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/**
 *Submitted for verification at Arbiscan.io on 2022-10-19
*/

// File: @prb/math/contracts/PRBMath.sol


pragma solidity >=0.8.4;

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivFixedPointOverflow(uint256 prod1);

/// @notice Emitted when the result overflows uint256.
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator);

/// @notice Emitted when one of the inputs is type(int256).min.
error PRBMath__MulDivSignedInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows int256.
error PRBMath__MulDivSignedOverflow(uint256 rAbs);

/// @notice Emitted when the input is MIN_SD59x18.
error PRBMathSD59x18__AbsInputTooSmall();

/// @notice Emitted when ceiling a number overflows SD59x18.
error PRBMathSD59x18__CeilOverflow(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__DivInputTooSmall();

/// @notice Emitted when one of the intermediary unsigned results overflows SD59x18.
error PRBMathSD59x18__DivOverflow(uint256 rAbs);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathSD59x18__ExpInputTooBig(int256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathSD59x18__Exp2InputTooBig(int256 x);

/// @notice Emitted when flooring a number underflows SD59x18.
error PRBMathSD59x18__FloorUnderflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
error PRBMathSD59x18__FromIntOverflow(int256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
error PRBMathSD59x18__FromIntUnderflow(int256 x);

/// @notice Emitted when the product of the inputs is negative.
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y);

/// @notice Emitted when multiplying the inputs overflows SD59x18.
error PRBMathSD59x18__GmOverflow(int256 x, int256 y);

/// @notice Emitted when the input is less than or equal to zero.
error PRBMathSD59x18__LogInputTooSmall(int256 x);

/// @notice Emitted when one of the inputs is MIN_SD59x18.
error PRBMathSD59x18__MulInputTooSmall();

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__MulOverflow(uint256 rAbs);

/// @notice Emitted when the intermediary absolute result overflows SD59x18.
error PRBMathSD59x18__PowuOverflow(uint256 rAbs);

/// @notice Emitted when the input is negative.
error PRBMathSD59x18__SqrtNegativeInput(int256 x);

/// @notice Emitted when the calculating the square root overflows SD59x18.
error PRBMathSD59x18__SqrtOverflow(int256 x);

/// @notice Emitted when addition overflows UD60x18.
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y);

/// @notice Emitted when ceiling a number overflows UD60x18.
error PRBMathUD60x18__CeilOverflow(uint256 x);

/// @notice Emitted when the input is greater than 133.084258667509499441.
error PRBMathUD60x18__ExpInputTooBig(uint256 x);

/// @notice Emitted when the input is greater than 192.
error PRBMathUD60x18__Exp2InputTooBig(uint256 x);

/// @notice Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
error PRBMathUD60x18__FromUintOverflow(uint256 x);

/// @notice Emitted when multiplying the inputs overflows UD60x18.
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y);

/// @notice Emitted when the input is less than 1.
error PRBMathUD60x18__LogInputTooSmall(uint256 x);

/// @notice Emitted when the calculating the square root overflows UD60x18.
error PRBMathUD60x18__SqrtOverflow(uint256 x);

/// @notice Emitted when subtraction underflows UD60x18.
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y);

/// @dev Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library
/// does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point
/// representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
library PRBMath {
    /// STRUCTS ///

    struct SD59x18 {
        int256 value;
    }

    struct UD60x18 {
        uint256 value;
    }

    /// STORAGE ///

    /// @dev How many trailing decimals can be represented.
    uint256 internal constant SCALE = 1e18;

    /// @dev Largest power of two divisor of SCALE.
    uint256 internal constant SCALE_LPOTD = 262144;

    /// @dev SCALE inverted mod 2^256.
    uint256 internal constant SCALE_INVERSE =
        78156646155174841979727994598816262306175212592076161876661_508869554232690281;

    /// FUNCTIONS ///

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    /// @dev Has to use 192.64-bit fixed-point numbers.
    /// See https://ethereum.stackexchange.com/a/96594/24693.
    /// @param x The exponent as an unsigned 192.64-bit fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function exp2(uint256 x) internal pure returns (uint256 result) {
        unchecked {
            // Start from 0.5 in the 192.64-bit fixed-point format.
            result = 0x800000000000000000000000000000000000000000000000;

            // Multiply the result by root(2, 2^-i) when the bit at position i is 1. None of the intermediary results overflows
            // because the initial result is 2^191 and all magic factors are less than 2^65.
            if (x & 0x8000000000000000 > 0) {
                result = (result * 0x16A09E667F3BCC909) >> 64;
            }
            if (x & 0x4000000000000000 > 0) {
                result = (result * 0x1306FE0A31B7152DF) >> 64;
            }
            if (x & 0x2000000000000000 > 0) {
                result = (result * 0x1172B83C7D517ADCE) >> 64;
            }
            if (x & 0x1000000000000000 > 0) {
                result = (result * 0x10B5586CF9890F62A) >> 64;
            }
            if (x & 0x800000000000000 > 0) {
                result = (result * 0x1059B0D31585743AE) >> 64;
            }
            if (x & 0x400000000000000 > 0) {
                result = (result * 0x102C9A3E778060EE7) >> 64;
            }
            if (x & 0x200000000000000 > 0) {
                result = (result * 0x10163DA9FB33356D8) >> 64;
            }
            if (x & 0x100000000000000 > 0) {
                result = (result * 0x100B1AFA5ABCBED61) >> 64;
            }
            if (x & 0x80000000000000 > 0) {
                result = (result * 0x10058C86DA1C09EA2) >> 64;
            }
            if (x & 0x40000000000000 > 0) {
                result = (result * 0x1002C605E2E8CEC50) >> 64;
            }
            if (x & 0x20000000000000 > 0) {
                result = (result * 0x100162F3904051FA1) >> 64;
            }
            if (x & 0x10000000000000 > 0) {
                result = (result * 0x1000B175EFFDC76BA) >> 64;
            }
            if (x & 0x8000000000000 > 0) {
                result = (result * 0x100058BA01FB9F96D) >> 64;
            }
            if (x & 0x4000000000000 > 0) {
                result = (result * 0x10002C5CC37DA9492) >> 64;
            }
            if (x & 0x2000000000000 > 0) {
                result = (result * 0x1000162E525EE0547) >> 64;
            }
            if (x & 0x1000000000000 > 0) {
                result = (result * 0x10000B17255775C04) >> 64;
            }
            if (x & 0x800000000000 > 0) {
                result = (result * 0x1000058B91B5BC9AE) >> 64;
            }
            if (x & 0x400000000000 > 0) {
                result = (result * 0x100002C5C89D5EC6D) >> 64;
            }
            if (x & 0x200000000000 > 0) {
                result = (result * 0x10000162E43F4F831) >> 64;
            }
            if (x & 0x100000000000 > 0) {
                result = (result * 0x100000B1721BCFC9A) >> 64;
            }
            if (x & 0x80000000000 > 0) {
                result = (result * 0x10000058B90CF1E6E) >> 64;
            }
            if (x & 0x40000000000 > 0) {
                result = (result * 0x1000002C5C863B73F) >> 64;
            }
            if (x & 0x20000000000 > 0) {
                result = (result * 0x100000162E430E5A2) >> 64;
            }
            if (x & 0x10000000000 > 0) {
                result = (result * 0x1000000B172183551) >> 64;
            }
            if (x & 0x8000000000 > 0) {
                result = (result * 0x100000058B90C0B49) >> 64;
            }
            if (x & 0x4000000000 > 0) {
                result = (result * 0x10000002C5C8601CC) >> 64;
            }
            if (x & 0x2000000000 > 0) {
                result = (result * 0x1000000162E42FFF0) >> 64;
            }
            if (x & 0x1000000000 > 0) {
                result = (result * 0x10000000B17217FBB) >> 64;
            }
            if (x & 0x800000000 > 0) {
                result = (result * 0x1000000058B90BFCE) >> 64;
            }
            if (x & 0x400000000 > 0) {
                result = (result * 0x100000002C5C85FE3) >> 64;
            }
            if (x & 0x200000000 > 0) {
                result = (result * 0x10000000162E42FF1) >> 64;
            }
            if (x & 0x100000000 > 0) {
                result = (result * 0x100000000B17217F8) >> 64;
            }
            if (x & 0x80000000 > 0) {
                result = (result * 0x10000000058B90BFC) >> 64;
            }
            if (x & 0x40000000 > 0) {
                result = (result * 0x1000000002C5C85FE) >> 64;
            }
            if (x & 0x20000000 > 0) {
                result = (result * 0x100000000162E42FF) >> 64;
            }
            if (x & 0x10000000 > 0) {
                result = (result * 0x1000000000B17217F) >> 64;
            }
            if (x & 0x8000000 > 0) {
                result = (result * 0x100000000058B90C0) >> 64;
            }
            if (x & 0x4000000 > 0) {
                result = (result * 0x10000000002C5C860) >> 64;
            }
            if (x & 0x2000000 > 0) {
                result = (result * 0x1000000000162E430) >> 64;
            }
            if (x & 0x1000000 > 0) {
                result = (result * 0x10000000000B17218) >> 64;
            }
            if (x & 0x800000 > 0) {
                result = (result * 0x1000000000058B90C) >> 64;
            }
            if (x & 0x400000 > 0) {
                result = (result * 0x100000000002C5C86) >> 64;
            }
            if (x & 0x200000 > 0) {
                result = (result * 0x10000000000162E43) >> 64;
            }
            if (x & 0x100000 > 0) {
                result = (result * 0x100000000000B1721) >> 64;
            }
            if (x & 0x80000 > 0) {
                result = (result * 0x10000000000058B91) >> 64;
            }
            if (x & 0x40000 > 0) {
                result = (result * 0x1000000000002C5C8) >> 64;
            }
            if (x & 0x20000 > 0) {
                result = (result * 0x100000000000162E4) >> 64;
            }
            if (x & 0x10000 > 0) {
                result = (result * 0x1000000000000B172) >> 64;
            }
            if (x & 0x8000 > 0) {
                result = (result * 0x100000000000058B9) >> 64;
            }
            if (x & 0x4000 > 0) {
                result = (result * 0x10000000000002C5D) >> 64;
            }
            if (x & 0x2000 > 0) {
                result = (result * 0x1000000000000162E) >> 64;
            }
            if (x & 0x1000 > 0) {
                result = (result * 0x10000000000000B17) >> 64;
            }
            if (x & 0x800 > 0) {
                result = (result * 0x1000000000000058C) >> 64;
            }
            if (x & 0x400 > 0) {
                result = (result * 0x100000000000002C6) >> 64;
            }
            if (x & 0x200 > 0) {
                result = (result * 0x10000000000000163) >> 64;
            }
            if (x & 0x100 > 0) {
                result = (result * 0x100000000000000B1) >> 64;
            }
            if (x & 0x80 > 0) {
                result = (result * 0x10000000000000059) >> 64;
            }
            if (x & 0x40 > 0) {
                result = (result * 0x1000000000000002C) >> 64;
            }
            if (x & 0x20 > 0) {
                result = (result * 0x10000000000000016) >> 64;
            }
            if (x & 0x10 > 0) {
                result = (result * 0x1000000000000000B) >> 64;
            }
            if (x & 0x8 > 0) {
                result = (result * 0x10000000000000006) >> 64;
            }
            if (x & 0x4 > 0) {
                result = (result * 0x10000000000000003) >> 64;
            }
            if (x & 0x2 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }
            if (x & 0x1 > 0) {
                result = (result * 0x10000000000000001) >> 64;
            }

            // We're doing two things at the same time:
            //
            //   1. Multiply the result by 2^n + 1, where "2^n" is the integer part and the one is added to account for
            //      the fact that we initially set the result to 0.5. This is accomplished by subtracting from 191
            //      rather than 192.
            //   2. Convert the result to the unsigned 60.18-decimal fixed-point format.
            //
            // This works because 2^(191-ip) = 2^ip / 2^191, where "ip" is the integer part "2^n".
            result *= SCALE;
            result >>= (191 - (x >> 64));
        }
    }

    /// @notice Finds the zero-based index of the first one in the binary representation of x.
    /// @dev See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
    /// @param x The uint256 number for which to find the index of the most significant bit.
    /// @return msb The index of the most significant bit as an uint256.
    function mostSignificantBit(uint256 x) internal pure returns (uint256 msb) {
        if (x >= 2**128) {
            x >>= 128;
            msb += 128;
        }
        if (x >= 2**64) {
            x >>= 64;
            msb += 64;
        }
        if (x >= 2**32) {
            x >>= 32;
            msb += 32;
        }
        if (x >= 2**16) {
            x >>= 16;
            msb += 16;
        }
        if (x >= 2**8) {
            x >>= 8;
            msb += 8;
        }
        if (x >= 2**4) {
            x >>= 4;
            msb += 4;
        }
        if (x >= 2**2) {
            x >>= 2;
            msb += 2;
        }
        if (x >= 2**1) {
            // No need to shift x any more.
            msb += 1;
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
    ///
    /// Requirements:
    /// - The denominator cannot be zero.
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The multiplicand as an uint256.
    /// @param y The multiplier as an uint256.
    /// @param denominator The divisor as an uint256.
    /// @return result The result as an uint256.
    function mulDiv(
        uint256 x,
        uint256 y,
        uint256 denominator
    ) internal pure returns (uint256 result) {
        // 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) {
            unchecked {
                result = prod0 / denominator;
            }
            return result;
        }

        // Make sure the result is less than 2^256. Also prevents denominator == 0.
        if (prod1 >= denominator) {
            revert PRBMath__MulDivOverflow(prod1, denominator);
        }

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

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

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

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

            // 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 floor(x*y÷1e18) with full precision.
    ///
    /// @dev Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the
    /// final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of
    /// being rounded to 1e-18.  See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
    ///
    /// Requirements:
    /// - The result must fit within uint256.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    /// - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations:
    ///     1. x * y = type(uint256).max * SCALE
    ///     2. (x * y) % SCALE >= SCALE / 2
    ///
    /// @param x The multiplicand as an unsigned 60.18-decimal fixed-point number.
    /// @param y The multiplier as an unsigned 60.18-decimal fixed-point number.
    /// @return result The result as an unsigned 60.18-decimal fixed-point number.
    function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result) {
        uint256 prod0;
        uint256 prod1;
        assembly {
            let mm := mulmod(x, y, not(0))
            prod0 := mul(x, y)
            prod1 := sub(sub(mm, prod0), lt(mm, prod0))
        }

        if (prod1 >= SCALE) {
            revert PRBMath__MulDivFixedPointOverflow(prod1);
        }

        uint256 remainder;
        uint256 roundUpUnit;
        assembly {
            remainder := mulmod(x, y, SCALE)
            roundUpUnit := gt(remainder, 499999999999999999)
        }

        if (prod1 == 0) {
            unchecked {
                result = (prod0 / SCALE) + roundUpUnit;
                return result;
            }
        }

        assembly {
            result := add(
                mul(
                    or(
                        div(sub(prod0, remainder), SCALE_LPOTD),
                        mul(sub(prod1, gt(remainder, prod0)), add(div(sub(0, SCALE_LPOTD), SCALE_LPOTD), 1))
                    ),
                    SCALE_INVERSE
                ),
                roundUpUnit
            )
        }
    }

    /// @notice Calculates floor(x*y÷denominator) with full precision.
    ///
    /// @dev An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - None of the inputs can be type(int256).min.
    /// - The result must fit within int256.
    ///
    /// @param x The multiplicand as an int256.
    /// @param y The multiplier as an int256.
    /// @param denominator The divisor as an int256.
    /// @return result The result as an int256.
    function mulDivSigned(
        int256 x,
        int256 y,
        int256 denominator
    ) internal pure returns (int256 result) {
        if (x == type(int256).min || y == type(int256).min || denominator == type(int256).min) {
            revert PRBMath__MulDivSignedInputTooSmall();
        }

        // Get hold of the absolute values of x, y and the denominator.
        uint256 ax;
        uint256 ay;
        uint256 ad;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
            ad = denominator < 0 ? uint256(-denominator) : uint256(denominator);
        }

        // Compute the absolute value of (x*y)÷denominator. The result must fit within int256.
        uint256 rAbs = mulDiv(ax, ay, ad);
        if (rAbs > uint256(type(int256).max)) {
            revert PRBMath__MulDivSignedOverflow(rAbs);
        }

        // Get the signs of x, y and the denominator.
        uint256 sx;
        uint256 sy;
        uint256 sd;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
            sd := sgt(denominator, sub(0, 1))
        }

        // XOR over sx, sy and sd. This is checking whether there are one or three negative signs in the inputs.
        // If yes, the result should be negative.
        result = sx ^ sy ^ sd == 0 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Caveats:
    /// - This function does not work with fixed-point numbers.
    ///
    /// @param x The uint256 number for which to calculate the square root.
    /// @return result The result as an uint256.
    function sqrt(uint256 x) internal pure returns (uint256 result) {
        if (x == 0) {
            return 0;
        }

        // Set the initial guess to the least power of two that is greater than or equal to sqrt(x).
        uint256 xAux = uint256(x);
        result = 1;
        if (xAux >= 0x100000000000000000000000000000000) {
            xAux >>= 128;
            result <<= 64;
        }
        if (xAux >= 0x10000000000000000) {
            xAux >>= 64;
            result <<= 32;
        }
        if (xAux >= 0x100000000) {
            xAux >>= 32;
            result <<= 16;
        }
        if (xAux >= 0x10000) {
            xAux >>= 16;
            result <<= 8;
        }
        if (xAux >= 0x100) {
            xAux >>= 8;
            result <<= 4;
        }
        if (xAux >= 0x10) {
            xAux >>= 4;
            result <<= 2;
        }
        if (xAux >= 0x8) {
            result <<= 1;
        }

        // The operations can never overflow because the result is max 2^127 when it enters this block.
        unchecked {
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1;
            result = (result + x / result) >> 1; // Seven iterations should be enough
            uint256 roundedDownResult = x / result;
            return result >= roundedDownResult ? roundedDownResult : result;
        }
    }
}

// File: @prb/math/contracts/PRBMathSD59x18.sol


pragma solidity >=0.8.4;


/// @title PRBMathSD59x18
/// @author Paul Razvan Berg
/// @notice Smart contract library for advanced fixed-point math that works with int256 numbers considered to have 18
/// trailing decimals. We call this number representation signed 59.18-decimal fixed-point, since the numbers can have
/// a sign and there can be up to 59 digits in the integer part and up to 18 decimals in the fractional part. The numbers
/// are bound by the minimum and the maximum values permitted by the Solidity type int256.
library PRBMathSD59x18 {
    /// @dev log2(e) as a signed 59.18-decimal fixed-point number.
    int256 internal constant LOG2_E = 1_442695040888963407;

    /// @dev Half the SCALE number.
    int256 internal constant HALF_SCALE = 5e17;

    /// @dev The maximum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_792003956564819967;

    /// @dev The maximum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MAX_WHOLE_SD59x18 =
        57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev The minimum value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_792003956564819968;

    /// @dev The minimum whole value a signed 59.18-decimal fixed-point number can have.
    int256 internal constant MIN_WHOLE_SD59x18 =
        -57896044618658097711785492504343953926634992332820282019728_000000000000000000;

    /// @dev How many trailing decimals can be represented.
    int256 internal constant SCALE = 1e18;

    /// INTERNAL FUNCTIONS ///

    /// @notice Calculate the absolute value of x.
    ///
    /// @dev Requirements:
    /// - x must be greater than MIN_SD59x18.
    ///
    /// @param x The number to calculate the absolute value for.
    /// @param result The absolute value of x.
    function abs(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x == MIN_SD59x18) {
                revert PRBMathSD59x18__AbsInputTooSmall();
            }
            result = x < 0 ? -x : x;
        }
    }

    /// @notice Calculates the arithmetic average of x and y, rounding down.
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The arithmetic average as a signed 59.18-decimal fixed-point number.
    function avg(int256 x, int256 y) internal pure returns (int256 result) {
        // The operations can never overflow.
        unchecked {
            int256 sum = (x >> 1) + (y >> 1);
            if (sum < 0) {
                // If at least one of x and y is odd, we add 1 to the result. This is because shifting negative numbers to the
                // right rounds down to infinity.
                assembly {
                    result := add(sum, and(or(x, y), 1))
                }
            } else {
                // If both x and y are odd, we add 1 to the result. This is because if both numbers are odd, the 0.5
                // remainder gets truncated twice.
                result = sum + (x & y & 1);
            }
        }
    }

    /// @notice Yields the least greatest signed 59.18 decimal fixed-point number greater than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be less than or equal to MAX_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to ceil.
    /// @param result The least integer greater than or equal to x, as a signed 58.18-decimal fixed-point number.
    function ceil(int256 x) internal pure returns (int256 result) {
        if (x > MAX_WHOLE_SD59x18) {
            revert PRBMathSD59x18__CeilOverflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x > 0) {
                    result += SCALE;
                }
            }
        }
    }

    /// @notice Divides two signed 59.18-decimal fixed-point numbers, returning a new signed 59.18-decimal fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers. Works by computing the signs and the absolute values separately.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDiv".
    /// - None of the inputs can be MIN_SD59x18.
    /// - The denominator cannot be zero.
    /// - The result must fit within int256.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDiv".
    ///
    /// @param x The numerator as a signed 59.18-decimal fixed-point number.
    /// @param y The denominator as a signed 59.18-decimal fixed-point number.
    /// @param result The quotient as a signed 59.18-decimal fixed-point number.
    function div(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__DivInputTooSmall();
        }

        // Get hold of the absolute values of x and y.
        uint256 ax;
        uint256 ay;
        unchecked {
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);
        }

        // Compute the absolute value of (x*SCALE)÷y. The result must fit within int256.
        uint256 rAbs = PRBMath.mulDiv(ax, uint256(SCALE), ay);
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__DivOverflow(rAbs);
        }

        // Get the signs of x and y.
        uint256 sx;
        uint256 sy;
        assembly {
            sx := sgt(x, sub(0, 1))
            sy := sgt(y, sub(0, 1))
        }

        // XOR over sx and sy. This is basically checking whether the inputs have the same sign. If yes, the result
        // should be positive. Otherwise, it should be negative.
        result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns Euler's number as a signed 59.18-decimal fixed-point number.
    /// @dev See https://en.wikipedia.org/wiki/E_(mathematical_constant).
    function e() internal pure returns (int256 result) {
        result = 2_718281828459045235;
    }

    /// @notice Calculates the natural exponent of x.
    ///
    /// @dev Based on the insight that e^x = 2^(x * log2(e)).
    ///
    /// Requirements:
    /// - All from "log2".
    /// - x must be less than 133.084258667509499441.
    ///
    /// Caveats:
    /// - All from "exp2".
    /// - For any x less than -41.446531673892822322, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp(int256 x) internal pure returns (int256 result) {
        // Without this check, the value passed to "exp2" would be less than -59.794705707972522261.
        if (x < -41_446531673892822322) {
            return 0;
        }

        // Without this check, the value passed to "exp2" would be greater than 192.
        if (x >= 133_084258667509499441) {
            revert PRBMathSD59x18__ExpInputTooBig(x);
        }

        // Do the fixed-point multiplication inline to save gas.
        unchecked {
            int256 doubleScaleProduct = x * LOG2_E;
            result = exp2((doubleScaleProduct + HALF_SCALE) / SCALE);
        }
    }

    /// @notice Calculates the binary exponent of x using the binary fraction method.
    ///
    /// @dev See https://ethereum.stackexchange.com/q/79903/24693.
    ///
    /// Requirements:
    /// - x must be 192 or less.
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - For any x less than -59.794705707972522261, the result is zero.
    ///
    /// @param x The exponent as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function exp2(int256 x) internal pure returns (int256 result) {
        // This works because 2^(-x) = 1/2^x.
        if (x < 0) {
            // 2^59.794705707972522262 is the maximum number whose inverse does not truncate down to zero.
            if (x < -59_794705707972522261) {
                return 0;
            }

            // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
            unchecked {
                result = 1e36 / exp2(-x);
            }
        } else {
            // 2^192 doesn't fit within the 192.64-bit format used internally in this function.
            if (x >= 192e18) {
                revert PRBMathSD59x18__Exp2InputTooBig(x);
            }

            unchecked {
                // Convert x to the 192.64-bit fixed-point format.
                uint256 x192x64 = (uint256(x) << 64) / uint256(SCALE);

                // Safe to convert the result to int256 directly because the maximum input allowed is 192.
                result = int256(PRBMath.exp2(x192x64));
            }
        }
    }

    /// @notice Yields the greatest signed 59.18 decimal fixed-point number less than or equal to x.
    ///
    /// @dev Optimized for fractional value inputs, because for every whole value there are (1e18 - 1) fractional counterparts.
    /// See https://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
    ///
    /// Requirements:
    /// - x must be greater than or equal to MIN_WHOLE_SD59x18.
    ///
    /// @param x The signed 59.18-decimal fixed-point number to floor.
    /// @param result The greatest integer less than or equal to x, as a signed 58.18-decimal fixed-point number.
    function floor(int256 x) internal pure returns (int256 result) {
        if (x < MIN_WHOLE_SD59x18) {
            revert PRBMathSD59x18__FloorUnderflow(x);
        }
        unchecked {
            int256 remainder = x % SCALE;
            if (remainder == 0) {
                result = x;
            } else {
                // Solidity uses C fmod style, which returns a modulus with the same sign as x.
                result = x - remainder;
                if (x < 0) {
                    result -= SCALE;
                }
            }
        }
    }

    /// @notice Yields the excess beyond the floor of x for positive numbers and the part of the number to the right
    /// of the radix point for negative numbers.
    /// @dev Based on the odd function definition. https://en.wikipedia.org/wiki/Fractional_part
    /// @param x The signed 59.18-decimal fixed-point number to get the fractional part of.
    /// @param result The fractional part of x as a signed 59.18-decimal fixed-point number.
    function frac(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x % SCALE;
        }
    }

    /// @notice Converts a number from basic integer form to signed 59.18-decimal fixed-point representation.
    ///
    /// @dev Requirements:
    /// - x must be greater than or equal to MIN_SD59x18 divided by SCALE.
    /// - x must be less than or equal to MAX_SD59x18 divided by SCALE.
    ///
    /// @param x The basic integer to convert.
    /// @param result The same number in signed 59.18-decimal fixed-point representation.
    function fromInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < MIN_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntUnderflow(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__FromIntOverflow(x);
            }
            result = x * SCALE;
        }
    }

    /// @notice Calculates geometric mean of x and y, i.e. sqrt(x * y), rounding down.
    ///
    /// @dev Requirements:
    /// - x * y must fit within MAX_SD59x18, lest it overflows.
    /// - x * y cannot be negative.
    ///
    /// @param x The first operand as a signed 59.18-decimal fixed-point number.
    /// @param y The second operand as a signed 59.18-decimal fixed-point number.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function gm(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            return 0;
        }

        unchecked {
            // Checking for overflow this way is faster than letting Solidity do it.
            int256 xy = x * y;
            if (xy / x != y) {
                revert PRBMathSD59x18__GmOverflow(x, y);
            }

            // The product cannot be negative.
            if (xy < 0) {
                revert PRBMathSD59x18__GmNegativeProduct(x, y);
            }

            // We don't need to multiply by the SCALE here because the x*y product had already picked up a factor of SCALE
            // during multiplication. See the comments within the "sqrt" function.
            result = int256(PRBMath.sqrt(uint256(xy)));
        }
    }

    /// @notice Calculates 1 / x, rounding toward zero.
    ///
    /// @dev Requirements:
    /// - x cannot be zero.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the inverse.
    /// @return result The inverse as a signed 59.18-decimal fixed-point number.
    function inv(int256 x) internal pure returns (int256 result) {
        unchecked {
            // 1e36 is SCALE * SCALE.
            result = 1e36 / x;
        }
    }

    /// @notice Calculates the natural logarithm of x.
    ///
    /// @dev Based on the insight that ln(x) = log2(x) / log2(e).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    /// - This doesn't return exactly 1 for 2718281828459045235, for that we would need more fine-grained precision.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the natural logarithm.
    /// @return result The natural logarithm as a signed 59.18-decimal fixed-point number.
    function ln(int256 x) internal pure returns (int256 result) {
        // Do the fixed-point multiplication inline to save gas. This is overflow-safe because the maximum value that log2(x)
        // can return is 195205294292027477728.
        unchecked {
            result = (log2(x) * SCALE) / LOG2_E;
        }
    }

    /// @notice Calculates the common logarithm of x.
    ///
    /// @dev First checks if x is an exact power of ten and it stops if yes. If it's not, calculates the common
    /// logarithm based on the insight that log10(x) = log2(x) / log2(10).
    ///
    /// Requirements:
    /// - All from "log2".
    ///
    /// Caveats:
    /// - All from "log2".
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the common logarithm.
    /// @return result The common logarithm as a signed 59.18-decimal fixed-point number.
    function log10(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }

        // Note that the "mul" in this block is the assembly mul operation, not the "mul" function defined in this contract.
        // prettier-ignore
        assembly {
            switch x
            case 1 { result := mul(SCALE, sub(0, 18)) }
            case 10 { result := mul(SCALE, sub(1, 18)) }
            case 100 { result := mul(SCALE, sub(2, 18)) }
            case 1000 { result := mul(SCALE, sub(3, 18)) }
            case 10000 { result := mul(SCALE, sub(4, 18)) }
            case 100000 { result := mul(SCALE, sub(5, 18)) }
            case 1000000 { result := mul(SCALE, sub(6, 18)) }
            case 10000000 { result := mul(SCALE, sub(7, 18)) }
            case 100000000 { result := mul(SCALE, sub(8, 18)) }
            case 1000000000 { result := mul(SCALE, sub(9, 18)) }
            case 10000000000 { result := mul(SCALE, sub(10, 18)) }
            case 100000000000 { result := mul(SCALE, sub(11, 18)) }
            case 1000000000000 { result := mul(SCALE, sub(12, 18)) }
            case 10000000000000 { result := mul(SCALE, sub(13, 18)) }
            case 100000000000000 { result := mul(SCALE, sub(14, 18)) }
            case 1000000000000000 { result := mul(SCALE, sub(15, 18)) }
            case 10000000000000000 { result := mul(SCALE, sub(16, 18)) }
            case 100000000000000000 { result := mul(SCALE, sub(17, 18)) }
            case 1000000000000000000 { result := 0 }
            case 10000000000000000000 { result := SCALE }
            case 100000000000000000000 { result := mul(SCALE, 2) }
            case 1000000000000000000000 { result := mul(SCALE, 3) }
            case 10000000000000000000000 { result := mul(SCALE, 4) }
            case 100000000000000000000000 { result := mul(SCALE, 5) }
            case 1000000000000000000000000 { result := mul(SCALE, 6) }
            case 10000000000000000000000000 { result := mul(SCALE, 7) }
            case 100000000000000000000000000 { result := mul(SCALE, 8) }
            case 1000000000000000000000000000 { result := mul(SCALE, 9) }
            case 10000000000000000000000000000 { result := mul(SCALE, 10) }
            case 100000000000000000000000000000 { result := mul(SCALE, 11) }
            case 1000000000000000000000000000000 { result := mul(SCALE, 12) }
            case 10000000000000000000000000000000 { result := mul(SCALE, 13) }
            case 100000000000000000000000000000000 { result := mul(SCALE, 14) }
            case 1000000000000000000000000000000000 { result := mul(SCALE, 15) }
            case 10000000000000000000000000000000000 { result := mul(SCALE, 16) }
            case 100000000000000000000000000000000000 { result := mul(SCALE, 17) }
            case 1000000000000000000000000000000000000 { result := mul(SCALE, 18) }
            case 10000000000000000000000000000000000000 { result := mul(SCALE, 19) }
            case 100000000000000000000000000000000000000 { result := mul(SCALE, 20) }
            case 1000000000000000000000000000000000000000 { result := mul(SCALE, 21) }
            case 10000000000000000000000000000000000000000 { result := mul(SCALE, 22) }
            case 100000000000000000000000000000000000000000 { result := mul(SCALE, 23) }
            case 1000000000000000000000000000000000000000000 { result := mul(SCALE, 24) }
            case 10000000000000000000000000000000000000000000 { result := mul(SCALE, 25) }
            case 100000000000000000000000000000000000000000000 { result := mul(SCALE, 26) }
            case 1000000000000000000000000000000000000000000000 { result := mul(SCALE, 27) }
            case 10000000000000000000000000000000000000000000000 { result := mul(SCALE, 28) }
            case 100000000000000000000000000000000000000000000000 { result := mul(SCALE, 29) }
            case 1000000000000000000000000000000000000000000000000 { result := mul(SCALE, 30) }
            case 10000000000000000000000000000000000000000000000000 { result := mul(SCALE, 31) }
            case 100000000000000000000000000000000000000000000000000 { result := mul(SCALE, 32) }
            case 1000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 33) }
            case 10000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 34) }
            case 100000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 35) }
            case 1000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 36) }
            case 10000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 37) }
            case 100000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 38) }
            case 1000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 39) }
            case 10000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 40) }
            case 100000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 41) }
            case 1000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 42) }
            case 10000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 43) }
            case 100000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 44) }
            case 1000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 45) }
            case 10000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 46) }
            case 100000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 47) }
            case 1000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 48) }
            case 10000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 49) }
            case 100000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 50) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 51) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 52) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 53) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 54) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 55) }
            case 100000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 56) }
            case 1000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 57) }
            case 10000000000000000000000000000000000000000000000000000000000000000000000000000 { result := mul(SCALE, 58) }
            default {
                result := MAX_SD59x18
            }
        }

        if (result == MAX_SD59x18) {
            // Do the fixed-point division inline to save gas. The denominator is log2(10).
            unchecked {
                result = (log2(x) * SCALE) / 3_321928094887362347;
            }
        }
    }

    /// @notice Calculates the binary logarithm of x.
    ///
    /// @dev Based on the iterative approximation algorithm.
    /// https://en.wikipedia.org/wiki/Binary_logarithm#Iterative_approximation
    ///
    /// Requirements:
    /// - x must be greater than zero.
    ///
    /// Caveats:
    /// - The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the binary logarithm.
    /// @return result The binary logarithm as a signed 59.18-decimal fixed-point number.
    function log2(int256 x) internal pure returns (int256 result) {
        if (x <= 0) {
            revert PRBMathSD59x18__LogInputTooSmall(x);
        }
        unchecked {
            // This works because log2(x) = -log2(1/x).
            int256 sign;
            if (x >= SCALE) {
                sign = 1;
            } else {
                sign = -1;
                // Do the fixed-point inversion inline to save gas. The numerator is SCALE * SCALE.
                assembly {
                    x := div(1000000000000000000000000000000000000, x)
                }
            }

            // Calculate the integer part of the logarithm and add it to the result and finally calculate y = x * 2^(-n).
            uint256 n = PRBMath.mostSignificantBit(uint256(x / SCALE));

            // The integer part of the logarithm as a signed 59.18-decimal fixed-point number. The operation can't overflow
            // because n is maximum 255, SCALE is 1e18 and sign is either 1 or -1.
            result = int256(n) * SCALE;

            // This is y = x * 2^(-n).
            int256 y = x >> n;

            // If y = 1, the fractional part is zero.
            if (y == SCALE) {
                return result * sign;
            }

            // Calculate the fractional part via the iterative approximation.
            // The "delta >>= 1" part is equivalent to "delta /= 2", but shifting bits is faster.
            for (int256 delta = int256(HALF_SCALE); delta > 0; delta >>= 1) {
                y = (y * y) / SCALE;

                // Is y^2 > 2 and so in the range [2,4)?
                if (y >= 2 * SCALE) {
                    // Add the 2^(-m) factor to the logarithm.
                    result += delta;

                    // Corresponds to z/2 on Wikipedia.
                    y >>= 1;
                }
            }
            result *= sign;
        }
    }

    /// @notice Multiplies two signed 59.18-decimal fixed-point numbers together, returning a new signed 59.18-decimal
    /// fixed-point number.
    ///
    /// @dev Variant of "mulDiv" that works with signed numbers and employs constant folding, i.e. the denominator is
    /// always 1e18.
    ///
    /// Requirements:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - None of the inputs can be MIN_SD59x18
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works.
    ///
    /// @param x The multiplicand as a signed 59.18-decimal fixed-point number.
    /// @param y The multiplier as a signed 59.18-decimal fixed-point number.
    /// @return result The product as a signed 59.18-decimal fixed-point number.
    function mul(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == MIN_SD59x18 || y == MIN_SD59x18) {
            revert PRBMathSD59x18__MulInputTooSmall();
        }

        unchecked {
            uint256 ax;
            uint256 ay;
            ax = x < 0 ? uint256(-x) : uint256(x);
            ay = y < 0 ? uint256(-y) : uint256(y);

            uint256 rAbs = PRBMath.mulDivFixedPoint(ax, ay);
            if (rAbs > uint256(MAX_SD59x18)) {
                revert PRBMathSD59x18__MulOverflow(rAbs);
            }

            uint256 sx;
            uint256 sy;
            assembly {
                sx := sgt(x, sub(0, 1))
                sy := sgt(y, sub(0, 1))
            }
            result = sx ^ sy == 1 ? -int256(rAbs) : int256(rAbs);
        }
    }

    /// @notice Returns PI as a signed 59.18-decimal fixed-point number.
    function pi() internal pure returns (int256 result) {
        result = 3_141592653589793238;
    }

    /// @notice Raises x to the power of y.
    ///
    /// @dev Based on the insight that x^y = 2^(log2(x) * y).
    ///
    /// Requirements:
    /// - All from "exp2", "log2" and "mul".
    /// - z cannot be zero.
    ///
    /// Caveats:
    /// - All from "exp2", "log2" and "mul".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x Number to raise to given power y, as a signed 59.18-decimal fixed-point number.
    /// @param y Exponent to raise x to, as a signed 59.18-decimal fixed-point number.
    /// @return result x raised to power y, as a signed 59.18-decimal fixed-point number.
    function pow(int256 x, int256 y) internal pure returns (int256 result) {
        if (x == 0) {
            result = y == 0 ? SCALE : int256(0);
        } else {
            result = exp2(mul(log2(x), y));
        }
    }

    /// @notice Raises x (signed 59.18-decimal fixed-point number) to the power of y (basic unsigned integer) using the
    /// famous algorithm "exponentiation by squaring".
    ///
    /// @dev See https://en.wikipedia.org/wiki/Exponentiation_by_squaring
    ///
    /// Requirements:
    /// - All from "abs" and "PRBMath.mulDivFixedPoint".
    /// - The result must fit within MAX_SD59x18.
    ///
    /// Caveats:
    /// - All from "PRBMath.mulDivFixedPoint".
    /// - Assumes 0^0 is 1.
    ///
    /// @param x The base as a signed 59.18-decimal fixed-point number.
    /// @param y The exponent as an uint256.
    /// @return result The result as a signed 59.18-decimal fixed-point number.
    function powu(int256 x, uint256 y) internal pure returns (int256 result) {
        uint256 xAbs = uint256(abs(x));

        // Calculate the first iteration of the loop in advance.
        uint256 rAbs = y & 1 > 0 ? xAbs : uint256(SCALE);

        // Equivalent to "for(y /= 2; y > 0; y /= 2)" but faster.
        uint256 yAux = y;
        for (yAux >>= 1; yAux > 0; yAux >>= 1) {
            xAbs = PRBMath.mulDivFixedPoint(xAbs, xAbs);

            // Equivalent to "y % 2 == 1" but faster.
            if (yAux & 1 > 0) {
                rAbs = PRBMath.mulDivFixedPoint(rAbs, xAbs);
            }
        }

        // The result must fit within the 59.18-decimal fixed-point representation.
        if (rAbs > uint256(MAX_SD59x18)) {
            revert PRBMathSD59x18__PowuOverflow(rAbs);
        }

        // Is the base negative and the exponent an odd number?
        bool isNegative = x < 0 && y & 1 == 1;
        result = isNegative ? -int256(rAbs) : int256(rAbs);
    }

    /// @notice Returns 1 as a signed 59.18-decimal fixed-point number.
    function scale() internal pure returns (int256 result) {
        result = SCALE;
    }

    /// @notice Calculates the square root of x, rounding down.
    /// @dev Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
    ///
    /// Requirements:
    /// - x cannot be negative.
    /// - x must be less than MAX_SD59x18 / SCALE.
    ///
    /// @param x The signed 59.18-decimal fixed-point number for which to calculate the square root.
    /// @return result The result as a signed 59.18-decimal fixed-point .
    function sqrt(int256 x) internal pure returns (int256 result) {
        unchecked {
            if (x < 0) {
                revert PRBMathSD59x18__SqrtNegativeInput(x);
            }
            if (x > MAX_SD59x18 / SCALE) {
                revert PRBMathSD59x18__SqrtOverflow(x);
            }
            // Multiply x by the SCALE to account for the factor of SCALE that is picked up when multiplying two signed
            // 59.18-decimal fixed-point numbers together (in this case, those two numbers are both the square root).
            result = int256(PRBMath.sqrt(uint256(x * SCALE)));
        }
    }

    /// @notice Converts a signed 59.18-decimal fixed-point number to basic integer form, rounding down in the process.
    /// @param x The signed 59.18-decimal fixed-point number to convert.
    /// @return result The same number in basic integer form.
    function toInt(int256 x) internal pure returns (int256 result) {
        unchecked {
            result = x / SCALE;
        }
    }
}

// File: @openzeppelin/contracts/utils/math/SafeCast.sol


// OpenZeppelin Contracts (last updated v4.7.0) (utils/math/SafeCast.sol)

pragma solidity ^0.8.0;

/**
 * @dev Wrappers over Solidity's uintXX/intXX casting operators with added overflow
 * checks.
 *
 * Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
 * easily result in undesired exploitation or bugs, since developers usually
 * assume that overflows raise errors. `SafeCast` restores this intuition by
 * reverting the transaction when such an operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
 * all math on `uint256` and `int256` and then downcasting.
 */
library SafeCast {
    /**
     * @dev Returns the downcasted uint248 from uint256, reverting on
     * overflow (when the input is greater than largest uint248).
     *
     * Counterpart to Solidity's `uint248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toUint248(uint256 value) internal pure returns (uint248) {
        require(value <= type(uint248).max, "SafeCast: value doesn't fit in 248 bits");
        return uint248(value);
    }

    /**
     * @dev Returns the downcasted uint240 from uint256, reverting on
     * overflow (when the input is greater than largest uint240).
     *
     * Counterpart to Solidity's `uint240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toUint240(uint256 value) internal pure returns (uint240) {
        require(value <= type(uint240).max, "SafeCast: value doesn't fit in 240 bits");
        return uint240(value);
    }

    /**
     * @dev Returns the downcasted uint232 from uint256, reverting on
     * overflow (when the input is greater than largest uint232).
     *
     * Counterpart to Solidity's `uint232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toUint232(uint256 value) internal pure returns (uint232) {
        require(value <= type(uint232).max, "SafeCast: value doesn't fit in 232 bits");
        return uint232(value);
    }

    /**
     * @dev Returns the downcasted uint224 from uint256, reverting on
     * overflow (when the input is greater than largest uint224).
     *
     * Counterpart to Solidity's `uint224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.2._
     */
    function toUint224(uint256 value) internal pure returns (uint224) {
        require(value <= type(uint224).max, "SafeCast: value doesn't fit in 224 bits");
        return uint224(value);
    }

    /**
     * @dev Returns the downcasted uint216 from uint256, reverting on
     * overflow (when the input is greater than largest uint216).
     *
     * Counterpart to Solidity's `uint216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toUint216(uint256 value) internal pure returns (uint216) {
        require(value <= type(uint216).max, "SafeCast: value doesn't fit in 216 bits");
        return uint216(value);
    }

    /**
     * @dev Returns the downcasted uint208 from uint256, reverting on
     * overflow (when the input is greater than largest uint208).
     *
     * Counterpart to Solidity's `uint208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toUint208(uint256 value) internal pure returns (uint208) {
        require(value <= type(uint208).max, "SafeCast: value doesn't fit in 208 bits");
        return uint208(value);
    }

    /**
     * @dev Returns the downcasted uint200 from uint256, reverting on
     * overflow (when the input is greater than largest uint200).
     *
     * Counterpart to Solidity's `uint200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toUint200(uint256 value) internal pure returns (uint200) {
        require(value <= type(uint200).max, "SafeCast: value doesn't fit in 200 bits");
        return uint200(value);
    }

    /**
     * @dev Returns the downcasted uint192 from uint256, reverting on
     * overflow (when the input is greater than largest uint192).
     *
     * Counterpart to Solidity's `uint192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toUint192(uint256 value) internal pure returns (uint192) {
        require(value <= type(uint192).max, "SafeCast: value doesn't fit in 192 bits");
        return uint192(value);
    }

    /**
     * @dev Returns the downcasted uint184 from uint256, reverting on
     * overflow (when the input is greater than largest uint184).
     *
     * Counterpart to Solidity's `uint184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toUint184(uint256 value) internal pure returns (uint184) {
        require(value <= type(uint184).max, "SafeCast: value doesn't fit in 184 bits");
        return uint184(value);
    }

    /**
     * @dev Returns the downcasted uint176 from uint256, reverting on
     * overflow (when the input is greater than largest uint176).
     *
     * Counterpart to Solidity's `uint176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toUint176(uint256 value) internal pure returns (uint176) {
        require(value <= type(uint176).max, "SafeCast: value doesn't fit in 176 bits");
        return uint176(value);
    }

    /**
     * @dev Returns the downcasted uint168 from uint256, reverting on
     * overflow (when the input is greater than largest uint168).
     *
     * Counterpart to Solidity's `uint168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toUint168(uint256 value) internal pure returns (uint168) {
        require(value <= type(uint168).max, "SafeCast: value doesn't fit in 168 bits");
        return uint168(value);
    }

    /**
     * @dev Returns the downcasted uint160 from uint256, reverting on
     * overflow (when the input is greater than largest uint160).
     *
     * Counterpart to Solidity's `uint160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toUint160(uint256 value) internal pure returns (uint160) {
        require(value <= type(uint160).max, "SafeCast: value doesn't fit in 160 bits");
        return uint160(value);
    }

    /**
     * @dev Returns the downcasted uint152 from uint256, reverting on
     * overflow (when the input is greater than largest uint152).
     *
     * Counterpart to Solidity's `uint152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toUint152(uint256 value) internal pure returns (uint152) {
        require(value <= type(uint152).max, "SafeCast: value doesn't fit in 152 bits");
        return uint152(value);
    }

    /**
     * @dev Returns the downcasted uint144 from uint256, reverting on
     * overflow (when the input is greater than largest uint144).
     *
     * Counterpart to Solidity's `uint144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toUint144(uint256 value) internal pure returns (uint144) {
        require(value <= type(uint144).max, "SafeCast: value doesn't fit in 144 bits");
        return uint144(value);
    }

    /**
     * @dev Returns the downcasted uint136 from uint256, reverting on
     * overflow (when the input is greater than largest uint136).
     *
     * Counterpart to Solidity's `uint136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toUint136(uint256 value) internal pure returns (uint136) {
        require(value <= type(uint136).max, "SafeCast: value doesn't fit in 136 bits");
        return uint136(value);
    }

    /**
     * @dev Returns the downcasted uint128 from uint256, reverting on
     * overflow (when the input is greater than largest uint128).
     *
     * Counterpart to Solidity's `uint128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v2.5._
     */
    function toUint128(uint256 value) internal pure returns (uint128) {
        require(value <= type(uint128).max, "SafeCast: value doesn't fit in 128 bits");
        return uint128(value);
    }

    /**
     * @dev Returns the downcasted uint120 from uint256, reverting on
     * overflow (when the input is greater than largest uint120).
     *
     * Counterpart to Solidity's `uint120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toUint120(uint256 value) internal pure returns (uint120) {
        require(value <= type(uint120).max, "SafeCast: value doesn't fit in 120 bits");
        return uint120(value);
    }

    /**
     * @dev Returns the downcasted uint112 from uint256, reverting on
     * overflow (when the input is greater than largest uint112).
     *
     * Counterpart to Solidity's `uint112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toUint112(uint256 value) internal pure returns (uint112) {
        require(value <= type(uint112).max, "SafeCast: value doesn't fit in 112 bits");
        return uint112(value);
    }

    /**
     * @dev Returns the downcasted uint104 from uint256, reverting on
     * overflow (when the input is greater than largest uint104).
     *
     * Counterpart to Solidity's `uint104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toUint104(uint256 value) internal pure returns (uint104) {
        require(value <= type(uint104).max, "SafeCast: value doesn't fit in 104 bits");
        return uint104(value);
    }

    /**
     * @dev Returns the downcasted uint96 from uint256, reverting on
     * overflow (when the input is greater than largest uint96).
     *
     * Counterpart to Solidity's `uint96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.2._
     */
    function toUint96(uint256 value) internal pure returns (uint96) {
        require(value <= type(uint96).max, "SafeCast: value doesn't fit in 96 bits");
        return uint96(value);
    }

    /**
     * @dev Returns the downcasted uint88 from uint256, reverting on
     * overflow (when the input is greater than largest uint88).
     *
     * Counterpart to Solidity's `uint88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toUint88(uint256 value) internal pure returns (uint88) {
        require(value <= type(uint88).max, "SafeCast: value doesn't fit in 88 bits");
        return uint88(value);
    }

    /**
     * @dev Returns the downcasted uint80 from uint256, reverting on
     * overflow (when the input is greater than largest uint80).
     *
     * Counterpart to Solidity's `uint80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toUint80(uint256 value) internal pure returns (uint80) {
        require(value <= type(uint80).max, "SafeCast: value doesn't fit in 80 bits");
        return uint80(value);
    }

    /**
     * @dev Returns the downcasted uint72 from uint256, reverting on
     * overflow (when the input is greater than largest uint72).
     *
     * Counterpart to Solidity's `uint72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toUint72(uint256 value) internal pure returns (uint72) {
        require(value <= type(uint72).max, "SafeCast: value doesn't fit in 72 bits");
        return uint72(value);
    }

    /**
     * @dev Returns the downcasted uint64 from uint256, reverting on
     * overflow (when the input is greater than largest uint64).
     *
     * Counterpart to Solidity's `uint64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v2.5._
     */
    function toUint64(uint256 value) internal pure returns (uint64) {
        require(value <= type(uint64).max, "SafeCast: value doesn't fit in 64 bits");
        return uint64(value);
    }

    /**
     * @dev Returns the downcasted uint56 from uint256, reverting on
     * overflow (when the input is greater than largest uint56).
     *
     * Counterpart to Solidity's `uint56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toUint56(uint256 value) internal pure returns (uint56) {
        require(value <= type(uint56).max, "SafeCast: value doesn't fit in 56 bits");
        return uint56(value);
    }

    /**
     * @dev Returns the downcasted uint48 from uint256, reverting on
     * overflow (when the input is greater than largest uint48).
     *
     * Counterpart to Solidity's `uint48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toUint48(uint256 value) internal pure returns (uint48) {
        require(value <= type(uint48).max, "SafeCast: value doesn't fit in 48 bits");
        return uint48(value);
    }

    /**
     * @dev Returns the downcasted uint40 from uint256, reverting on
     * overflow (when the input is greater than largest uint40).
     *
     * Counterpart to Solidity's `uint40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toUint40(uint256 value) internal pure returns (uint40) {
        require(value <= type(uint40).max, "SafeCast: value doesn't fit in 40 bits");
        return uint40(value);
    }

    /**
     * @dev Returns the downcasted uint32 from uint256, reverting on
     * overflow (when the input is greater than largest uint32).
     *
     * Counterpart to Solidity's `uint32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v2.5._
     */
    function toUint32(uint256 value) internal pure returns (uint32) {
        require(value <= type(uint32).max, "SafeCast: value doesn't fit in 32 bits");
        return uint32(value);
    }

    /**
     * @dev Returns the downcasted uint24 from uint256, reverting on
     * overflow (when the input is greater than largest uint24).
     *
     * Counterpart to Solidity's `uint24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toUint24(uint256 value) internal pure returns (uint24) {
        require(value <= type(uint24).max, "SafeCast: value doesn't fit in 24 bits");
        return uint24(value);
    }

    /**
     * @dev Returns the downcasted uint16 from uint256, reverting on
     * overflow (when the input is greater than largest uint16).
     *
     * Counterpart to Solidity's `uint16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v2.5._
     */
    function toUint16(uint256 value) internal pure returns (uint16) {
        require(value <= type(uint16).max, "SafeCast: value doesn't fit in 16 bits");
        return uint16(value);
    }

    /**
     * @dev Returns the downcasted uint8 from uint256, reverting on
     * overflow (when the input is greater than largest uint8).
     *
     * Counterpart to Solidity's `uint8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v2.5._
     */
    function toUint8(uint256 value) internal pure returns (uint8) {
        require(value <= type(uint8).max, "SafeCast: value doesn't fit in 8 bits");
        return uint8(value);
    }

    /**
     * @dev Converts a signed int256 into an unsigned uint256.
     *
     * Requirements:
     *
     * - input must be greater than or equal to 0.
     *
     * _Available since v3.0._
     */
    function toUint256(int256 value) internal pure returns (uint256) {
        require(value >= 0, "SafeCast: value must be positive");
        return uint256(value);
    }

    /**
     * @dev Returns the downcasted int248 from int256, reverting on
     * overflow (when the input is less than smallest int248 or
     * greater than largest int248).
     *
     * Counterpart to Solidity's `int248` operator.
     *
     * Requirements:
     *
     * - input must fit into 248 bits
     *
     * _Available since v4.7._
     */
    function toInt248(int256 value) internal pure returns (int248) {
        require(value >= type(int248).min && value <= type(int248).max, "SafeCast: value doesn't fit in 248 bits");
        return int248(value);
    }

    /**
     * @dev Returns the downcasted int240 from int256, reverting on
     * overflow (when the input is less than smallest int240 or
     * greater than largest int240).
     *
     * Counterpart to Solidity's `int240` operator.
     *
     * Requirements:
     *
     * - input must fit into 240 bits
     *
     * _Available since v4.7._
     */
    function toInt240(int256 value) internal pure returns (int240) {
        require(value >= type(int240).min && value <= type(int240).max, "SafeCast: value doesn't fit in 240 bits");
        return int240(value);
    }

    /**
     * @dev Returns the downcasted int232 from int256, reverting on
     * overflow (when the input is less than smallest int232 or
     * greater than largest int232).
     *
     * Counterpart to Solidity's `int232` operator.
     *
     * Requirements:
     *
     * - input must fit into 232 bits
     *
     * _Available since v4.7._
     */
    function toInt232(int256 value) internal pure returns (int232) {
        require(value >= type(int232).min && value <= type(int232).max, "SafeCast: value doesn't fit in 232 bits");
        return int232(value);
    }

    /**
     * @dev Returns the downcasted int224 from int256, reverting on
     * overflow (when the input is less than smallest int224 or
     * greater than largest int224).
     *
     * Counterpart to Solidity's `int224` operator.
     *
     * Requirements:
     *
     * - input must fit into 224 bits
     *
     * _Available since v4.7._
     */
    function toInt224(int256 value) internal pure returns (int224) {
        require(value >= type(int224).min && value <= type(int224).max, "SafeCast: value doesn't fit in 224 bits");
        return int224(value);
    }

    /**
     * @dev Returns the downcasted int216 from int256, reverting on
     * overflow (when the input is less than smallest int216 or
     * greater than largest int216).
     *
     * Counterpart to Solidity's `int216` operator.
     *
     * Requirements:
     *
     * - input must fit into 216 bits
     *
     * _Available since v4.7._
     */
    function toInt216(int256 value) internal pure returns (int216) {
        require(value >= type(int216).min && value <= type(int216).max, "SafeCast: value doesn't fit in 216 bits");
        return int216(value);
    }

    /**
     * @dev Returns the downcasted int208 from int256, reverting on
     * overflow (when the input is less than smallest int208 or
     * greater than largest int208).
     *
     * Counterpart to Solidity's `int208` operator.
     *
     * Requirements:
     *
     * - input must fit into 208 bits
     *
     * _Available since v4.7._
     */
    function toInt208(int256 value) internal pure returns (int208) {
        require(value >= type(int208).min && value <= type(int208).max, "SafeCast: value doesn't fit in 208 bits");
        return int208(value);
    }

    /**
     * @dev Returns the downcasted int200 from int256, reverting on
     * overflow (when the input is less than smallest int200 or
     * greater than largest int200).
     *
     * Counterpart to Solidity's `int200` operator.
     *
     * Requirements:
     *
     * - input must fit into 200 bits
     *
     * _Available since v4.7._
     */
    function toInt200(int256 value) internal pure returns (int200) {
        require(value >= type(int200).min && value <= type(int200).max, "SafeCast: value doesn't fit in 200 bits");
        return int200(value);
    }

    /**
     * @dev Returns the downcasted int192 from int256, reverting on
     * overflow (when the input is less than smallest int192 or
     * greater than largest int192).
     *
     * Counterpart to Solidity's `int192` operator.
     *
     * Requirements:
     *
     * - input must fit into 192 bits
     *
     * _Available since v4.7._
     */
    function toInt192(int256 value) internal pure returns (int192) {
        require(value >= type(int192).min && value <= type(int192).max, "SafeCast: value doesn't fit in 192 bits");
        return int192(value);
    }

    /**
     * @dev Returns the downcasted int184 from int256, reverting on
     * overflow (when the input is less than smallest int184 or
     * greater than largest int184).
     *
     * Counterpart to Solidity's `int184` operator.
     *
     * Requirements:
     *
     * - input must fit into 184 bits
     *
     * _Available since v4.7._
     */
    function toInt184(int256 value) internal pure returns (int184) {
        require(value >= type(int184).min && value <= type(int184).max, "SafeCast: value doesn't fit in 184 bits");
        return int184(value);
    }

    /**
     * @dev Returns the downcasted int176 from int256, reverting on
     * overflow (when the input is less than smallest int176 or
     * greater than largest int176).
     *
     * Counterpart to Solidity's `int176` operator.
     *
     * Requirements:
     *
     * - input must fit into 176 bits
     *
     * _Available since v4.7._
     */
    function toInt176(int256 value) internal pure returns (int176) {
        require(value >= type(int176).min && value <= type(int176).max, "SafeCast: value doesn't fit in 176 bits");
        return int176(value);
    }

    /**
     * @dev Returns the downcasted int168 from int256, reverting on
     * overflow (when the input is less than smallest int168 or
     * greater than largest int168).
     *
     * Counterpart to Solidity's `int168` operator.
     *
     * Requirements:
     *
     * - input must fit into 168 bits
     *
     * _Available since v4.7._
     */
    function toInt168(int256 value) internal pure returns (int168) {
        require(value >= type(int168).min && value <= type(int168).max, "SafeCast: value doesn't fit in 168 bits");
        return int168(value);
    }

    /**
     * @dev Returns the downcasted int160 from int256, reverting on
     * overflow (when the input is less than smallest int160 or
     * greater than largest int160).
     *
     * Counterpart to Solidity's `int160` operator.
     *
     * Requirements:
     *
     * - input must fit into 160 bits
     *
     * _Available since v4.7._
     */
    function toInt160(int256 value) internal pure returns (int160) {
        require(value >= type(int160).min && value <= type(int160).max, "SafeCast: value doesn't fit in 160 bits");
        return int160(value);
    }

    /**
     * @dev Returns the downcasted int152 from int256, reverting on
     * overflow (when the input is less than smallest int152 or
     * greater than largest int152).
     *
     * Counterpart to Solidity's `int152` operator.
     *
     * Requirements:
     *
     * - input must fit into 152 bits
     *
     * _Available since v4.7._
     */
    function toInt152(int256 value) internal pure returns (int152) {
        require(value >= type(int152).min && value <= type(int152).max, "SafeCast: value doesn't fit in 152 bits");
        return int152(value);
    }

    /**
     * @dev Returns the downcasted int144 from int256, reverting on
     * overflow (when the input is less than smallest int144 or
     * greater than largest int144).
     *
     * Counterpart to Solidity's `int144` operator.
     *
     * Requirements:
     *
     * - input must fit into 144 bits
     *
     * _Available since v4.7._
     */
    function toInt144(int256 value) internal pure returns (int144) {
        require(value >= type(int144).min && value <= type(int144).max, "SafeCast: value doesn't fit in 144 bits");
        return int144(value);
    }

    /**
     * @dev Returns the downcasted int136 from int256, reverting on
     * overflow (when the input is less than smallest int136 or
     * greater than largest int136).
     *
     * Counterpart to Solidity's `int136` operator.
     *
     * Requirements:
     *
     * - input must fit into 136 bits
     *
     * _Available since v4.7._
     */
    function toInt136(int256 value) internal pure returns (int136) {
        require(value >= type(int136).min && value <= type(int136).max, "SafeCast: value doesn't fit in 136 bits");
        return int136(value);
    }

    /**
     * @dev Returns the downcasted int128 from int256, reverting on
     * overflow (when the input is less than smallest int128 or
     * greater than largest int128).
     *
     * Counterpart to Solidity's `int128` operator.
     *
     * Requirements:
     *
     * - input must fit into 128 bits
     *
     * _Available since v3.1._
     */
    function toInt128(int256 value) internal pure returns (int128) {
        require(value >= type(int128).min && value <= type(int128).max, "SafeCast: value doesn't fit in 128 bits");
        return int128(value);
    }

    /**
     * @dev Returns the downcasted int120 from int256, reverting on
     * overflow (when the input is less than smallest int120 or
     * greater than largest int120).
     *
     * Counterpart to Solidity's `int120` operator.
     *
     * Requirements:
     *
     * - input must fit into 120 bits
     *
     * _Available since v4.7._
     */
    function toInt120(int256 value) internal pure returns (int120) {
        require(value >= type(int120).min && value <= type(int120).max, "SafeCast: value doesn't fit in 120 bits");
        return int120(value);
    }

    /**
     * @dev Returns the downcasted int112 from int256, reverting on
     * overflow (when the input is less than smallest int112 or
     * greater than largest int112).
     *
     * Counterpart to Solidity's `int112` operator.
     *
     * Requirements:
     *
     * - input must fit into 112 bits
     *
     * _Available since v4.7._
     */
    function toInt112(int256 value) internal pure returns (int112) {
        require(value >= type(int112).min && value <= type(int112).max, "SafeCast: value doesn't fit in 112 bits");
        return int112(value);
    }

    /**
     * @dev Returns the downcasted int104 from int256, reverting on
     * overflow (when the input is less than smallest int104 or
     * greater than largest int104).
     *
     * Counterpart to Solidity's `int104` operator.
     *
     * Requirements:
     *
     * - input must fit into 104 bits
     *
     * _Available since v4.7._
     */
    function toInt104(int256 value) internal pure returns (int104) {
        require(value >= type(int104).min && value <= type(int104).max, "SafeCast: value doesn't fit in 104 bits");
        return int104(value);
    }

    /**
     * @dev Returns the downcasted int96 from int256, reverting on
     * overflow (when the input is less than smallest int96 or
     * greater than largest int96).
     *
     * Counterpart to Solidity's `int96` operator.
     *
     * Requirements:
     *
     * - input must fit into 96 bits
     *
     * _Available since v4.7._
     */
    function toInt96(int256 value) internal pure returns (int96) {
        require(value >= type(int96).min && value <= type(int96).max, "SafeCast: value doesn't fit in 96 bits");
        return int96(value);
    }

    /**
     * @dev Returns the downcasted int88 from int256, reverting on
     * overflow (when the input is less than smallest int88 or
     * greater than largest int88).
     *
     * Counterpart to Solidity's `int88` operator.
     *
     * Requirements:
     *
     * - input must fit into 88 bits
     *
     * _Available since v4.7._
     */
    function toInt88(int256 value) internal pure returns (int88) {
        require(value >= type(int88).min && value <= type(int88).max, "SafeCast: value doesn't fit in 88 bits");
        return int88(value);
    }

    /**
     * @dev Returns the downcasted int80 from int256, reverting on
     * overflow (when the input is less than smallest int80 or
     * greater than largest int80).
     *
     * Counterpart to Solidity's `int80` operator.
     *
     * Requirements:
     *
     * - input must fit into 80 bits
     *
     * _Available since v4.7._
     */
    function toInt80(int256 value) internal pure returns (int80) {
        require(value >= type(int80).min && value <= type(int80).max, "SafeCast: value doesn't fit in 80 bits");
        return int80(value);
    }

    /**
     * @dev Returns the downcasted int72 from int256, reverting on
     * overflow (when the input is less than smallest int72 or
     * greater than largest int72).
     *
     * Counterpart to Solidity's `int72` operator.
     *
     * Requirements:
     *
     * - input must fit into 72 bits
     *
     * _Available since v4.7._
     */
    function toInt72(int256 value) internal pure returns (int72) {
        require(value >= type(int72).min && value <= type(int72).max, "SafeCast: value doesn't fit in 72 bits");
        return int72(value);
    }

    /**
     * @dev Returns the downcasted int64 from int256, reverting on
     * overflow (when the input is less than smallest int64 or
     * greater than largest int64).
     *
     * Counterpart to Solidity's `int64` operator.
     *
     * Requirements:
     *
     * - input must fit into 64 bits
     *
     * _Available since v3.1._
     */
    function toInt64(int256 value) internal pure returns (int64) {
        require(value >= type(int64).min && value <= type(int64).max, "SafeCast: value doesn't fit in 64 bits");
        return int64(value);
    }

    /**
     * @dev Returns the downcasted int56 from int256, reverting on
     * overflow (when the input is less than smallest int56 or
     * greater than largest int56).
     *
     * Counterpart to Solidity's `int56` operator.
     *
     * Requirements:
     *
     * - input must fit into 56 bits
     *
     * _Available since v4.7._
     */
    function toInt56(int256 value) internal pure returns (int56) {
        require(value >= type(int56).min && value <= type(int56).max, "SafeCast: value doesn't fit in 56 bits");
        return int56(value);
    }

    /**
     * @dev Returns the downcasted int48 from int256, reverting on
     * overflow (when the input is less than smallest int48 or
     * greater than largest int48).
     *
     * Counterpart to Solidity's `int48` operator.
     *
     * Requirements:
     *
     * - input must fit into 48 bits
     *
     * _Available since v4.7._
     */
    function toInt48(int256 value) internal pure returns (int48) {
        require(value >= type(int48).min && value <= type(int48).max, "SafeCast: value doesn't fit in 48 bits");
        return int48(value);
    }

    /**
     * @dev Returns the downcasted int40 from int256, reverting on
     * overflow (when the input is less than smallest int40 or
     * greater than largest int40).
     *
     * Counterpart to Solidity's `int40` operator.
     *
     * Requirements:
     *
     * - input must fit into 40 bits
     *
     * _Available since v4.7._
     */
    function toInt40(int256 value) internal pure returns (int40) {
        require(value >= type(int40).min && value <= type(int40).max, "SafeCast: value doesn't fit in 40 bits");
        return int40(value);
    }

    /**
     * @dev Returns the downcasted int32 from int256, reverting on
     * overflow (when the input is less than smallest int32 or
     * greater than largest int32).
     *
     * Counterpart to Solidity's `int32` operator.
     *
     * Requirements:
     *
     * - input must fit into 32 bits
     *
     * _Available since v3.1._
     */
    function toInt32(int256 value) internal pure returns (int32) {
        require(value >= type(int32).min && value <= type(int32).max, "SafeCast: value doesn't fit in 32 bits");
        return int32(value);
    }

    /**
     * @dev Returns the downcasted int24 from int256, reverting on
     * overflow (when the input is less than smallest int24 or
     * greater than largest int24).
     *
     * Counterpart to Solidity's `int24` operator.
     *
     * Requirements:
     *
     * - input must fit into 24 bits
     *
     * _Available since v4.7._
     */
    function toInt24(int256 value) internal pure returns (int24) {
        require(value >= type(int24).min && value <= type(int24).max, "SafeCast: value doesn't fit in 24 bits");
        return int24(value);
    }

    /**
     * @dev Returns the downcasted int16 from int256, reverting on
     * overflow (when the input is less than smallest int16 or
     * greater than largest int16).
     *
     * Counterpart to Solidity's `int16` operator.
     *
     * Requirements:
     *
     * - input must fit into 16 bits
     *
     * _Available since v3.1._
     */
    function toInt16(int256 value) internal pure returns (int16) {
        require(value >= type(int16).min && value <= type(int16).max, "SafeCast: value doesn't fit in 16 bits");
        return int16(value);
    }

    /**
     * @dev Returns the downcasted int8 from int256, reverting on
     * overflow (when the input is less than smallest int8 or
     * greater than largest int8).
     *
     * Counterpart to Solidity's `int8` operator.
     *
     * Requirements:
     *
     * - input must fit into 8 bits
     *
     * _Available since v3.1._
     */
    function toInt8(int256 value) internal pure returns (int8) {
        require(value >= type(int8).min && value <= type(int8).max, "SafeCast: value doesn't fit in 8 bits");
        return int8(value);
    }

    /**
     * @dev Converts an unsigned uint256 into a signed int256.
     *
     * Requirements:
     *
     * - input must be less than or equal to maxInt256.
     *
     * _Available since v3.0._
     */
    function toInt256(uint256 value) internal pure returns (int256) {
        // Note: Unsafe cast below is okay because `type(int256).max` is guaranteed to be positive
        require(value <= uint256(type(int256).max), "SafeCast: value doesn't fit in an int256");
        return int256(value);
    }
}

// File: contracts/interfaces/WrapperContractInterface.sol

pragma solidity ^0.8.0;

interface WrapperContractInterface {
  function withdraw(uint256 amount) external;
}
// File: @openzeppelin/contracts/utils/structs/EnumerableSet.sol


// OpenZeppelin Contracts (last updated v4.7.0) (utils/structs/EnumerableSet.sol)

pragma solidity ^0.8.0;

/**
 * @dev Library for managing
 * https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
 * types.
 *
 * Sets have the following properties:
 *
 * - Elements are added, removed, and checked for existence in constant time
 * (O(1)).
 * - Elements are enumerated in O(n). No guarantees are made on the ordering.
 *
 * ```
 * contract Example {
 *     // Add the library methods
 *     using EnumerableSet for EnumerableSet.AddressSet;
 *
 *     // Declare a set state variable
 *     EnumerableSet.AddressSet private mySet;
 * }
 * ```
 *
 * As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
 * and `uint256` (`UintSet`) are supported.
 *
 * [WARNING]
 * ====
 *  Trying to delete such a structure from storage will likely result in data corruption, rendering the structure unusable.
 *  See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.
 *
 *  In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an array of EnumerableSet.
 * ====
 */
library EnumerableSet {
    // To implement this library for multiple types with as little code
    // repetition as possible, we write it in terms of a generic Set type with
    // bytes32 values.
    // The Set implementation uses private functions, and user-facing
    // implementations (such as AddressSet) are just wrappers around the
    // underlying Set.
    // This means that we can only create new EnumerableSets for types that fit
    // in bytes32.

    struct Set {
        // Storage of set values
        bytes32[] _values;
        // Position of the value in the `values` array, plus 1 because index 0
        // means a value is not in the set.
        mapping(bytes32 => uint256) _indexes;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function _add(Set storage set, bytes32 value) private returns (bool) {
        if (!_contains(set, value)) {
            set._values.push(value);
            // The value is stored at length-1, but we add 1 to all indexes
            // and use 0 as a sentinel value
            set._indexes[value] = set._values.length;
            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function _remove(Set storage set, bytes32 value) private returns (bool) {
        // We read and store the value's index to prevent multiple reads from the same storage slot
        uint256 valueIndex = set._indexes[value];

        if (valueIndex != 0) {
            // Equivalent to contains(set, value)
            // To delete an element from the _values array in O(1), we swap the element to delete with the last one in
            // the array, and then remove the last element (sometimes called as 'swap and pop').
            // This modifies the order of the array, as noted in {at}.

            uint256 toDeleteIndex = valueIndex - 1;
            uint256 lastIndex = set._values.length - 1;

            if (lastIndex != toDeleteIndex) {
                bytes32 lastValue = set._values[lastIndex];

                // Move the last value to the index where the value to delete is
                set._values[toDeleteIndex] = lastValue;
                // Update the index for the moved value
                set._indexes[lastValue] = valueIndex; // Replace lastValue's index to valueIndex
            }

            // Delete the slot where the moved value was stored
            set._values.pop();

            // Delete the index for the deleted slot
            delete set._indexes[value];

            return true;
        } else {
            return false;
        }
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function _contains(Set storage set, bytes32 value) private view returns (bool) {
        return set._indexes[value] != 0;
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function _length(Set storage set) private view returns (uint256) {
        return set._values.length;
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function _at(Set storage set, uint256 index) private view returns (bytes32) {
        return set._values[index];
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function _values(Set storage set) private view returns (bytes32[] memory) {
        return set._values;
    }

    // Bytes32Set

    struct Bytes32Set {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _add(set._inner, value);
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(Bytes32Set storage set, bytes32 value) internal returns (bool) {
        return _remove(set._inner, value);
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(Bytes32Set storage set, bytes32 value) internal view returns (bool) {
        return _contains(set._inner, value);
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(Bytes32Set storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(Bytes32Set storage set, uint256 index) internal view returns (bytes32) {
        return _at(set._inner, index);
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(Bytes32Set storage set) internal view returns (bytes32[] memory) {
        return _values(set._inner);
    }

    // AddressSet

    struct AddressSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(AddressSet storage set, address value) internal returns (bool) {
        return _add(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(AddressSet storage set, address value) internal returns (bool) {
        return _remove(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(AddressSet storage set, address value) internal view returns (bool) {
        return _contains(set._inner, bytes32(uint256(uint160(value))));
    }

    /**
     * @dev Returns the number of values in the set. O(1).
     */
    function length(AddressSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(AddressSet storage set, uint256 index) internal view returns (address) {
        return address(uint160(uint256(_at(set._inner, index))));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(AddressSet storage set) internal view returns (address[] memory) {
        bytes32[] memory store = _values(set._inner);
        address[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }

    // UintSet

    struct UintSet {
        Set _inner;
    }

    /**
     * @dev Add a value to a set. O(1).
     *
     * Returns true if the value was added to the set, that is if it was not
     * already present.
     */
    function add(UintSet storage set, uint256 value) internal returns (bool) {
        return _add(set._inner, bytes32(value));
    }

    /**
     * @dev Removes a value from a set. O(1).
     *
     * Returns true if the value was removed from the set, that is if it was
     * present.
     */
    function remove(UintSet storage set, uint256 value) internal returns (bool) {
        return _remove(set._inner, bytes32(value));
    }

    /**
     * @dev Returns true if the value is in the set. O(1).
     */
    function contains(UintSet storage set, uint256 value) internal view returns (bool) {
        return _contains(set._inner, bytes32(value));
    }

    /**
     * @dev Returns the number of values on the set. O(1).
     */
    function length(UintSet storage set) internal view returns (uint256) {
        return _length(set._inner);
    }

    /**
     * @dev Returns the value stored at position `index` in the set. O(1).
     *
     * Note that there are no guarantees on the ordering of values inside the
     * array, and it may change when more values are added or removed.
     *
     * Requirements:
     *
     * - `index` must be strictly less than {length}.
     */
    function at(UintSet storage set, uint256 index) internal view returns (uint256) {
        return uint256(_at(set._inner, index));
    }

    /**
     * @dev Return the entire set in an array
     *
     * WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
     * to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
     * this function has an unbounded cost, and using it as part of a state-changing function may render the function
     * uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.
     */
    function values(UintSet storage set) internal view returns (uint256[] memory) {
        bytes32[] memory store = _values(set._inner);
        uint256[] memory result;

        /// @solidity memory-safe-assembly
        assembly {
            result := store
        }

        return result;
    }
}

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


// OpenZeppelin Contracts (last updated v4.7.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _HEX_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) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

        if (value == 0) {
            return "0";
        }
        uint256 temp = value;
        uint256 digits;
        while (temp != 0) {
            digits++;
            temp /= 10;
        }
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
            value /= 10;
        }
        return string(buffer);
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        if (value == 0) {
            return "0x00";
        }
        uint256 temp = value;
        uint256 length = 0;
        while (temp != 0) {
            length++;
            temp >>= 8;
        }
        return toHexString(value, length);
    }

    /**
     * @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] = _HEX_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);
    }
}

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


// OpenZeppelin Contracts (last updated v4.7.3) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;


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

    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");
        } else if (error == RecoverError.InvalidSignatureV) {
            revert("ECDSA: invalid signature 'v' 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 (v != 27 && v != 28) {
            return (address(0), RecoverError.InvalidSignatureV);
        }

        // 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) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n32", hash));
    }

    /**
     * @dev Returns an Ethereum Signed 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) {
        return keccak256(abi.encodePacked("\x19\x01", domainSeparator, structHash));
    }
}

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


// 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;
    }
}

// File: @openzeppelin/contracts/security/ReentrancyGuard.sol


// OpenZeppelin Contracts v4.4.1 (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() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

        _;

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

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


// OpenZeppelin Contracts (last updated v4.7.0) (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
     * ====
     *
     * [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://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

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

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

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

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

        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

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

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

        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

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

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

        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verifies that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason 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 {
            // 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);
            }
        }
    }
}

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


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

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


// 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);
}

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


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

pragma solidity ^0.8.0;


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

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

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

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


// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;




/**
 * @dev Implementation of the {IERC20} interface.
 *
 * This implementation is agnostic to the way tokens are created. This means
 * that a supply mechanism has to be added in a derived contract using {_mint}.
 * For a generic mechanism see {ERC20PresetMinterPauser}.
 *
 * TIP: For a detailed writeup see our guide
 * https://forum.zeppelin.solutions/t/how-to-implement-erc20-supply-mechanisms/226[How
 * to implement supply mechanisms].
 *
 * We have followed general OpenZeppelin 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}.
     *
     * The default value of {decimals} is 18. To select a different value for
     * {decimals} you should overload it.
     *
     * All two of these values are immutable: they can only be set once during
     * construction.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

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

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

    /**
     * @dev Returns the number of decimals used to get its user representation.
     * For example, if `decimals` equals `2`, a balance of `505` tokens should
     * be displayed to a user as `5.05` (`505 / 10 ** 2`).
     *
     * Tokens usually opt for a value of 18, imitating the relationship between
     * Ether and Wei. This is the value {ERC20} uses, unless this function is
     * overridden;
     *
     * NOTE: This information is only used for _display_ purposes: it in
     * no way affects any of the arithmetic of the contract, including
     * {IERC20-balanceOf} and {IERC20-transfer}.
     */
    function decimals() public view virtual override returns (uint8) {
        return 18;
    }

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

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

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `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;
        }
        _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;
        _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;
        }
        _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 {}
}

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


// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC20/utils/SafeERC20.sol)

pragma solidity ^0.8.0;




/**
 * @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");
        }
    }
}

// File: contracts/ClipperCommonExchange.sol

pragma solidity ^0.8.0;








abstract contract ClipperCommonExchange is ERC20, ReentrancyGuard {

  using SafeERC20 for IERC20;
  using EnumerableSet for EnumerableSet.AddressSet;

  struct Signature {
    uint8 v;
    bytes32 r;
    bytes32 s;
  }

  struct Deposit {
      uint lockedUntil;
      uint256 poolTokenAmount;
  }

  uint256 constant ONE_IN_TEN_DECIMALS = 1e10;
  // Allow for inputs up to 0.5% more than quoted values to have scaled output.
  // Inputs higher than this value just get 0.5% more.
  uint256 constant MAX_ALLOWED_OVER_TEN_DECIMALS = ONE_IN_TEN_DECIMALS+50*1e6;

  // Signer is passed in on construction, hence "immutable"
  address immutable public DESIGNATED_SIGNER;
  address immutable public WRAPPER_CONTRACT;
  // Constant values for EIP-712 signing
  bytes32 immutable DOMAIN_SEPARATOR;
  string constant VERSION = "1.0.0";
  string constant NAME = "ClipperDirect";

  address constant CLIPPER_ETH_SIGIL = address(0);

  bytes32 constant EIP712DOMAIN_TYPEHASH = keccak256(
     abi.encodePacked("EIP712Domain(string name,string version,uint256 chainId,address verifyingContract)")
  );

  bytes32 constant OFFERSTRUCT_TYPEHASH = keccak256(
    abi.encodePacked("OfferStruct(address input_token,address output_token,uint256 input_amount,uint256 output_amount,uint256 good_until,address destination_address)")
  );

  bytes32 constant DEPOSITSTRUCT_TYPEHASH = keccak256(
    abi.encodePacked("DepositStruct(address sender,uint256[] deposit_amounts,uint256 days_locked,uint256 pool_tokens,uint256 good_until)")
  );

  bytes32 constant SINGLEDEPOSITSTRUCT_TYPEHASH = keccak256(
    abi.encodePacked("SingleDepositStruct(address sender,address token,uint256 amount,uint256 days_locked,uint256 pool_tokens,uint256 good_until)")
  );

  bytes32 constant WITHDRAWALSTRUCT_TYPEHASH = keccak256(
    abi.encodePacked("WithdrawalStruct(address token_holder,uint256 pool_token_amount_to_burn,address asset_address,uint256 asset_amount,uint256 good_until)")
  );

  // Assets
  // lastBalances: used for "transmit then swap then sync" modality
  // assetSet is a set of keys that have lastBalances
  mapping(address => uint256) public lastBalances;
  EnumerableSet.AddressSet assetSet;


  // Allows lookup
  mapping(address => Deposit) public vestingDeposits;

  // Events
  event Swapped(
    address indexed inAsset,
    address indexed outAsset,
    address indexed recipient,
    uint256 inAmount,
    uint256 outAmount,
    bytes auxiliaryData
  );

  event Deposited(
    address indexed depositor,
    uint256 poolTokens,
    uint256 nDays
  );

  event Withdrawn(
    address indexed withdrawer,
    uint256 poolTokens,
    uint256 fractionOfPool
  );

  event AssetWithdrawn(
    address indexed withdrawer,
    uint256 poolTokens,    
    address indexed assetAddress,
    uint256 assetAmount
  );

  // Take in the designated signer address and the token list
  constructor(address theSigner, address theWrapper, address[] memory tokens) ERC20("ClipperDirect Pool Token", "CLPRDRPL") {
    DESIGNATED_SIGNER = theSigner;
    uint i;
    uint n = tokens.length;
    while(i < n) {
        assetSet.add(tokens[i]);
        i++;
    }
    DOMAIN_SEPARATOR = createDomainSeparator(NAME, VERSION, address(this));
    WRAPPER_CONTRACT = theWrapper;
  }

  // Allows the receipt of ETH directly
  receive() external payable {
  }

  function safeEthSend(address recipient, uint256 howMuch) internal {
    (bool success, ) = payable(recipient).call{value: howMuch}("");
    require(success, "Call with value failed");
  }

  /* TOKEN AND ASSET FUNCTIONS */
  function nTokens() public view returns (uint) {
    return assetSet.length();
  }

  function tokenAt(uint i) public view returns (address) {
    return assetSet.at(i);
  }

  function isToken(address token) public view returns (bool) {
    return assetSet.contains(token);
  }

  function _sync(address token) internal virtual;

  // Can be overridden as in Caravel
  function getLastBalance(address token) public view virtual returns (uint256) {
    return lastBalances[token];
  }

  function allTokensBalance() external view returns (uint256[] memory, address[] memory, uint256){
    uint n = nTokens();
    uint256[] memory balances = new uint256[](n);
    address[] memory tokens = new address[](n);
    for (uint i = 0; i < n; i++) {
      address token = tokenAt(i);
      balances[i] = getLastBalance(token);
      tokens[i] = token;
    }

    return (balances, tokens, totalSupply());
  }

  // nonReentrant asset transfer
  function transferAsset(address token, address recipient, uint256 amount) internal nonReentrant {
    IERC20(token).safeTransfer(recipient, amount);
    // We never want to transfer an asset without sync'ing
    _sync(token);
  }

  function calculateFairOutput(uint256 statedInput, uint256 actualInput, uint256 statedOutput) internal pure returns (uint256) {
    if(actualInput == statedInput) {
      return statedOutput;
    } else {
      uint256 theFraction = (ONE_IN_TEN_DECIMALS*actualInput)/statedInput;
      if(theFraction >= MAX_ALLOWED_OVER_TEN_DECIMALS) {
        return (MAX_ALLOWED_OVER_TEN_DECIMALS*statedOutput)/ONE_IN_TEN_DECIMALS;
      } else {
        return (theFraction*statedOutput)/ONE_IN_TEN_DECIMALS;
      }
    }
  }

  /* DEPOSIT FUNCTIONALITY */
  function canUnlockDeposit(address theAddress) public view returns (bool) {
      Deposit storage myDeposit = vestingDeposits[theAddress];
      return (myDeposit.poolTokenAmount > 0) && (myDeposit.lockedUntil <= block.timestamp);
  }

  function unlockDeposit() external returns (uint256 poolTokens) {
    require(canUnlockDeposit(msg.sender), "ClipperDirect: Deposit cannot be unlocked");
    poolTokens = vestingDeposits[msg.sender].poolTokenAmount;
    delete vestingDeposits[msg.sender];

    _transfer(address(this), msg.sender, poolTokens);
  }

  function _mintOrVesting(address sender, uint256 nDays, uint256 poolTokens) internal {
    if(nDays==0){
      // No vesting period required - mint tokens directly for the user
      _mint(sender, poolTokens);
    } else {
      // Set up a vesting deposit for the sender
      _createVestingDeposit(sender, nDays, poolTokens);
    }
  }

  // Mints tokens to this contract to hold for vesting
  function _createVestingDeposit(address theAddress, uint256 nDays, uint256 numPoolTokens) internal {
    require(nDays > 0, "ClipperDirect: Cannot create vesting deposit without positive vesting period");
    require(vestingDeposits[theAddress].poolTokenAmount==0, "ClipperDirect: Depositor already has an active deposit");

    Deposit memory myDeposit = Deposit({
      lockedUntil: block.timestamp + (nDays * 1 days),
      poolTokenAmount: numPoolTokens
    });
    vestingDeposits[theAddress] = myDeposit;
    _mint(address(this), numPoolTokens);
  }

  function transmitAndDeposit(uint256[] calldata depositAmounts, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) external {
    uint i=0;
    uint n = depositAmounts.length;
    while(i < n){
      uint256 transferAmount = depositAmounts[i];
      if(transferAmount > 0){
        IERC20(tokenAt(i)).safeTransferFrom(msg.sender, address(this), transferAmount);
      }
      i++;
    }
    deposit(msg.sender, depositAmounts, nDays, poolTokens, goodUntil, theSignature);
  }

  function transmitAndDepositSingleAsset(address inputToken, uint256 inputAmount, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) external virtual;

  function deposit(address sender, uint256[] calldata depositAmounts, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) public payable virtual;

  function depositSingleAsset(address sender, address inputToken, uint256 inputAmount, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) public payable virtual;

  /* WITHDRAWAL FUNCTIONALITY */
  function _proportionalWithdrawal(uint256 myFraction) internal {
    uint256 toTransfer;

    uint i;
    uint n = nTokens();
    while(i < n) {
        address theToken = tokenAt(i);
        toTransfer = (myFraction*getLastBalance(theToken)) / ONE_IN_TEN_DECIMALS;
        // syncs done automatically on transfer
        transferAsset(theToken, msg.sender, toTransfer);
        i++;
    }
  }

  function burnToWithdraw(uint256 amount) external {
    // Capture the fraction first, before burning
    uint256 theFractionBaseTen = (ONE_IN_TEN_DECIMALS*amount)/totalSupply();
    
    // Reverts if balance is insufficient
    _burn(msg.sender, amount);

    _proportionalWithdrawal(theFractionBaseTen);
    emit Withdrawn(msg.sender, amount, theFractionBaseTen);
  }

  function withdrawSingleAsset(address tokenHolder, uint256 poolTokenAmountToBurn, address assetAddress, uint256 assetAmount, uint256 goodUntil, Signature calldata theSignature) external virtual;

  /* SWAP Functionality: Virtual */
  function sellEthForToken(address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external payable virtual;
  function sellTokenForEth(address inputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external virtual;
  function transmitAndSellTokenForEth(address inputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external virtual;
  function transmitAndSwap(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external virtual;
  function swap(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) public virtual;

  /* SIGNING Functionality */
  function createDomainSeparator(string memory name, string memory version, address theSigner) internal view returns (bytes32) {
    return keccak256(abi.encode(
        EIP712DOMAIN_TYPEHASH,
        keccak256(abi.encodePacked(name)),
        keccak256(abi.encodePacked(version)),
        uint256(block.chainid),
        theSigner
      ));
  }

  function hashInputOffer(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress) internal pure returns (bytes32) {
    return keccak256(abi.encode(
            OFFERSTRUCT_TYPEHASH,
            inputToken,
            outputToken,
            inputAmount,
            outputAmount,
            goodUntil,
            destinationAddress
        ));
  }

  function hashDeposit(address sender, uint256[] calldata depositAmounts, uint256 daysLocked, uint256 poolTokens, uint256 goodUntil) internal pure returns (bytes32) {
    bytes32 depositAmountsHash = keccak256(abi.encodePacked(depositAmounts));
    return keccak256(abi.encode(
        DEPOSITSTRUCT_TYPEHASH,
        sender,
        depositAmountsHash,
        daysLocked,
        poolTokens,
        goodUntil
      ));
  }

  function hashSingleDeposit(address sender, address inputToken, uint256 inputAmount, uint256 daysLocked, uint256 poolTokens, uint256 goodUntil) internal pure returns (bytes32) {
    return keccak256(abi.encode(
        SINGLEDEPOSITSTRUCT_TYPEHASH,
        sender,
        inputToken,
        inputAmount,
        daysLocked,
        poolTokens,
        goodUntil
      ));
  }

  function hashWithdrawal(address tokenHolder, uint256 poolTokenAmountToBurn, address assetAddress, uint256 assetAmount,
                    uint256 goodUntil) internal pure returns (bytes32) {
    return keccak256(abi.encode(
        WITHDRAWALSTRUCT_TYPEHASH,
        tokenHolder,
        poolTokenAmountToBurn,
        assetAddress,
        assetAmount,
        goodUntil
      ));
  }

  function createSwapDigest(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress) internal view returns (bytes32 digest){
    bytes32 hashedInput = hashInputOffer(inputToken, outputToken, inputAmount, outputAmount, goodUntil, destinationAddress);    
    digest = ECDSA.toTypedDataHash(DOMAIN_SEPARATOR, hashedInput);
  }

  function createDepositDigest(address sender, uint256[] calldata depositAmounts, uint256 nDays, uint256 poolTokens, uint256 goodUntil) internal view returns (bytes32 depositDigest){
    bytes32 hashedInput = hashDeposit(sender, depositAmounts, nDays, poolTokens, goodUntil);    
    depositDigest = ECDSA.toTypedDataHash(DOMAIN_SEPARATOR, hashedInput);
  }

  function createSingleDepositDigest(address sender, address inputToken, uint256 inputAmount, uint256 nDays, uint256 poolTokens, uint256 goodUntil) internal view returns (bytes32 depositDigest){
    bytes32 hashedInput = hashSingleDeposit(sender, inputToken, inputAmount, nDays, poolTokens, goodUntil);
    depositDigest = ECDSA.toTypedDataHash(DOMAIN_SEPARATOR, hashedInput);
  }

  function createWithdrawalDigest(address tokenHolder, uint256 poolTokenAmountToBurn, address assetAddress, uint256 assetAmount,
                    uint256 goodUntil) internal view returns (bytes32 withdrawalDigest){
    bytes32 hashedInput = hashWithdrawal(tokenHolder, poolTokenAmountToBurn, assetAddress, assetAmount, goodUntil);
    withdrawalDigest = ECDSA.toTypedDataHash(DOMAIN_SEPARATOR, hashedInput);
  }

  function verifyDigestSignature(bytes32 theDigest, Signature calldata theSignature) internal view {
    address signingAddress = ecrecover(theDigest, theSignature.v, theSignature.r, theSignature.s);

    require(signingAddress==DESIGNATED_SIGNER, "Message signed by incorrect address");
  }

}

// File: contracts/ClipperDirectExchange.sol

pragma solidity ^0.8.0;









contract ClipperDirectExchange is ClipperCommonExchange {
  
  using SafeERC20 for IERC20;
  using EnumerableSet for EnumerableSet.AddressSet;

  // For prevention of replay attacks
  mapping(bytes32 => bool) invalidatedDigests;

  constructor(address theSigner, address theWrapper, address[] memory tokens) 
    ClipperCommonExchange(theSigner, theWrapper, tokens)
    {}

  function currentDeltaOverLastBalance(address token) internal view returns (uint256) {
    return IERC20(token).balanceOf(address(this))-lastBalances[token];
  }

  function _sync(address token) internal override {
    lastBalances[token] = IERC20(token).balanceOf(address(this));
  }

  function _syncAll() internal {
    uint i;
    uint n=assetSet.length();
    while(i < n) {
      _sync(tokenAt(i));
      i++;
    }
  }


  // syncAndTransfer() and unwrapAndForwardEth() are the two additional ways tokens leave the pool
  // Since they transfer assets, they are all marked as nonReentrant
  function syncAndTransfer(address inputToken, address outputToken, address recipient, uint256 amount) internal nonReentrant {
    _sync(inputToken);
    IERC20(outputToken).safeTransfer(recipient, amount);
    _sync(outputToken);
  }

  // Essentially transferAsset, but for raw ETH
  function unwrapAndForwardEth(address recipient, uint256 amount) internal nonReentrant {
    /* EFFECTS */
    WrapperContractInterface(WRAPPER_CONTRACT).withdraw(amount);
    _sync(WRAPPER_CONTRACT);
    /* INTERACTIONS */
    safeEthSend(recipient, amount);
  }

  /* DEPOSIT FUNCTIONALITY */
  function deposit(address sender, uint256[] calldata depositAmounts, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) public payable override {
    // Wrap if it's there
    if(msg.value > 0){
      safeEthSend(WRAPPER_CONTRACT, msg.value);
    }
    require(msg.sender==sender, "Listed sender does not match msg.sender");
    // Did we actually deposit what we said we would? Revert otherwise
    verifyDepositAmounts(depositAmounts);
    // Check the signature
    bytes32 depositDigest = createDepositDigest(sender, depositAmounts, nDays, poolTokens, goodUntil);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(depositDigest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(depositDigest, goodUntil);
    // OK now we're good
    _syncAll();
    _mintOrVesting(sender, nDays, poolTokens);
    emit Deposited(sender, poolTokens, nDays);
  }

  function depositSingleAsset(address sender, address inputToken, uint256 inputAmount, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) public payable override {
    // Wrap if it's there
    if(msg.value > 0){
      safeEthSend(WRAPPER_CONTRACT, msg.value);
    }
    require(msg.sender==sender && isToken(inputToken), "Invalid input");

    // Did we actually deposit what we said we would? Revert otherwise
    uint256 delta = currentDeltaOverLastBalance(inputToken);
    require(delta >= inputAmount, "Insufficient token deposit");

    // Check the signature
    bytes32 depositDigest = createSingleDepositDigest(sender, inputToken, inputAmount, nDays, poolTokens, goodUntil);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(depositDigest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(depositDigest, goodUntil);

    // OK now we're good
    _sync(inputToken);
    _mintOrVesting(sender, nDays, poolTokens);
    emit Deposited(sender, poolTokens, nDays);
  }

  function verifyDepositAmounts(uint256[] calldata depositAmounts) internal view {
    uint i=0;
    uint n = depositAmounts.length;
    while(i < n){
      uint256 myDeposit = depositAmounts[i];
      if(myDeposit > 0){
        address token = tokenAt(i);
        uint256 delta = currentDeltaOverLastBalance(token);
        require(delta >= myDeposit, "Insufficient token deposit");
      }
      i++;
    }
  }

  /* Single asset withdrawal functionality */
  function withdrawSingleAsset(address tokenHolder, uint256 poolTokenAmountToBurn, address assetAddress, uint256 assetAmount, uint256 goodUntil, Signature calldata theSignature) external override {
    // Make sure the withdrawer is allowed
    require(msg.sender==tokenHolder, "tokenHolder does not match msg.sender");
    
    bool sendEthBack;
    if(assetAddress == CLIPPER_ETH_SIGIL) {
      assetAddress = WRAPPER_CONTRACT;
      sendEthBack = true;
    }

    // Check the signature
    bytes32 withdrawalDigest = createWithdrawalDigest(tokenHolder, poolTokenAmountToBurn, assetAddress, assetAmount, goodUntil);
    // Reverts if it's signed by the wrong address
    verifyDigestSignature(withdrawalDigest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(withdrawalDigest, goodUntil);
    // Reverts if balance is insufficient
    _burn(msg.sender, poolTokenAmountToBurn);
    // Reverts if balance is insufficient
    // syncs done automatically on transfer
    if(sendEthBack){
      unwrapAndForwardEth(msg.sender, assetAmount);
    } else {
      transferAsset(assetAddress, msg.sender, assetAmount);
    }

    emit AssetWithdrawn(tokenHolder, poolTokenAmountToBurn, assetAddress, assetAmount);
  }

  /* SWAP Functionality */

  // Don't need a separate "transmit" function here since it's already payable
  function sellEthForToken(address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external payable override {
    // Wrap ETH (as balance or value) as input
    safeEthSend(WRAPPER_CONTRACT, inputAmount);
    swap(WRAPPER_CONTRACT, outputToken, inputAmount, outputAmount, goodUntil, destinationAddress, theSignature, auxiliaryData);
  }

  // Mostly copied from swap functionality
  function sellTokenForEth(address inputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external virtual override {
    (uint256 actualInput, uint256 fairOutput) = verifyTokensAndGetAmounts(inputToken, WRAPPER_CONTRACT, inputAmount, outputAmount);
    
    bytes32 digest = createSwapDigest(inputToken, WRAPPER_CONTRACT, inputAmount, outputAmount, goodUntil, destinationAddress);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(digest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(digest, goodUntil);
    
    // We have to _sync the input token manually here
    _sync(inputToken);
    unwrapAndForwardEth(destinationAddress, fairOutput);

    emit Swapped(inputToken, WRAPPER_CONTRACT, destinationAddress, actualInput, fairOutput, auxiliaryData);
  }

  function transmitAndDepositSingleAsset(address inputToken, uint256 inputAmount, uint256 nDays, uint256 poolTokens, uint256 goodUntil, Signature calldata theSignature) external override{
    IERC20(inputToken).safeTransferFrom(msg.sender, address(this), inputAmount);
    depositSingleAsset(msg.sender, inputToken, inputAmount, nDays, poolTokens, goodUntil, theSignature);
  }

  function transmitAndSellTokenForEth(address inputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external override {
    IERC20(inputToken).safeTransferFrom(msg.sender, address(this), inputAmount);
    this.sellTokenForEth(inputToken, inputAmount, outputAmount, goodUntil, destinationAddress, theSignature, auxiliaryData);
  }

  // all-in-one transfer from msg.sender to destinationAddress.
  function transmitAndSwap(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external override {
    IERC20(inputToken).safeTransferFrom(msg.sender, address(this), inputAmount);
    swap(inputToken, outputToken, inputAmount, outputAmount, goodUntil, destinationAddress, theSignature, auxiliaryData);
  }

  function swap(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 goodUntil, address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) public virtual override {
    // Revert if the tokens don't exist
    (uint256 actualInput, uint256 fairOutput) = verifyTokensAndGetAmounts(inputToken, outputToken, inputAmount, outputAmount);
    
    bytes32 digest = createSwapDigest(inputToken, outputToken, inputAmount, outputAmount, goodUntil, destinationAddress);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(digest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(digest, goodUntil);
    // OK, now we are safe to transfer
    syncAndTransfer(inputToken, outputToken, destinationAddress, fairOutput);
    emit Swapped(inputToken, outputToken, destinationAddress, actualInput, fairOutput, auxiliaryData);
  }

  function verifyTokensAndGetAmounts(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount) internal view returns (uint256 actualInput, uint256 fairOutput) {
    require(isToken(inputToken) && isToken(outputToken), "Tokens not present in pool");
    actualInput = currentDeltaOverLastBalance(inputToken);
    fairOutput = calculateFairOutput(inputAmount, actualInput, outputAmount);
  }

  // Used to invalidate swap and deposit digests
  function checkTimestampAndInvalidateDigest(bytes32 theDigest, uint256 goodUntil) internal {
    require(!invalidatedDigests[theDigest], "Message digest already present");
    require(goodUntil >= block.timestamp, "Message received after allowed timestamp");
    invalidatedDigests[theDigest] = true;
  }

}

// File: contracts/ClipperVerifiedExchange.sol

pragma solidity ^0.8.0;






contract ClipperVerifiedExchange is ClipperDirectExchange {

  using PRBMathSD59x18 for int256;
  using SafeCast for uint256;
  using SafeCast for int256;

  uint256 constant ONE_IN_DEFAULT_DECIMALS = 1e18;
  uint256 constant ONE_IN_PRICE_DECIMALS = 1e8;

  struct UtilStruct {
    uint256 qX;
    uint256 qY;
    uint256 decimalMultiplierX;
    uint256 decimalMultiplierY;
  }

  constructor(address theSigner, address theWrapper, address[] memory tokens)
    ClipperDirectExchange(theSigner, theWrapper, tokens)
  {}

  function sellTokenForEth(address inputToken, uint256 inputAmount, uint256 outputAmount, uint256 packedGoodUntil,
    address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) external override {

    (uint256 actualInput, uint256 fairOutput) = verifyTokensAndGetAmounts(inputToken, WRAPPER_CONTRACT, inputAmount, outputAmount);

    uint256 goodUntil = unpackAndCheckInvariant(inputToken, actualInput, WRAPPER_CONTRACT, fairOutput, packedGoodUntil);

    bytes32 digest = createSwapDigest(inputToken, WRAPPER_CONTRACT, inputAmount, outputAmount, packedGoodUntil, destinationAddress);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(digest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(digest, goodUntil);

    // We have to _sync the input token manually here
    _sync(inputToken);
    unwrapAndForwardEth(destinationAddress, fairOutput);

    emit Swapped(inputToken, WRAPPER_CONTRACT, destinationAddress, actualInput, fairOutput, auxiliaryData);
  }

  function swap(address inputToken, address outputToken, uint256 inputAmount, uint256 outputAmount, uint256 packedGoodUntil,
    address destinationAddress, Signature calldata theSignature, bytes calldata auxiliaryData) public override {

    // Revert if the tokens don't exist
    (uint256 actualInput, uint256 fairOutput) = verifyTokensAndGetAmounts(inputToken, outputToken, inputAmount, outputAmount);
    uint256 goodUntil = unpackAndCheckInvariant(inputToken, actualInput, outputToken, fairOutput, packedGoodUntil);

    bytes32 digest = createSwapDigest(inputToken, outputToken, inputAmount, outputAmount, packedGoodUntil, destinationAddress);
    // Revert if it's signed by the wrong address
    verifyDigestSignature(digest, theSignature);
    // Revert if it's a replay, or if the timestamp is too late
    checkTimestampAndInvalidateDigest(digest, goodUntil);
    // OK, now we are safe to transfer
    syncAndTransfer(inputToken, outputToken, destinationAddress, fairOutput);
    emit Swapped(inputToken, outputToken, destinationAddress, actualInput, fairOutput, auxiliaryData);
  }

  function unpackAndCheckInvariant(address inputToken, uint256 inputAmount, address outputToken, uint256 outputAmount,
    uint256 packedGoodUntil) internal view returns (uint256) {

    UtilStruct memory s;

    (uint256 pX, uint256 pY,uint256 wX, uint256 wY, uint256 k) = unpackGoodUntil(packedGoodUntil);
    s.qX = lastBalances[inputToken];
    s.qY = lastBalances[outputToken];
    s.decimalMultiplierX = 10**(18 - IERC20Metadata(inputToken).decimals());
    s.decimalMultiplierY = 10**(18 - IERC20Metadata(outputToken).decimals());

    require(swapIncreasesInvariant(inputAmount * s.decimalMultiplierX, pX, s.qX * s.decimalMultiplierX, wX,
        outputAmount * s.decimalMultiplierY, pY, s.qY * s.decimalMultiplierY, wY, k), "Invariant check failed");

    return uint256(uint32(packedGoodUntil));
  }

  function unpackGoodUntil(uint256 packedGoodUntil) public pure
    returns (uint256 pX, uint256 pY, uint256 wX, uint256 wY, uint256 k) {
    /*
        * Input asset price in 8 decimals - uint64
        * Output asset price in 8 decimals - uint64
        * k value in 18 decimals - uint64
        * Input asset weight - uint16
        * Output asset weight - uint16
        * Current good until value - uint32 - can be taken as uint256(uint32(packedGoodUntil))
    */
    // goodUntil = uint256(uint32(packedGoodUntil));
    packedGoodUntil = packedGoodUntil >> 32;
    wY = uint256(uint16(packedGoodUntil));
    packedGoodUntil = packedGoodUntil >> 16;
    wX = uint256(uint16(packedGoodUntil));
    packedGoodUntil = packedGoodUntil >> 16;
    k = uint256(uint64(packedGoodUntil));
    packedGoodUntil = packedGoodUntil >> 64;
    pY = uint256(uint64(packedGoodUntil));
    packedGoodUntil = packedGoodUntil >> 64;
    pX = uint256(uint64(packedGoodUntil));
  }

  /*
  Before calling:
  Set qX = lastBalances[inAsset];
  Set qY = lastBalances[outAsset];

  Multiply all quantities (q and in/out) by 10**(18-asset.decimals()).
  This puts all quantities in 18 decimals.

  Assumed decimals:
  K: 18
  Quantities: 18 (ONE_IN_DEFAULT_DECIMALS = 1e18)
  Prices: 8 (ONE_IN_PRICE_DECIMALS = 1e8)
  Weights: 0 (100 = 100)
  */
  function swapIncreasesInvariant(uint256 inX, uint256 pX, uint256 qX, uint256 wX, uint256 outY, uint256 pY, uint256 qY,
    uint256 wY, uint256 k) internal pure returns (bool) {

    uint256 invariantBefore;
    uint256 invariantAfter;
    {
      uint256 pqX = pX * qX / ONE_IN_PRICE_DECIMALS;
      uint256 pqwXk = fractionalPow(pqX * wX, k);
      if (pqwXk > 0) {
        invariantBefore += (ONE_IN_DEFAULT_DECIMALS * pqX) / pqwXk;
      }

      uint256 pqY = pY * qY / ONE_IN_PRICE_DECIMALS;
      uint256 pqwYk = fractionalPow(pqY * wY, k);
      if (pqwYk > 0) {
        invariantBefore += (ONE_IN_DEFAULT_DECIMALS * pqY) / pqwYk;
      }
    }
    {
      uint256 pqXinX = (pX * (qX + inX)) / ONE_IN_PRICE_DECIMALS;
      uint256 pqwXinXk = fractionalPow(pqXinX * wX, k);
      if (pqwXinXk > 0) {
        invariantAfter += (ONE_IN_DEFAULT_DECIMALS * pqXinX) / pqwXinXk;
      }

      uint256 pqYoutY = pY * (qY - outY) / ONE_IN_PRICE_DECIMALS;
      uint256 pqwYoutYk = fractionalPow(pqYoutY * wY, k);
      if (pqwYoutYk > 0) {
        invariantAfter += (ONE_IN_DEFAULT_DECIMALS * pqYoutY) / pqwYoutYk;
      }
    }
    return invariantAfter > invariantBefore;
  }

  function fractionalPow(uint256 input, uint256 pow) internal pure returns (uint256) {
    if (input == 0) {
      return 0;
    } else {
      // input^(pow/1e18) -> exp2( (pow * log2( input ) / 1e18 ) )
      return exp2((int256(pow) * log2(input.toInt256())) / int256(ONE_IN_DEFAULT_DECIMALS));
    }
  }

  function exp2(int256 x) internal pure returns (uint256) {
    return x.exp2().toUint256();
  }

  function log2(int256 x) internal pure returns (int256 y) {
    y = x.log2();
  }

}

// File: contracts/ClipperCommonPacked.sol

pragma solidity ^0.8.0;




abstract contract ClipperCommonPacked is ClipperCommonExchange {
  using SafeERC20 for IERC20;
 
  /*
    unpack: internal function to unpack uint256 representation
    Input arguments:
      amountAndAddress: uint256 where first 24 hexchars are a uint96 shortened uint256
                         and last 40 hexchars are an address
    Returns: unpacked amount and address
  */
  function unpack(uint256 amountAndAddress) internal pure returns (uint256 amount, address contractAddress) {
    // uint256 -> uint160 automatically takes just last 40 hexchars
    contractAddress = address(uint160(amountAndAddress));
    // shift over the 40 hexchars to capture the amount
    amount = amountAndAddress >> 160;
  }

  function unpackAndSwap(uint256 packedInput, uint256 packedOutput, uint256 packedDestination, bytes32 auxData, bytes32 r, bytes32 vs, bool performTransfer) internal virtual;

  // external function to transfer tokens and perform swap from packed calldata
  function packedTransmitAndSwap(uint256 packedInput, uint256 packedOutput, uint256 packedDestination, bytes32 auxData, bytes32 r, bytes32 vs) external payable {
    unpackAndSwap(packedInput, packedOutput, packedDestination, auxData, r, vs, true);
  }
  
  // external function to perform swap from packed calldata
  function packedSwap(uint256 packedInput, uint256 packedOutput, uint256 packedDestination, bytes32 auxData, bytes32 r, bytes32 vs) external payable {
    unpackAndSwap(packedInput, packedOutput, packedDestination, auxData, r, vs, false);
  }

  /*
    packedTransmitAndDepositOneAsset: deposit a single asset in a calldata-efficient way
    Input arguments:
      packedInput: Amount and contract address of asset to deposit
      packedConfig: First 32 hexchars are poolTokens, next 24 are goodUntil, next 6 are nDays, final 2 are v
      r, s: Signature values
  */
  function packedTransmitAndDepositOneAsset(uint256 packedInput, uint256 packedConfig, bytes32 r, bytes32 s) external payable {
    (uint256 inputAmount, address inputContractAddress) = unpack(packedInput);
    uint256 poolTokens = packedConfig >> 128;
    uint256 goodUntil = uint256(uint96(packedConfig >> 32));
    uint256 nDays = uint256(uint24(packedConfig >> 8));
    uint8 v = uint8(packedConfig);
    bool inputIsRawEth = (inputContractAddress==CLIPPER_ETH_SIGIL);

    Signature memory theSignature = Signature(v,r,s);
    delete v;

    if(inputIsRawEth){
      // Don't need to wrap the ETH here, do it in the deposit function
      inputContractAddress = WRAPPER_CONTRACT;
    } else {
      IERC20(inputContractAddress).safeTransferFrom(msg.sender, address(this), inputAmount);
    }

    uint i = 0;
    uint n = nTokens();
    uint256[] memory depositAmounts = new uint256[](n); 

    while(i < n){
      depositAmounts[i] = (tokenAt(i) == inputContractAddress) ? inputAmount : 0;
      i++;
    }

    // Have to use delegatecall to preserve msg.sender context
    (bool success, ) = address(this).delegatecall(
      abi.encodeWithSignature(
        "deposit(address,uint256[],uint256,uint256,uint256,(uint8,bytes32,bytes32))",
        msg.sender,
        depositAmounts,
        nDays,
        poolTokens,
        goodUntil,
        theSignature));
    require(success, "Clipper: Deposit failed");
  }

}

// File: contracts/ClipperPackedVerifiedExchange.sol

//SPDX-License-Identifier: Copyright 2022 Shipyard Software, Inc.
pragma solidity ^0.8.0;




contract ClipperPackedVerifiedExchange is ClipperCommonPacked, ClipperVerifiedExchange {
  using SafeERC20 for IERC20;
 
  constructor(address theSigner, address theWrapper, address[] memory tokens) 
    ClipperVerifiedExchange(theSigner, theWrapper, tokens)
    {}

  /*
    unpackAndSwap: internal function that performs unpacks a set of calldata-packed inputs and performs a swap
    Input arguments:
      packedInput: input amount and contract
      packedOutput: output amount and contract
      packedGoodUntil: packed good until (for verifier, direct from server)
      auxData: bytes32, identifier. Final 20 bytes are destination address. First 12 bytes are auxData identifier string.
      r, vs: Signature values using EIP 2098 - https://eips.ethereum.org/EIPS/eip-2098
      performTransfer: if tokens should be transferred from msg.sender
  */
  function unpackAndSwap(uint256 packedInput, uint256 packedOutput, uint256 packedGoodUntil, bytes32 auxData, bytes32 r, bytes32 vs, bool performTransfer) internal override {    
    (uint256 inputAmount, address inputContractAddress) = unpack(packedInput);
    (uint256 outputAmount, address outputContractAddress) = unpack(packedOutput);
    Signature memory theSignature;

    {
      // Directly from https://eips.ethereum.org/EIPS/eip-2098
      bytes32 s = vs & 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff;
      uint8 v = 27 + uint8(uint256(vs) >> 255);

      theSignature = Signature(v,r,s);
    }

    if(performTransfer && (inputContractAddress!=CLIPPER_ETH_SIGIL)) {
      IERC20(inputContractAddress).safeTransferFrom(msg.sender, address(this), inputAmount);
    }

    performUnpackedSwap(inputContractAddress, outputContractAddress, inputAmount, outputAmount, packedGoodUntil, auxData, theSignature);
  }

  function performUnpackedSwap(address inputContractAddress, address outputContractAddress, uint256 inputAmount, uint256 outputAmount, uint256 packedGoodUntil, bytes32 auxData, Signature memory theSignature) internal {
      address destinationAddress = address(uint160(uint256(auxData)));
      bytes memory auxiliaryData = abi.encodePacked(auxData >> 160);
      
      if(inputContractAddress==CLIPPER_ETH_SIGIL) {
        this.sellEthForToken(outputContractAddress, inputAmount, outputAmount, packedGoodUntil, destinationAddress, theSignature, auxiliaryData);
      } else if(outputContractAddress==CLIPPER_ETH_SIGIL) {
        this.sellTokenForEth(inputContractAddress, inputAmount, outputAmount, packedGoodUntil, destinationAddress, theSignature, auxiliaryData);
      } else {
        this.swap(inputContractAddress, outputContractAddress, inputAmount, outputAmount, packedGoodUntil, destinationAddress, theSignature, auxiliaryData);
      }

  }
}

• No Contract Security Audit Submitted- Submit Audit Here

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components":[{"internalType":"uint8","name":"v","type":"uint8"},{"internalType":"bytes32","name":"r","type":"bytes32"},{"internalType":"bytes32","name":"s","type":"bytes32"}],"internalType":"struct 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ClipperCommonExchange.Signature","name":"theSignature","type":"tuple"}],"name":"withdrawSingleAsset","outputs":[],"stateMutability":"nonpayable","type":"function"},{"stateMutability":"payable","type":"receive"}]

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

-----Decoded View---------------
Arg [0] : theSigner (address): 0x08938a61BA9523298dbCAceE0cda5B371FB7f1F8
Arg [1] : theWrapper (address): 0x82aF49447D8a07e3bd95BD0d56f35241523fBab1
Arg [2] : tokens (address[]): 0xFF970A61A04b1cA14834A43f5dE4533eBDDB5CC8,0x82aF49447D8a07e3bd95BD0d56f35241523fBab1,0xFd086bC7CD5C481DCC9C85ebE478A1C0b69FCbb9,0xDA10009cBd5D07dd0CeCc66161FC93D7c9000da1,0x2f2a2543B76A4166549F7aaB2e75Bef0aefC5B0f

-----Encoded View---------------
9 Constructor Arguments found :
Arg [0] : 00000000000000000000000008938a61ba9523298dbcacee0cda5b371fb7f1f8
Arg [1] : 00000000000000000000000082af49447d8a07e3bd95bd0d56f35241523fbab1
Arg [2] : 0000000000000000000000000000000000000000000000000000000000000060
Arg [3] : 0000000000000000000000000000000000000000000000000000000000000005
Arg [4] : 000000000000000000000000ff970a61a04b1ca14834a43f5de4533ebddb5cc8
Arg [5] : 00000000000000000000000082af49447d8a07e3bd95bd0d56f35241523fbab1
Arg [6] : 000000000000000000000000fd086bc7cd5c481dcc9c85ebe478a1c0b69fcbb9
Arg [7] : 000000000000000000000000da10009cbd5d07dd0cecc66161fc93d7c9000da1
Arg [8] : 0000000000000000000000002f2a2543b76a4166549f7aab2e75bef0aefc5b0f

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