
    ) public pure returns (address pair) {
        (address token0, address token1) = sortTokens(tokenA, tokenB);
        pair = address(
            uint256(
                keccak256(
                    abi.encodePacked(
                        hex'ff',
                        factory,
                        keccak256(abi.encodePacked(token0, token1)),
                        V2_INIT_CODE_HASH
                    )
                )
            )
        );
    }

    // fetches and sorts the reserves for a pair
    function getReserves(
        address factory,
        address tokenA,
        address tokenB
    ) public view returns (uint256 reserveA, uint256 reserveB) {
        (address token0, ) = sortTokens(tokenA, tokenB);
        (uint256 reserve0, uint256 reserve1, ) = IUniswapV2Pair(pairFor(factory, tokenA, tokenB)).getReserves();
        (reserveA, reserveB) = tokenA == token0 ? (reserve0, reserve1) : (reserve1, reserve0);
    }

    // given an input amount of an asset and pair reserves, returns the maximum output amount of the other asset
    function getAmountOut(
        uint256 amountIn,
        uint256 reserveIn,
        uint256 reserveOut
    ) public pure returns (uint256 amountOut) {
        require(amountIn > 0, 'INSUFFICIENT_INPUT_AMOUNT');
        require(reserveIn > 0 && reserveOut > 0);
        uint256 amountInWithFee = amountIn.mul(9975);
        uint256 numerator = amountInWithFee.mul(reserveOut);
        uint256 denominator = reserveIn.mul(10000).add(amountInWithFee);
        amountOut = numerator / denominator;
    }

    // given an output amount of an asset and pair reserves, returns a required input amount of the other asset
    function getAmountIn(
        uint256 amountOut,
        uint256 reserveIn,
        uint256 reserveOut
    ) public pure returns (uint256 amountIn) {
        require(amountOut > 0, 'INSUFFICIENT_OUTPUT_AMOUNT');
        require(reserveIn > 0 && reserveOut > 0);
        uint256 numerator = reserveIn.mul(amountOut).mul(10000);
        uint256 denominator = reserveOut.sub(amountOut).mul(9975);
        amountIn = (numerator / denominator).add(1);
    }

    // performs chained getAmountIn calculations on any number of pairs
    function getAmountsIn(
        address factory,
        uint256 amountOut,
        address[] memory path
    ) public view returns (uint256[] memory amounts) {
        require(path.length >= 2);
        amounts = new uint256[](path.length);
        amounts[amounts.length - 1] = amountOut;
        for (uint256 i = path.length - 1; i > 0; i--) {
            (uint256 reserveIn, uint256 reserveOut) = getReserves(factory, path[i - 1], path[i]);
            amounts[i - 1] = getAmountIn(amounts[i], reserveIn, reserveOut);
        }
    }



    /************************************************** V3 **************************************************/

    bytes32 internal constant V3_INIT_CODE_HASH = 0x6ce8eb472fa82df5469c6ab6d485f17c3ad13c8cd7af59b3d4a8026c5ce0f7e2;

    /// @notice The identifying key of the pool
    struct PoolKey {
        address token0;
        address token1;
        uint24 fee;
    }

    /// @notice Returns PoolKey: the ordered tokens with the matched fee levels
    /// @param tokenA The first token of a pool, unsorted
    /// @param tokenB The second token of a pool, unsorted
    /// @param fee The fee level of the pool
    /// @return Poolkey The pool details with ordered token0 and token1 assignments
    function getPoolKey(
        address tokenA,
        address tokenB,
        uint24 fee
    ) public pure returns (PoolKey memory) {
        if (tokenA > tokenB) (tokenA, tokenB) = (tokenB, tokenA);
        return PoolKey({token0: tokenA, token1: tokenB, fee: fee});
    }

    /// @notice Deterministically computes the pool address given the deployer and PoolKey
    /// @param deployer The PancakeSwap V3 deployer contract address
    /// @param key The PoolKey
    /// @return pool The contract address of the V3 pool
    function computeAddress(address deployer, PoolKey memory key) public pure returns (address pool) {
        require(key.token0 < key.token1);
        pool = address(
            uint256(
                keccak256(
                    abi.encodePacked(
                        hex'ff',
                        deployer,
                        keccak256(abi.encode(key.token0, key.token1, key.fee)),
                        V3_INIT_CODE_HASH
                    )
                )
            )
        );
    }

    /// @dev Returns the pool for the given token pair and fee. The pool contract may or may not exist.
    function getPool(
        address deployer,
        address tokenA,
        address tokenB,
        uint24 fee
    ) public pure returns (IPancakeV3Pool) {
        return IPancakeV3Pool(computeAddress(deployer, getPoolKey(tokenA, tokenB, fee)));
    }

    /// @notice Returns the address of a valid PancakeSwap V3 Pool
    /// @param deployer The contract address of the PancakeSwap V3 deployer
    /// @param tokenA The contract address of either token0 or token1
    /// @param tokenB The contract address of the other token
    /// @param fee The fee collected upon every swap in the pool, denominated in hundredths of a bip
    /// @return pool The V3 pool contract address
    function verifyCallback(
        address deployer,
        address tokenA,
        address tokenB,
        uint24 fee
    ) public view returns (IPancakeV3Pool pool) {
        return verifyCallback(deployer, getPoolKey(tokenA, tokenB, fee));
    }

    /// @notice Returns the address of a valid PancakeSwap V3 Pool
    /// @param deployer The contract address of the PancakeSwap V3 deployer
    /// @param poolKey The identifying key of the V3 pool
    /// @return pool The V3 pool contract address
    function verifyCallback(address deployer, PoolKey memory poolKey)
        public
        view
        returns (IPancakeV3Pool pool)
    {
        pool = IPancakeV3Pool(computeAddress(deployer, poolKey));
        require(msg.sender == address(pool));
    }
}