Token

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.19;

import {Math} from "@openzeppelin/contracts/utils/math/Math.sol";
import {IPool} from "./interfaces/IPool.sol";
import {IVoter} from "./interfaces/IVoter.sol";
import {IPoolCallee} from "./interfaces/IPoolCallee.sol";
import {IPoolFactory} from "./interfaces/factories/IPoolFactory.sol";
import {PoolFees} from "./PoolFees.sol";
import {SafeERC20} from "@openzeppelin/contracts/token/ERC20/utils/SafeERC20.sol";
import {ERC20} from "@openzeppelin/contracts/token/ERC20/ERC20.sol";
import {IERC20} from "@openzeppelin/contracts/token/ERC20/IERC20.sol";
import {ERC20Permit} from "@openzeppelin/contracts/token/ERC20/extensions/ERC20Permit.sol";
import {ReentrancyGuard} from "@openzeppelin/contracts/security/ReentrancyGuard.sol";

/// @title Pool
/// @author velodrome.finance, @figs999, @pegahcarter
/// @notice Veldrome V2 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;

    // Used to denote stable or volatile pool
    bool public stable;

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

    address public token0;
    address public token1;
    address public poolFees;
    address public factory;

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

    // Capture oracle reading every 30 minutes
    uint256 constant periodSize = 1800;

    Observation[] public observations;

    uint256 internal decimals0;
    uint256 internal decimals1;

    uint256 public reserve0;
    uint256 public reserve1;
    uint256 public blockTimestampLast;

    uint256 public reserve0CumulativeLast;
    uint256 public reserve1CumulativeLast;

    // index0 and index1 are used to accumulate fees, this is split out from normal trades to keep the swap "clean"
    // this further allows LP holders to easily claim fees for tokens they have/staked
    uint256 public index0 = 0;
    uint256 public index1 = 0;

    // position assigned to each LP to track their current index0 & index1 vs the global position
    mapping(address => uint256) public supplyIndex0;
    mapping(address => uint256) public supplyIndex1;

    // tracks the amount of unclaimed, but claimable tokens off of fees for token0 and token1
    mapping(address => uint256) public claimable0;
    mapping(address => uint256) public claimable1;

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

    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("StableV2 AMM - ", symbol0, "/", symbol1));
            _symbol = string(abi.encodePacked("sAMMV2-", symbol0, "/", symbol1));
        } else {
            _name = string(abi.encodePacked("VolatileV2 AMM - ", symbol0, "/", symbol1));
            _symbol = string(abi.encodePacked("vAMMV2-", symbol0, "/", symbol1));
        }

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

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

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

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

    function observationLength() external view returns (uint256) {
        return observations.length;
    }

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

    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);
    }

    function tokens() external view returns (address, address) {
        return (token0, token1);
    }

    // claim accumulated but unclaimed fees (viewable via claimable0 and claimable1)
    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);
        }
    }

    // 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);
    }

    // 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);
    }

    // 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;
        }
    }

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

    // 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);
    }

    // produces the cumulative price using counterfactuals to save gas and avoid a call to sync.
    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;
        }
    }

    // provides twap price with user configured granularity, up to the full window size
    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;
    }

    // returns a memory set of twap prices
    function prices(address tokenIn, uint256 amountIn, uint256 points) external view returns (uint256[] memory) {
        return sample(tokenIn, amountIn, points, 1);
    }

    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;
    }

    // this low-level function should be called by addLiquidity functions in Router.sol, which performs important safety checks
    // standard uniswap v2 implementation
    function mint(address to) external 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);
    }

    // this low-level function should be called from a contract which performs important safety checks
    // standard uniswap v2 implementation
    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);
    }

    // this low-level function should be called from a contract which performs important safety checks
    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);
    }

    // force balances to match reserves
    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));
    }

    // force reserves to match balances
    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");
    }

    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);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @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);
        }
    }
}

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

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);

    function metadata()
        external
        view
        returns (uint256 dec0, uint256 dec1, uint256 r0, uint256 r1, bool st, address t0, address t1);

    function claimFees() external returns (uint256, uint256);

    function tokens() external view returns (address, address);

    function token0() external view returns (address);

    function token1() external view returns (address);

    function stable() external view returns (bool);

    function swap(uint256 amount0Out, uint256 amount1Out, address to, bytes calldata data) external;

    function burn(address to) external returns (uint256 amount0, uint256 amount1);

    function mint(address to) external returns (uint256 liquidity);

    function getReserves() external view returns (uint256 _reserve0, uint256 _reserve1, uint256 _blockTimestampLast);

    function getAmountOut(uint256, address) external view returns (uint256);

    function skim(address to) external;

    function initialize(address _token0, address _token1, bool _stable) external;
}

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

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);

    // mappings
    function gauges(address pool) external view returns (address);

    function poolForGauge(address gauge) external view returns (address);

    function gaugeToFees(address gauge) external view returns (address);

    function gaugeToBribe(address gauge) external view returns (address);

    function weights(address pool) external view returns (uint256);

    function votes(uint256 tokenId, address pool) external view returns (uint256);

    function usedWeights(uint256 tokenId) external view returns (uint256);

    function lastVoted(uint256 tokenId) external view returns (uint256);

    function isGauge(address) external view returns (bool);

    function isWhitelistedToken(address token) external view returns (bool);

    function isWhitelistedNFT(uint256 tokenId) external view returns (bool);

    function isAlive(address gauge) external view returns (bool);

    function ve() external view returns (address);

    function governor() external view returns (address);

    function epochGovernor() external view returns (address);

    function emergencyCouncil() external view returns (address);

    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 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.
    /// @dev V1 gauges can only be created by governor.
    /// @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;
}

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

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

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

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 NotSinkConverter();
    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 Support for Velodrome v1 which wraps around isPool(pool);
    /// @param .
    function isPair(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);

    /// @notice Support for Velodrome v1 pools as a "pool" was previously referenced as "pair"
    /// @notice Wraps around getPool(tokenA,tokenB,stable)
    function getPair(address tokenA, address tokenB, bool stable) 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 setSinkConverter(address _sinkConvert, address _velo, address _veloV2) 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);

    /// @notice Support for Velodrome v1 which wraps around createPool(tokenA,tokenB,stable)
    function createPair(address tokenA, address tokenB, bool stable) external returns (address pool);

    function isPaused() external view returns (bool);

    function velo() external view returns (address);

    function veloV2() external view returns (address);

    function voter() external view returns (address);

    function sinkConverter() external view returns (address);

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

// SPDX-License-Identifier: BUSL-1.1
pragma solidity 0.8.19;

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

/// @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);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";
import "../extensions/IERC20Permit.sol";
import "../../../utils/Address.sol";

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

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

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

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        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");
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

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

/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.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 {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/IERC20.sol)

pragma solidity ^0.8.0;

/**
 * @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);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC20/extensions/ERC20Permit.sol)

pragma solidity ^0.8.0;

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

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

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

    // solhint-disable-next-line var-name-mixedcase
    bytes32 private 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();
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (security/ReentrancyGuard.sol)

pragma solidity ^0.8.0;

/**
 * @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;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Permit.sol)

pragma solidity ^0.8.0;

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @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);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/IERC20Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Context.sol)

pragma solidity ^0.8.0;

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

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @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));
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/cryptography/EIP712.sol)

pragma solidity ^0.8.8;

import "./ECDSA.sol";
import "../ShortStrings.sol";
import "../../interfaces/IERC5267.sol";

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/Counters.sol)

pragma solidity ^0.8.0;

/**
 * @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;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @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));
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.8;

import "./StorageSlot.sol";

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;
        }
    }
}

// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

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
        );
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @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);
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.0;

/**
 * @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
        }
    }
}

{
  "remappings": [
    "@opengsn/=lib/gsn/packages/",
    "@openzeppelin/=lib/openzeppelin-contracts/",
    "@uniswap/v3-core/=lib/v3-core/",
    "concentrated-liquidity/=lib/concentrated-liquidity/",
    "ds-test/=lib/ds-test/src/",
    "erc4626-tests/=lib/openzeppelin-contracts/lib/erc4626-tests/",
    "eth-gas-reporter/=node_modules/eth-gas-reporter/",
    "forge-std/=lib/forge-std/src/",
    "gsn/=lib/gsn/",
    "hardhat-deploy/=node_modules/hardhat-deploy/",
    "hardhat/=node_modules/hardhat/",
    "openzeppelin-contracts/=lib/openzeppelin-contracts/",
    "utils/=test/utils/",
    "v3-core/=lib/v3-core/"
  ],
  "optimizer": {
    "enabled": true,
    "runs": 200
  },
  "metadata": {
    "bytecodeHash": "ipfs",
    "appendCBOR": true
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  },
  "evmVersion": "paris",
  "libraries": {
    "contracts/art/PerlinNoise.sol": {
      "PerlinNoise": "0x08947e304064b3f3ef2b99fca7e549c5fc3f75d4"
    },
    "contracts/art/Trig.sol": {
      "Trig": "0xbdd6f9662e904a9176aafcbdded45d076b5170ef"
    },
    "contracts/libraries/BalanceLogicLibrary.sol": {
      "BalanceLogicLibrary": "0x79bca9bcc19e157cb5f8c5a2f4d6cb951b1f8dce"
    },
    "contracts/libraries/DelegationLogicLibrary.sol": {
      "DelegationLogicLibrary": "0x73746410b0dd4526e1fa00d0854e99ba54aefd30"
    }
  }
}

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ateMutability":"nonpayable","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"}],"name":"claimable0","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"","type":"address"}],"name":"claimable1","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"currentCumulativePrices","outputs":[{"internalType":"uint256","name":"reserve0Cumulative","type":"uint256"},{"internalType":"uint256","name":"reserve1Cumulative","type":"uint256"},{"internalType":"uint256","name":"blockTimestamp","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"decimals","outputs":[{"internalType":"uint8","name":"","type":"uint8"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"subtractedValue","type":"uint256"}],"name":"decreaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"eip712Domain","outputs":[{"internalType":"bytes1","name":"fields","type":"bytes1"},{"internalType":"string","name":"name","type":"string"},{"internalType":"string","name":"version","type":"string"},{"internalType":"uint256","name":"chainId","type":"uint256"},{"internalType":"address","name":"verifyingContract","type":"address"},{"internalType":"bytes32","name":"salt","type":"bytes32"},{"internalType":"uint256[]","name":"extensions","type":"uint256[]"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"factory","outputs":[{"internalType":"address","name":"","type":"address"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"uint256","name":"amountIn","type":"uint256"},{"internalType":"address","name":"tokenIn","type":"address"}],"name":"getAmountOut","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"getReserves","outputs":[{"internalType":"uint256","name":"_reserve0","type":"uint256"},{"internalType":"uint256","name":"_reserve1","type":"uint256"},{"internalType":"uint256","name":"_blockTimestampLast","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"spender","type":"address"},{"internalType":"uint256","name":"addedValue","type":"uint256"}],"name":"increaseAllowance","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"index0","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[],"name":"index1","outputs":[{"internalType":"uint256","name":"","type":"uint256"}],"stateMutability":"view","type":"function"},{"inputs":[{"internalType":"address","name":"_token0","type":"address"},{"internalType":"address","name":"_token1","type":"address"},{"internalType":"bool","name":"_stable","type":"bool"}],"name":"initialize","outputs":[],"stateMutability":"nonpayable","type":"function"},{"inputs":[],"name":"lastObservation","outputs":[{"components":[{"internalType":"uint256","name":"timestamp","type":"uint256"},{"internalType":"uint256","name":"reserve0Cumulative","type":"uint256"},{"internalType":"uint256","name":"reserve1Cumulative","type":"uint256"}],"internalType":"struct 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