// SPDX-License-Identifier: BSD-4-Clause
/*
 * ABDK Math 64.64 Smart Contract Library.  Copyright © 2019 by ABDK Consulting.
 * Author: Mikhail Vladimirov <mikhail.vladimirov@gmail.com>
 */
pragma solidity ^0.8.6;

/**
 * Smart contract library of mathematical functions operating with signed
 * 64.64-bit fixed point numbers.  Signed 64.64-bit fixed point number is
 * basically a simple fraction whose numerator is signed 128-bit integer and
 * denominator is 2^64.  As long as denominator is always the same, there is no
 * need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
 * represented by int128 type holding only the numerator.
 */
library ABDKMath64x64 {
    /*
     * Minimum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;

    /*
     * Maximum value signed 64.64-bit fixed point number may have.
     */
    int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

    /**
     * Convert signed 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromInt(int256 x) internal pure returns (int128) {
        unchecked {
            require(x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
            return int128(x << 64);
        }
    }

    /**
     * Convert signed 64.64 fixed point number into signed 64-bit integer number
     * rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64-bit integer number
     */
    function toInt(int128 x) internal pure returns (int64) {
        unchecked {
            return int64(x >> 64);
        }
    }

    /**
     * Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
     * number.  Revert on overflow.
     *
     * @param x unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function fromUInt(uint256 x) internal pure returns (int128) {
        unchecked {
            require(x <= 0x7FFFFFFFFFFFFFFF);
            return int128(int256(x << 64));
        }
    }

    /**
     * Convert signed 64.64 fixed point number into unsigned 64-bit integer
     * number rounding down.  Revert on underflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return unsigned 64-bit integer number
     */
    function toUInt(int128 x) internal pure returns (uint64) {
        unchecked {
            require(x >= 0);
            return uint64(uint128(x >> 64));
        }
    }

    /**
     * Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
     * number rounding down.  Revert on overflow.
     *
     * @param x signed 128.128-bin fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function from128x128(int256 x) internal pure returns (int128) {
        unchecked {
            int256 result = x >> 64;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Convert signed 64.64 fixed point number into signed 128.128 fixed point
     * number.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 128.128 fixed point number
     */
    function to128x128(int128 x) internal pure returns (int256) {
        unchecked {
            return int256(x) << 64;
        }
    }

    /**
     * Calculate x + y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function add(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) + y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x - y.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sub(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = int256(x) - y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x * y rounding down.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function mul(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 result = (int256(x) * y) >> 64;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
     * number and y is signed 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y signed 256-bit integer number
     * @return signed 256-bit integer number
     */
    function muli(int128 x, int256 y) internal pure returns (int256) {
        unchecked {
            if (x == MIN_64x64) {
                require(
                    y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
                        y <= 0x1000000000000000000000000000000000000000000000000
                );
                return -y << 63;
            } else {
                bool negativeResult = false;
                if (x < 0) {
                    x = -x;
                    negativeResult = true;
                }
                if (y < 0) {
                    y = -y; // We rely on overflow behavior here
                    negativeResult = !negativeResult;
                }
                uint256 absoluteResult = mulu(x, uint256(y));
                if (negativeResult) {
                    require(
                        absoluteResult <=
                            0x8000000000000000000000000000000000000000000000000000000000000000
                    );
                    return -int256(absoluteResult); // We rely on overflow behavior here
                } else {
                    require(
                        absoluteResult <=
                            0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
                    );
                    return int256(absoluteResult);
                }
            }
        }
    }

    /**
     * Calculate x * y rounding down, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64 fixed point number
     * @param y unsigned 256-bit integer number
     * @return unsigned 256-bit integer number
     */
    function mulu(int128 x, uint256 y) internal pure returns (uint256) {
        unchecked {
            if (y == 0) return 0;

            require(x >= 0);

            uint256 lo = (uint256(int256(x)) *
                (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
            uint256 hi = uint256(int256(x)) * (y >> 128);

            require(hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            hi <<= 64;

            require(
                hi <=
                    0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF -
                        lo
            );
            return hi + lo;
        }
    }

    /**
     * Calculate x / y rounding towards zero.  Revert on overflow or when y is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function div(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);
            int256 result = (int256(x) << 64) / y;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are signed 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x signed 256-bit integer number
     * @param y signed 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divi(int256 x, int256 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);

            bool negativeResult = false;
            if (x < 0) {
                x = -x; // We rely on overflow behavior here
                negativeResult = true;
            }
            if (y < 0) {
                y = -y; // We rely on overflow behavior here
                negativeResult = !negativeResult;
            }
            uint128 absoluteResult = divuu(uint256(x), uint256(y));
            if (negativeResult) {
                require(absoluteResult <= 0x80000000000000000000000000000000);
                return -int128(absoluteResult); // We rely on overflow behavior here
            } else {
                require(absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
                return int128(absoluteResult); // We rely on overflow behavior here
            }
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return signed 64.64-bit fixed point number
     */
    function divu(uint256 x, uint256 y) internal pure returns (int128) {
        unchecked {
            require(y != 0);
            uint128 result = divuu(x, y);
            require(result <= uint128(MAX_64x64));
            return int128(result);
        }
    }

    /**
     * Calculate -x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function neg(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != MIN_64x64);
            return -x;
        }
    }

    /**
     * Calculate |x|.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function abs(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != MIN_64x64);
            return x < 0 ? -x : x;
        }
    }

    /**
     * Calculate 1 / x rounding towards zero.  Revert on overflow or when x is
     * zero.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function inv(int128 x) internal pure returns (int128) {
        unchecked {
            require(x != 0);
            int256 result = int256(0x100000000000000000000000000000000) / x;
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function avg(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            return int128((int256(x) + int256(y)) >> 1);
        }
    }

    /**
     * Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
     * Revert on overflow or in case x * y is negative.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function gavg(int128 x, int128 y) internal pure returns (int128) {
        unchecked {
            int256 m = int256(x) * int256(y);
            require(m >= 0);
            require(
                m <
                    0x4000000000000000000000000000000000000000000000000000000000000000
            );
            return int128(sqrtu(uint256(m)));
        }
    }

    /**
     * Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
     * and y is unsigned 256-bit integer number.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @param y uint256 value
     * @return signed 64.64-bit fixed point number
     */
    function pow(int128 x, uint256 y) internal pure returns (int128) {
        unchecked {
            bool negative = x < 0 && y & 1 == 1;

            uint256 absX = uint128(x < 0 ? -x : x);
            uint256 absResult;
            absResult = 0x100000000000000000000000000000000;

            if (absX <= 0x10000000000000000) {
                absX <<= 63;
                while (y != 0) {
                    if (y & 0x1 != 0) {
                        absResult = (absResult * absX) >> 127;
                    }
                    absX = (absX * absX) >> 127;

                    if (y & 0x2 != 0) {
                        absResult = (absResult * absX) >> 127;
                    }
                    absX = (absX * absX) >> 127;

                    if (y & 0x4 != 0) {
                        absResult = (absResult * absX) >> 127;
                    }
                    absX = (absX * absX) >> 127;

                    if (y & 0x8 != 0) {
                        absResult = (absResult * absX) >> 127;
                    }
                    absX = (absX * absX) >> 127;

                    y >>= 4;
                }

                absResult >>= 64;
            } else {
                uint256 absXShift = 63;
                if (absX < 0x1000000000000000000000000) {
                    absX <<= 32;
                    absXShift -= 32;
                }
                if (absX < 0x10000000000000000000000000000) {
                    absX <<= 16;
                    absXShift -= 16;
                }
                if (absX < 0x1000000000000000000000000000000) {
                    absX <<= 8;
                    absXShift -= 8;
                }
                if (absX < 0x10000000000000000000000000000000) {
                    absX <<= 4;
                    absXShift -= 4;
                }
                if (absX < 0x40000000000000000000000000000000) {
                    absX <<= 2;
                    absXShift -= 2;
                }
                if (absX < 0x80000000000000000000000000000000) {
                    absX <<= 1;
                    absXShift -= 1;
                }

                uint256 resultShift = 0;
                while (y != 0) {
                    require(absXShift < 64);

                    if (y & 0x1 != 0) {
                        absResult = (absResult * absX) >> 127;
                        resultShift += absXShift;
                        if (absResult > 0x100000000000000000000000000000000) {
                            absResult >>= 1;
                            resultShift += 1;
                        }
                    }
                    absX = (absX * absX) >> 127;
                    absXShift <<= 1;
                    if (absX >= 0x100000000000000000000000000000000) {
                        absX >>= 1;
                        absXShift += 1;
                    }

                    y >>= 1;
                }

                require(resultShift < 64);
                absResult >>= 64 - resultShift;
            }
            int256 result = negative ? -int256(absResult) : int256(absResult);
            require(result >= MIN_64x64 && result <= MAX_64x64);
            return int128(result);
        }
    }

    /**
     * Calculate sqrt (x) rounding down.  Revert if x < 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function sqrt(int128 x) internal pure returns (int128) {
        unchecked {
            require(x >= 0);
            return int128(sqrtu(uint256(int256(x)) << 64));
        }
    }

    /**
     * Calculate binary logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function log_2(int128 x) internal pure returns (int128) {
        unchecked {
            require(x > 0);

            int256 msb = 0;
            int256 xc = x;
            if (xc >= 0x10000000000000000) {
                xc >>= 64;
                msb += 64;
            }
            if (xc >= 0x100000000) {
                xc >>= 32;
                msb += 32;
            }
            if (xc >= 0x10000) {
                xc >>= 16;
                msb += 16;
            }
            if (xc >= 0x100) {
                xc >>= 8;
                msb += 8;
            }
            if (xc >= 0x10) {
                xc >>= 4;
                msb += 4;
            }
            if (xc >= 0x4) {
                xc >>= 2;
                msb += 2;
            }
            if (xc >= 0x2) msb += 1; // No need to shift xc anymore

            int256 result = (msb - 64) << 64;
            uint256 ux = uint256(int256(x)) << uint256(127 - msb);
            for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
                ux *= ux;
                uint256 b = ux >> 255;
                ux >>= 127 + b;
                result += bit * int256(b);
            }

            return int128(result);
        }
    }

    /**
     * Calculate natural logarithm of x.  Revert if x <= 0.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function ln(int128 x) internal pure returns (int128) {
        unchecked {
            require(x > 0);

            return
                int128(
                    int256(
                        (uint256(int256(log_2(x))) *
                            0xB17217F7D1CF79ABC9E3B39803F2F6AF) >> 128
                    )
                );
        }
    }

    /**
     * Calculate binary exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp_2(int128 x) internal pure returns (int128) {
        unchecked {
            require(x < 0x400000000000000000); // Overflow

            if (x < -0x400000000000000000) return 0; // Underflow

            uint256 result = 0x80000000000000000000000000000000;

            if (x & 0x8000000000000000 > 0)
                result = (result * 0x16A09E667F3BCC908B2FB1366EA957D3E) >> 128;
            if (x & 0x4000000000000000 > 0)
                result = (result * 0x1306FE0A31B7152DE8D5A46305C85EDEC) >> 128;
            if (x & 0x2000000000000000 > 0)
                result = (result * 0x1172B83C7D517ADCDF7C8C50EB14A791F) >> 128;
            if (x & 0x1000000000000000 > 0)
                result = (result * 0x10B5586CF9890F6298B92B71842A98363) >> 128;
            if (x & 0x800000000000000 > 0)
                result = (result * 0x1059B0D31585743AE7C548EB68CA417FD) >> 128;
            if (x & 0x400000000000000 > 0)
                result = (result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8) >> 128;
            if (x & 0x200000000000000 > 0)
                result = (result * 0x10163DA9FB33356D84A66AE336DCDFA3F) >> 128;
            if (x & 0x100000000000000 > 0)
                result = (result * 0x100B1AFA5ABCBED6129AB13EC11DC9543) >> 128;
            if (x & 0x80000000000000 > 0)
                result = (result * 0x10058C86DA1C09EA1FF19D294CF2F679B) >> 128;
            if (x & 0x40000000000000 > 0)
                result = (result * 0x1002C605E2E8CEC506D21BFC89A23A00F) >> 128;
            if (x & 0x20000000000000 > 0)
                result = (result * 0x100162F3904051FA128BCA9C55C31E5DF) >> 128;
            if (x & 0x10000000000000 > 0)
                result = (result * 0x1000B175EFFDC76BA38E31671CA939725) >> 128;
            if (x & 0x8000000000000 > 0)
                result = (result * 0x100058BA01FB9F96D6CACD4B180917C3D) >> 128;
            if (x & 0x4000000000000 > 0)
                result = (result * 0x10002C5CC37DA9491D0985C348C68E7B3) >> 128;
            if (x & 0x2000000000000 > 0)
                result = (result * 0x1000162E525EE054754457D5995292026) >> 128;
            if (x & 0x1000000000000 > 0)
                result = (result * 0x10000B17255775C040618BF4A4ADE83FC) >> 128;
            if (x & 0x800000000000 > 0)
                result = (result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB) >> 128;
            if (x & 0x400000000000 > 0)
                result = (result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9) >> 128;
            if (x & 0x200000000000 > 0)
                result = (result * 0x10000162E43F4F831060E02D839A9D16D) >> 128;
            if (x & 0x100000000000 > 0)
                result = (result * 0x100000B1721BCFC99D9F890EA06911763) >> 128;
            if (x & 0x80000000000 > 0)
                result = (result * 0x10000058B90CF1E6D97F9CA14DBCC1628) >> 128;
            if (x & 0x40000000000 > 0)
                result = (result * 0x1000002C5C863B73F016468F6BAC5CA2B) >> 128;
            if (x & 0x20000000000 > 0)
                result = (result * 0x100000162E430E5A18F6119E3C02282A5) >> 128;
            if (x & 0x10000000000 > 0)
                result = (result * 0x1000000B1721835514B86E6D96EFD1BFE) >> 128;
            if (x & 0x8000000000 > 0)
                result = (result * 0x100000058B90C0B48C6BE5DF846C5B2EF) >> 128;
            if (x & 0x4000000000 > 0)
                result = (result * 0x10000002C5C8601CC6B9E94213C72737A) >> 128;
            if (x & 0x2000000000 > 0)
                result = (result * 0x1000000162E42FFF037DF38AA2B219F06) >> 128;
            if (x & 0x1000000000 > 0)
                result = (result * 0x10000000B17217FBA9C739AA5819F44F9) >> 128;
            if (x & 0x800000000 > 0)
                result = (result * 0x1000000058B90BFCDEE5ACD3C1CEDC823) >> 128;
            if (x & 0x400000000 > 0)
                result = (result * 0x100000002C5C85FE31F35A6A30DA1BE50) >> 128;
            if (x & 0x200000000 > 0)
                result = (result * 0x10000000162E42FF0999CE3541B9FFFCF) >> 128;
            if (x & 0x100000000 > 0)
                result = (result * 0x100000000B17217F80F4EF5AADDA45554) >> 128;
            if (x & 0x80000000 > 0)
                result = (result * 0x10000000058B90BFBF8479BD5A81B51AD) >> 128;
            if (x & 0x40000000 > 0)
                result = (result * 0x1000000002C5C85FDF84BD62AE30A74CC) >> 128;
            if (x & 0x20000000 > 0)
                result = (result * 0x100000000162E42FEFB2FED257559BDAA) >> 128;
            if (x & 0x10000000 > 0)
                result = (result * 0x1000000000B17217F7D5A7716BBA4A9AE) >> 128;
            if (x & 0x8000000 > 0)
                result = (result * 0x100000000058B90BFBE9DDBAC5E109CCE) >> 128;
            if (x & 0x4000000 > 0)
                result = (result * 0x10000000002C5C85FDF4B15DE6F17EB0D) >> 128;
            if (x & 0x2000000 > 0)
                result = (result * 0x1000000000162E42FEFA494F1478FDE05) >> 128;
            if (x & 0x1000000 > 0)
                result = (result * 0x10000000000B17217F7D20CF927C8E94C) >> 128;
            if (x & 0x800000 > 0)
                result = (result * 0x1000000000058B90BFBE8F71CB4E4B33D) >> 128;
            if (x & 0x400000 > 0)
                result = (result * 0x100000000002C5C85FDF477B662B26945) >> 128;
            if (x & 0x200000 > 0)
                result = (result * 0x10000000000162E42FEFA3AE53369388C) >> 128;
            if (x & 0x100000 > 0)
                result = (result * 0x100000000000B17217F7D1D351A389D40) >> 128;
            if (x & 0x80000 > 0)
                result = (result * 0x10000000000058B90BFBE8E8B2D3D4EDE) >> 128;
            if (x & 0x40000 > 0)
                result = (result * 0x1000000000002C5C85FDF4741BEA6E77E) >> 128;
            if (x & 0x20000 > 0)
                result = (result * 0x100000000000162E42FEFA39FE95583C2) >> 128;
            if (x & 0x10000 > 0)
                result = (result * 0x1000000000000B17217F7D1CFB72B45E1) >> 128;
            if (x & 0x8000 > 0)
                result = (result * 0x100000000000058B90BFBE8E7CC35C3F0) >> 128;
            if (x & 0x4000 > 0)
                result = (result * 0x10000000000002C5C85FDF473E242EA38) >> 128;
            if (x & 0x2000 > 0)
                result = (result * 0x1000000000000162E42FEFA39F02B772C) >> 128;
            if (x & 0x1000 > 0)
                result = (result * 0x10000000000000B17217F7D1CF7D83C1A) >> 128;
            if (x & 0x800 > 0)
                result = (result * 0x1000000000000058B90BFBE8E7BDCBE2E) >> 128;
            if (x & 0x400 > 0)
                result = (result * 0x100000000000002C5C85FDF473DEA871F) >> 128;
            if (x & 0x200 > 0)
                result = (result * 0x10000000000000162E42FEFA39EF44D91) >> 128;
            if (x & 0x100 > 0)
                result = (result * 0x100000000000000B17217F7D1CF79E949) >> 128;
            if (x & 0x80 > 0)
                result = (result * 0x10000000000000058B90BFBE8E7BCE544) >> 128;
            if (x & 0x40 > 0)
                result = (result * 0x1000000000000002C5C85FDF473DE6ECA) >> 128;
            if (x & 0x20 > 0)
                result = (result * 0x100000000000000162E42FEFA39EF366F) >> 128;
            if (x & 0x10 > 0)
                result = (result * 0x1000000000000000B17217F7D1CF79AFA) >> 128;
            if (x & 0x8 > 0)
                result = (result * 0x100000000000000058B90BFBE8E7BCD6D) >> 128;
            if (x & 0x4 > 0)
                result = (result * 0x10000000000000002C5C85FDF473DE6B2) >> 128;
            if (x & 0x2 > 0)
                result = (result * 0x1000000000000000162E42FEFA39EF358) >> 128;
            if (x & 0x1 > 0)
                result = (result * 0x10000000000000000B17217F7D1CF79AB) >> 128;

            result >>= uint256(int256(63 - (x >> 64)));
            require(result <= uint256(int256(MAX_64x64)));

            return int128(int256(result));
        }
    }

    /**
     * Calculate natural exponent of x.  Revert on overflow.
     *
     * @param x signed 64.64-bit fixed point number
     * @return signed 64.64-bit fixed point number
     */
    function exp(int128 x) internal pure returns (int128) {
        unchecked {
            require(x < 0x400000000000000000); // Overflow

            if (x < -0x400000000000000000) return 0; // Underflow

            return
                exp_2(
                    int128(
                        (int256(x) * 0x171547652B82FE1777D0FFDA0D23A7D12) >> 128
                    )
                );
        }
    }

    /**
     * Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
     * integer numbers.  Revert on overflow or when y is zero.
     *
     * @param x unsigned 256-bit integer number
     * @param y unsigned 256-bit integer number
     * @return unsigned 64.64-bit fixed point number
     */
    function divuu(uint256 x, uint256 y) private pure returns (uint128) {
        unchecked {
            require(y != 0);

            uint256 result;

            if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
                result = (x << 64) / y;
            else {
                uint256 msb = 192;
                uint256 xc = x >> 192;
                if (xc >= 0x100000000) {
                    xc >>= 32;
                    msb += 32;
                }
                if (xc >= 0x10000) {
                    xc >>= 16;
                    msb += 16;
                }
                if (xc >= 0x100) {
                    xc >>= 8;
                    msb += 8;
                }
                if (xc >= 0x10) {
                    xc >>= 4;
                    msb += 4;
                }
                if (xc >= 0x4) {
                    xc >>= 2;
                    msb += 2;
                }
                if (xc >= 0x2) msb += 1; // No need to shift xc anymore

                result = (x << (255 - msb)) / (((y - 1) >> (msb - 191)) + 1);
                require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

                uint256 hi = result * (y >> 128);
                uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

                uint256 xh = x >> 192;
                uint256 xl = x << 64;

                if (xl < lo) xh -= 1;
                xl -= lo; // We rely on overflow behavior here
                lo = hi << 128;
                if (xl < lo) xh -= 1;
                xl -= lo; // We rely on overflow behavior here

                assert(xh == hi >> 128);

                result += xl / y;
            }

            require(result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
            return uint128(result);
        }
    }

    /**
     * Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
     * number.
     *
     * @param x unsigned 256-bit integer number
     * @return unsigned 128-bit integer number
     */
    function sqrtu(uint256 x) private pure returns (uint128) {
        unchecked {
            if (x == 0) return 0;
            else {
                uint256 xx = x;
                uint256 r = 1;
                if (xx >= 0x100000000000000000000000000000000) {
                    xx >>= 128;
                    r <<= 64;
                }
                if (xx >= 0x10000000000000000) {
                    xx >>= 64;
                    r <<= 32;
                }
                if (xx >= 0x100000000) {
                    xx >>= 32;
                    r <<= 16;
                }
                if (xx >= 0x10000) {
                    xx >>= 16;
                    r <<= 8;
                }
                if (xx >= 0x100) {
                    xx >>= 8;
                    r <<= 4;
                }
                if (xx >= 0x10) {
                    xx >>= 4;
                    r <<= 2;
                }
                if (xx >= 0x8) {
                    r <<= 1;
                }
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1;
                r = (r + x / r) >> 1; // Seven iterations should be enough
                uint256 r1 = x / r;
                return uint128(r < r1 ? r : r1);
            }
        }
    }
}




abstract contract Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }
}




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 functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}



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);
}




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);
}



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);
}



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;
            // Overflow not possible: the sum of all balances is capped by totalSupply, and the sum is preserved by
            // decrementing then incrementing.
            _balances[to] += amount;
        }

        emit Transfer(from, to, amount);

        _afterTokenTransfer(from, to, amount);
    }

    /** @dev Creates `amount` tokens and assigns them to `account`, increasing
     * the total supply.
     *
     * Emits a {Transfer} event with `from` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     */
    function _mint(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: mint to the zero address");

        _beforeTokenTransfer(address(0), account, amount);

        _totalSupply += amount;
        unchecked {
            // Overflow not possible: balance + amount is at most totalSupply + amount, which is checked above.
            _balances[account] += amount;
        }
        emit Transfer(address(0), account, amount);

        _afterTokenTransfer(address(0), account, amount);
    }

    /**
     * @dev Destroys `amount` tokens from `account`, reducing the
     * total supply.
     *
     * Emits a {Transfer} event with `to` set to the zero address.
     *
     * Requirements:
     *
     * - `account` cannot be the zero address.
     * - `account` must have at least `amount` tokens.
     */
    function _burn(address account, uint256 amount) internal virtual {
        require(account != address(0), "ERC20: burn from the zero address");

        _beforeTokenTransfer(account, address(0), amount);

        uint256 accountBalance = _balances[account];
        require(accountBalance >= amount, "ERC20: burn amount exceeds balance");
        unchecked {
            _balances[account] = accountBalance - amount;
            // Overflow not possible: amount <= accountBalance <= totalSupply.
            _totalSupply -= amount;
        }

        emit Transfer(account, address(0), amount);

        _afterTokenTransfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner` s tokens.
     *
     * This internal function is equivalent to `approve`, and can be used to
     * e.g. set automatic allowances for certain subsystems, etc.
     *
     * Emits an {Approval} event.
     *
     * Requirements:
     *
     * - `owner` cannot be the zero address.
     * - `spender` cannot be the zero address.
     */
    function _approve(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        require(owner != address(0), "ERC20: approve from the zero address");
        require(spender != address(0), "ERC20: approve to the zero address");

        _allowances[owner][spender] = amount;
        emit Approval(owner, spender, amount);
    }

    /**
     * @dev Updates `owner` s allowance for `spender` based on spent `amount`.
     *
     * Does not update the allowance amount in case of infinite allowance.
     * Revert if not enough allowance is available.
     *
     * Might emit an {Approval} event.
     */
    function _spendAllowance(
        address owner,
        address spender,
        uint256 amount
    ) internal virtual {
        uint256 currentAllowance = allowance(owner, spender);
        if (currentAllowance != type(uint256).max) {
            require(currentAllowance >= amount, "ERC20: insufficient allowance");
            unchecked {
                _approve(owner, spender, currentAllowance - amount);
            }
        }
    }

    /**
     * @dev Hook that is called before any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * will be transferred to `to`.
     * - when `from` is zero, `amount` tokens will be minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens will be burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _beforeTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}

    /**
     * @dev Hook that is called after any transfer of tokens. This includes
     * minting and burning.
     *
     * Calling conditions:
     *
     * - when `from` and `to` are both non-zero, `amount` of ``from``'s tokens
     * has been transferred to `to`.
     * - when `from` is zero, `amount` tokens have been minted for `to`.
     * - when `to` is zero, `amount` of ``from``'s tokens have been burned.
     * - `from` and `to` are never both zero.
     *
     * To learn more about hooks, head to xref:ROOT:extending-contracts.adoc#using-hooks[Using Hooks].
     */
    function _afterTokenTransfer(
        address from,
        address to,
        uint256 amount
    ) internal virtual {}
}


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");
        }
    }
}



contract WISH is ERC20 {
    /* WISH  starts at $0.00000001 on 2023 Mar 6th, enriches 100m times till 2033 Jan 21st, and stablizes at $1.00000005841 */
    using SafeERC20 for ERC20;
    mapping(address => bool) public isUSD;
    mapping(address => uint256) public Decimals;
    uint256 public constant launchTime = 1678104000; /* Mon Mar 06 2023 12:00:00 GMT+0000 */
    uint256 public constant stableTime = 1989925200; /* Fri Jan 21 2033 13:00:00 GMT+0000 */
    address private constant wishFundationAddr =
        0x709D83004eB79Cf752B5D4f021d3652c97Ad1561; 

    constructor(
        address usdt,
        uint256 usdtDecimal,
        address usdc,
        uint256 usdcDecimal,
        address busd,
        uint256 busdDecimal,
        address dai,
        uint256 daiDecimal
    ) ERC20("WISH", "WISH") {
        isUSD[usdt] = true;
        Decimals[usdt] = usdtDecimal;
        isUSD[usdc] = true;
        Decimals[usdc] = usdcDecimal;
        isUSD[busd] = true;
        Decimals[busd] = busdDecimal;
        isUSD[dai] = true;
        Decimals[dai] = daiDecimal;
    }

    function convert6To18(uint256 amount, uint256 decimal)
        public
        pure
        returns (uint256)
    {
        if (decimal == 6) return amount * 1e12;

        return amount;
    }

    function convert18To6(uint256 usd, uint256 decimal)
        public
        pure
        returns (uint256)
    {
        if (decimal == 6) return usd / 1e12;

        return usd;
    }

    function getWishFundationAddress() public pure returns (address) {
        return wishFundationAddr;
    }

    /**
     * The current price of WISH is always 6.4428653X of the price a year ago
     *   y = 6.4428653^(ticktock / 365 days)
     */
    function getPrice() public view returns (uint256) {
        uint256 ticktock;

        if (block.timestamp <= launchTime) return 10000000000; /* WISH price stablizes at $0.00000001 before 2023 Mar 6 */
        if (block.timestamp >= stableTime) return 1000000058410266000; /* WISH price stablizes at $1.00000005841 after 2033 Jan 21 */

        ticktock = block.timestamp - launchTime;

        int128 base = ABDKMath64x64.div(
            ABDKMath64x64.fromUInt(64428653),
            ABDKMath64x64.fromUInt(10000000)
        );
        int128 exponential = ABDKMath64x64.div(
            ABDKMath64x64.fromUInt(ticktock),
            ABDKMath64x64.fromUInt(365 days)
        );

        /**
         * Basic logarithm rule:
         *   x = a^(log_a(x))
         * And deduce it:
         *   x^y = a^(y*log_a(x))
         * When a equals 2
         *   x^y = 2^(y*log_2(x))
         */
        return
            ABDKMath64x64.mulu(
                ABDKMath64x64.exp_2(
                    ABDKMath64x64.mul(exponential, ABDKMath64x64.log_2(base))
                ),
                1e10
            );
    }

    function Buy(address usd, uint256 amount) external returns (bool) {
        require(isUSD[usd], "USD ERROR");
        uint256 _commissionFee = ((amount * 5) / 100);
        uint256 remain = amount - _commissionFee;

        ERC20(usd).safeTransferFrom(
            msg.sender,
            getWishFundationAddress(),
            _commissionFee
        );
        ERC20(usd).safeTransferFrom(msg.sender, address(this), remain);

        remain = convert6To18(remain, Decimals[usd]);
        uint256 wishes = (remain * 1e18) / getPrice();

        _mint(msg.sender, wishes);

        return true;
    }

    function Sell(address usd, uint256 wishes) external returns (bool) {
        require(isUSD[usd], "USD ERROR");

        _burn(msg.sender, wishes);

        uint256 _usd = (wishes * getPrice()) / 1e18;
        _usd = convert18To6(_usd, Decimals[usd]);
        uint256 _commissionFee = ((_usd * 2) / 10);
        uint256 _remain = _usd - _commissionFee;

        ERC20(usd).safeTransfer(getWishFundationAddress(), _commissionFee);
        ERC20(usd).safeTransfer(msg.sender, _remain);
        return true;
    }

    function burn(uint256 wishes) external {
        _burn(msg.sender, wishes);
    }
}