// 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 ^0.8.0;

/**
 * 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

        result += xh == hi >> 128 ? xl / y : 1;
      }

      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 >= 0x4) { 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);
      }
    }
  }
}

// SPDX-License-Identifier: MIT
// 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);
            }
        }
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

library Array {
    function idx(uint256[] memory arr, uint256 item) internal pure returns (uint256 i) {
        for (i = 1; i <= arr.length; i++) {
            if (arr[i - 1] == item) {
                return i;
            }
        }
        i = 0;
    }

    function addItem(uint256[] storage arr, uint256 item) internal {
        if (idx(arr, item) == 0) {
            arr.push(item);
        }
    }

    function removeItem(uint256[] storage arr, uint256 item) internal {
        uint256 i = idx(arr, item);
        if (i > 0) {
            arr[i - 1] = arr[arr.length - 1];
            arr.pop();
        }
    }

    function contains(uint256[] memory container, uint256[] memory items) internal pure returns (bool) {
        if (items.length == 0) return true;
        for (uint256 i = 0; i < items.length; i++) {
            bool itemIsContained = false;
            for (uint256 j = 0; j < container.length; j++) {
                itemIsContained = items[i] == container[j];
            }
            if (!itemIsContained) return false;
        }
        return true;
    }

    function asSingletonArray(uint256 element) internal pure returns (uint256[] memory) {
        uint256[] memory array = new uint256[](1);
        array[0] = element;
        return array;
    }

    function hasDuplicatesOrZeros(uint256[] memory array) internal pure returns (bool) {
        for (uint256 i = 0; i < array.length; i++) {
            if (array[i] == 0) return true;
            for (uint256 j = 0; j < array.length; j++) {
                if (array[i] == array[j] && i != j) return true;
            }
        }
        return false;
    }

    function hasRoguesOrZeros(uint256[] memory array) internal pure returns (bool) {
        uint256 _first = array[0];
        for (uint256 i = 0; i < array.length; i++) {
            if (array[i] == 0 || array[i] != _first) return true;
        }
        return false;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (utils/Base64.sol)

pragma solidity ^0.8.0;

/**
 * @dev Provides a set of functions to operate with Base64 strings.
 *
 * _Available since v4.5._
 */
library Base64 {
    /**
     * @dev Base64 Encoding/Decoding Table
     */
    string internal constant _TABLE = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";

    /**
     * @dev Converts a `bytes` to its Bytes64 `string` representation.
     */
    function encode(bytes memory data) internal pure returns (string memory) {
        /**
         * Inspired by Brecht Devos (Brechtpd) implementation - MIT licence
         * https://github.com/Brechtpd/base64/blob/e78d9fd951e7b0977ddca77d92dc85183770daf4/base64.sol
         */
        if (data.length == 0) return "";

        // Loads the table into memory
        string memory table = _TABLE;

        // Encoding takes 3 bytes chunks of binary data from `bytes` data parameter
        // and split into 4 numbers of 6 bits.
        // The final Base64 length should be `bytes` data length multiplied by 4/3 rounded up
        // - `data.length + 2`  -> Round up
        // - `/ 3`              -> Number of 3-bytes chunks
        // - `4 *`              -> 4 characters for each chunk
        string memory result = new string(4 * ((data.length + 2) / 3));

        /// @solidity memory-safe-assembly
        assembly {
            // Prepare the lookup table (skip the first "length" byte)
            let tablePtr := add(table, 1)

            // Prepare result pointer, jump over length
            let resultPtr := add(result, 32)

            // Run over the input, 3 bytes at a time
            for {
                let dataPtr := data
                let endPtr := add(data, mload(data))
            } lt(dataPtr, endPtr) {

            } {
                // Advance 3 bytes
                dataPtr := add(dataPtr, 3)
                let input := mload(dataPtr)

                // To write each character, shift the 3 bytes (18 bits) chunk
                // 4 times in blocks of 6 bits for each character (18, 12, 6, 0)
                // and apply logical AND with 0x3F which is the number of
                // the previous character in the ASCII table prior to the Base64 Table
                // The result is then added to the table to get the character to write,
                // and finally write it in the result pointer but with a left shift
                // of 256 (1 byte) - 8 (1 ASCII char) = 248 bits

                mstore8(resultPtr, mload(add(tablePtr, and(shr(18, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(shr(12, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(shr(6, input), 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance

                mstore8(resultPtr, mload(add(tablePtr, and(input, 0x3F))))
                resultPtr := add(resultPtr, 1) // Advance
            }

            // When data `bytes` is not exactly 3 bytes long
            // it is padded with `=` characters at the end
            switch mod(mload(data), 3)
            case 1 {
                mstore8(sub(resultPtr, 1), 0x3d)
                mstore8(sub(resultPtr, 2), 0x3d)
            }
            case 2 {
                mstore8(sub(resultPtr, 1), 0x3d)
            }
        }

        return result;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

// ----------------------------------------------------------------------------
// BokkyPooBah's DateTime Library v1.01
//
// A gas-efficient Solidity date and time library
//
// https://github.com/bokkypoobah/BokkyPooBahsDateTimeLibrary
//
// Tested date range 1970/01/01 to 2345/12/31
//
// Conventions:
// Unit      | Range         | Notes
// :-------- |:-------------:|:-----
// timestamp | >= 0          | Unix timestamp, number of seconds since 1970/01/01 00:00:00 UTC
// year      | 1970 ... 2345 |
// month     | 1 ... 12      |
// day       | 1 ... 31      |
// hour      | 0 ... 23      |
// minute    | 0 ... 59      |
// second    | 0 ... 59      |
// dayOfWeek | 1 ... 7       | 1 = Monday, ..., 7 = Sunday
//
//
// Enjoy. (c) BokkyPooBah / Bok Consulting Pty Ltd 2018-2019. The MIT Licence.
// ----------------------------------------------------------------------------

library BokkyPooBahsDateTimeLibrary {
    uint256 constant _SECONDS_PER_DAY = 24 * 60 * 60;
    uint256 constant _SECONDS_PER_HOUR = 60 * 60;
    uint256 constant _SECONDS_PER_MINUTE = 60;
    int256 constant _OFFSET19700101 = 2440588;

    uint256 constant _DOW_FRI = 5;
    uint256 constant _DOW_SAT = 6;

    // ------------------------------------------------------------------------
    // Calculate the number of days from 1970/01/01 to year/month/day using
    // the date conversion algorithm from
    //   https://aa.usno.navy.mil/faq/JD_formula.html
    // and subtracting the offset 2440588 so that 1970/01/01 is day 0
    //
    // days = day
    //      - 32075
    //      + 1461 * (year + 4800 + (month - 14) / 12) / 4
    //      + 367 * (month - 2 - (month - 14) / 12 * 12) / 12
    //      - 3 * ((year + 4900 + (month - 14) / 12) / 100) / 4
    //      - offset
    // ------------------------------------------------------------------------
    function _daysFromDate(
        uint256 year,
        uint256 month,
        uint256 day
    ) private pure returns (uint256 _days) {
        require(year >= 1970);
        int256 _year = int256(year);
        int256 _month = int256(month);
        int256 _day = int256(day);

        int256 __days = _day -
            32075 +
            (1461 * (_year + 4800 + (_month - 14) / 12)) /
            4 +
            (367 * (_month - 2 - ((_month - 14) / 12) * 12)) /
            12 -
            (3 * ((_year + 4900 + (_month - 14) / 12) / 100)) /
            4 -
            _OFFSET19700101;

        _days = uint256(__days);
    }

    // ------------------------------------------------------------------------
    // Calculate year/month/day from the number of days since 1970/01/01 using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // and adding the offset 2440588 so that 1970/01/01 is day 0
    //
    // int L = days + 68569 + offset
    // int N = 4 * L / 146097
    // L = L - (146097 * N + 3) / 4
    // year = 4000 * (L + 1) / 1461001
    // L = L - 1461 * year / 4 + 31
    // month = 80 * L / 2447
    // dd = L - 2447 * month / 80
    // L = month / 11
    // month = month + 2 - 12 * L
    // year = 100 * (N - 49) + year + L
    // ------------------------------------------------------------------------
    function _daysToDate(uint256 _days)
        private
        pure
        returns (
            uint256 year,
            uint256 month,
            uint256 day
        )
    {
        int256 __days = int256(_days);

        int256 L = __days + 68569 + _OFFSET19700101;
        int256 N = (4 * L) / 146097;
        L = L - (146097 * N + 3) / 4;
        int256 _year = (4000 * (L + 1)) / 1461001;
        L = L - (1461 * _year) / 4 + 31;
        int256 _month = (80 * L) / 2447;
        int256 _day = L - (2447 * _month) / 80;
        L = _month / 11;
        _month = _month + 2 - 12 * L;
        _year = 100 * (N - 49) + _year + L;

        year = uint256(_year);
        month = uint256(_month);
        day = uint256(_day);
    }

    function timestampFromDate(
        uint256 year,
        uint256 month,
        uint256 day
    ) internal pure returns (uint256 timestamp) {
        timestamp = _daysFromDate(year, month, day) * _SECONDS_PER_DAY;
    }

    function timestampFromDateTime(
        uint256 year,
        uint256 month,
        uint256 day,
        uint256 hour,
        uint256 minute,
        uint256 second
    ) internal pure returns (uint256 timestamp) {
        timestamp =
            _daysFromDate(year, month, day) *
            _SECONDS_PER_DAY +
            hour *
            _SECONDS_PER_HOUR +
            minute *
            _SECONDS_PER_MINUTE +
            second;
    }

    function timestampToDate(uint256 timestamp)
        internal
        pure
        returns (
            uint256 year,
            uint256 month,
            uint256 day
        )
    {
        (year, month, day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
    }

    function timestampToDateTime(uint256 timestamp)
        internal
        pure
        returns (
            uint256 year,
            uint256 month,
            uint256 day,
            uint256 hour,
            uint256 minute,
            uint256 second
        )
    {
        (year, month, day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        uint256 secs = timestamp % _SECONDS_PER_DAY;
        hour = secs / _SECONDS_PER_HOUR;
        secs = secs % _SECONDS_PER_HOUR;
        minute = secs / _SECONDS_PER_MINUTE;
        second = secs % _SECONDS_PER_MINUTE;
    }

    function isValidDate(
        uint256 year,
        uint256 month,
        uint256 day
    ) internal pure returns (bool valid) {
        if (year >= 1970 && month > 0 && month <= 12) {
            uint256 daysInMonth = _getDaysInMonth(year, month);
            if (day > 0 && day <= daysInMonth) {
                valid = true;
            }
        }
    }

    function isValidDateTime(
        uint256 year,
        uint256 month,
        uint256 day,
        uint256 hour,
        uint256 minute,
        uint256 second
    ) internal pure returns (bool valid) {
        if (isValidDate(year, month, day)) {
            if (hour < 24 && minute < 60 && second < 60) {
                valid = true;
            }
        }
    }

    function isLeapYear(uint256 timestamp) internal pure returns (bool leapYear) {
        (uint256 year, , ) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        leapYear = _isLeapYear(year);
    }

    function _isLeapYear(uint256 year) private pure returns (bool leapYear) {
        leapYear = ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
    }

    function isWeekDay(uint256 timestamp) internal pure returns (bool weekDay) {
        weekDay = getDayOfWeek(timestamp) <= _DOW_FRI;
    }

    function isWeekEnd(uint256 timestamp) internal pure returns (bool weekEnd) {
        weekEnd = getDayOfWeek(timestamp) >= _DOW_SAT;
    }

    function getDaysInMonth(uint256 timestamp) internal pure returns (uint256 daysInMonth) {
        (uint256 year, uint256 month, ) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        daysInMonth = _getDaysInMonth(year, month);
    }

    function _getDaysInMonth(uint256 year, uint256 month) private pure returns (uint256 daysInMonth) {
        if (month == 1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12) {
            daysInMonth = 31;
        } else if (month != 2) {
            daysInMonth = 30;
        } else {
            daysInMonth = _isLeapYear(year) ? 29 : 28;
        }
    }

    // 1 = Monday, 7 = Sunday
    function getDayOfWeek(uint256 timestamp) internal pure returns (uint256 dayOfWeek) {
        uint256 _days = timestamp / _SECONDS_PER_DAY;
        dayOfWeek = ((_days + 3) % 7) + 1;
    }

    function getYear(uint256 timestamp) internal pure returns (uint256 year) {
        (year, , ) = _daysToDate(timestamp / _SECONDS_PER_DAY);
    }

    function getMonth(uint256 timestamp) internal pure returns (uint256 month) {
        (, month, ) = _daysToDate(timestamp / _SECONDS_PER_DAY);
    }

    function getDay(uint256 timestamp) internal pure returns (uint256 day) {
        (, , day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
    }

    function getHour(uint256 timestamp) internal pure returns (uint256 hour) {
        uint256 secs = timestamp % _SECONDS_PER_DAY;
        hour = secs / _SECONDS_PER_HOUR;
    }

    function getMinute(uint256 timestamp) internal pure returns (uint256 minute) {
        uint256 secs = timestamp % _SECONDS_PER_HOUR;
        minute = secs / _SECONDS_PER_MINUTE;
    }

    function getSecond(uint256 timestamp) internal pure returns (uint256 second) {
        second = timestamp % _SECONDS_PER_MINUTE;
    }

    function addYears(uint256 timestamp, uint256 _years) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        year += _years;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * _SECONDS_PER_DAY + (timestamp % _SECONDS_PER_DAY);
        require(newTimestamp >= timestamp);
    }

    function addMonths(uint256 timestamp, uint256 _months) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        month += _months;
        year += (month - 1) / 12;
        month = ((month - 1) % 12) + 1;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * _SECONDS_PER_DAY + (timestamp % _SECONDS_PER_DAY);
        require(newTimestamp >= timestamp);
    }

    function addDays(uint256 timestamp, uint256 _days) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _days * _SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }

    function addHours(uint256 timestamp, uint256 _hours) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _hours * _SECONDS_PER_HOUR;
        require(newTimestamp >= timestamp);
    }

    function addMinutes(uint256 timestamp, uint256 _minutes) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _minutes * _SECONDS_PER_MINUTE;
        require(newTimestamp >= timestamp);
    }

    function addSeconds(uint256 timestamp, uint256 _seconds) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp + _seconds;
        require(newTimestamp >= timestamp);
    }

    function subYears(uint256 timestamp, uint256 _years) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        year -= _years;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * _SECONDS_PER_DAY + (timestamp % _SECONDS_PER_DAY);
        require(newTimestamp <= timestamp);
    }

    function subMonths(uint256 timestamp, uint256 _months) internal pure returns (uint256 newTimestamp) {
        (uint256 year, uint256 month, uint256 day) = _daysToDate(timestamp / _SECONDS_PER_DAY);
        uint256 yearMonth = year * 12 + (month - 1) - _months;
        year = yearMonth / 12;
        month = (yearMonth % 12) + 1;
        uint256 daysInMonth = _getDaysInMonth(year, month);
        if (day > daysInMonth) {
            day = daysInMonth;
        }
        newTimestamp = _daysFromDate(year, month, day) * _SECONDS_PER_DAY + (timestamp % _SECONDS_PER_DAY);
        require(newTimestamp <= timestamp);
    }

    function subDays(uint256 timestamp, uint256 _days) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _days * _SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }

    function subHours(uint256 timestamp, uint256 _hours) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _hours * _SECONDS_PER_HOUR;
        require(newTimestamp <= timestamp);
    }

    function subMinutes(uint256 timestamp, uint256 _minutes) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _minutes * _SECONDS_PER_MINUTE;
        require(newTimestamp <= timestamp);
    }

    function subSeconds(uint256 timestamp, uint256 _seconds) internal pure returns (uint256 newTimestamp) {
        newTimestamp = timestamp - _seconds;
        require(newTimestamp <= timestamp);
    }

    function diffYears(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _years) {
        require(fromTimestamp <= toTimestamp);
        (uint256 fromYear, , ) = _daysToDate(fromTimestamp / _SECONDS_PER_DAY);
        (uint256 toYear, , ) = _daysToDate(toTimestamp / _SECONDS_PER_DAY);
        _years = toYear - fromYear;
    }

    function diffMonths(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _months) {
        require(fromTimestamp <= toTimestamp);
        (uint256 fromYear, uint256 fromMonth, ) = _daysToDate(fromTimestamp / _SECONDS_PER_DAY);
        (uint256 toYear, uint256 toMonth, ) = _daysToDate(toTimestamp / _SECONDS_PER_DAY);
        _months = toYear * 12 + toMonth - fromYear * 12 - fromMonth;
    }

    function diffDays(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _days) {
        require(fromTimestamp <= toTimestamp);
        _days = (toTimestamp - fromTimestamp) / _SECONDS_PER_DAY;
    }

    function diffHours(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _hours) {
        require(fromTimestamp <= toTimestamp);
        _hours = (toTimestamp - fromTimestamp) / _SECONDS_PER_HOUR;
    }

    function diffMinutes(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _minutes) {
        require(fromTimestamp <= toTimestamp);
        _minutes = (toTimestamp - fromTimestamp) / _SECONDS_PER_MINUTE;
    }

    function diffSeconds(uint256 fromTimestamp, uint256 toTimestamp) internal pure returns (uint256 _seconds) {
        require(fromTimestamp <= toTimestamp);
        _seconds = toTimestamp - fromTimestamp;
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

address constant CANONICAL_OPERATOR_FILTER_REGISTRY_ADDRESS = 0x000000000000AAeB6D7670E522A718067333cd4E;
address constant CANONICAL_CORI_SUBSCRIPTION = 0x3cc6CddA760b79bAfa08dF41ECFA224f810dCeB6;

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

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

import "@openzeppelin/contracts/utils/Strings.sol";
import "./BokkyPooBahsDateTimeLibrary.sol";

/*
    @dev        Library to convert epoch timestamp to a human-readable Date-Time string
    @dependency uses BokkyPooBahsDateTimeLibrary.sol library internally
 */
library DateTime {
    using Strings for uint256;

    bytes public constant MONTHS = bytes("JanFebMarAprMayJunJulAugSepOctNovDec");

    /**
     *   @dev returns month as short (3-letter) string
     */
    function monthAsString(uint256 idx) internal pure returns (string memory) {
        require(idx > 0, "bad idx");
        bytes memory str = new bytes(3);
        uint256 offset = (idx - 1) * 3;
        str[0] = bytes1(MONTHS[offset]);
        str[1] = bytes1(MONTHS[offset + 1]);
        str[2] = bytes1(MONTHS[offset + 2]);
        return string(str);
    }

    /**
     *   @dev returns string representation of number left-padded for 2 symbols
     */
    function asPaddedString(uint256 n) internal pure returns (string memory) {
        if (n == 0) return "00";
        if (n < 10) return string.concat("0", n.toString());
        return n.toString();
    }

    /**
     *   @dev returns string of format 'Jan 01, 2022 18:00 UTC' for a given timestamp
     */
    function asString(uint256 ts) external pure returns (string memory) {
        (uint256 year, uint256 month, uint256 day, uint256 hour, uint256 minute, ) = BokkyPooBahsDateTimeLibrary
            .timestampToDateTime(ts);
        return
            string(
                abi.encodePacked(
                    monthAsString(month),
                    " ",
                    day.toString(),
                    ", ",
                    year.toString(),
                    " ",
                    asPaddedString(hour),
                    ":",
                    asPaddedString(minute),
                    " UTC"
                )
            );
    }

    /**
     *   @dev returns (year, month as string) components of a date by timestamp
     */
    function yearAndMonth(uint256 ts) external pure returns (uint256, string memory) {
        (uint256 year, uint256 month, , , , ) = BokkyPooBahsDateTimeLibrary.timestampToDateTime(ts);
        return (year, monthAsString(month));
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

import {OperatorFilterer} from "./OperatorFilterer.sol";
import {CANONICAL_CORI_SUBSCRIPTION} from "./lib/Constants.sol";
/**
 * @title  DefaultOperatorFilterer
 * @notice Inherits from OperatorFilterer and automatically subscribes to the default OpenSea subscription.
 * @dev    Please note that if your token contract does not provide an owner with EIP-173, it must provide
 *         administration methods on the contract itself to interact with the registry otherwise the subscription
 *         will be locked to the options set during construction.
 */

abstract contract DefaultOperatorFilterer is OperatorFilterer {
    /// @dev The constructor that is called when the contract is being deployed.
    constructor() OperatorFilterer(CANONICAL_CORI_SUBSCRIPTION, true) {}
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/ERC165.sol)

pragma solidity ^0.8.0;

import "./IERC165.sol";

/**
 * @dev Implementation of the {IERC165} interface.
 *
 * Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
 * for the additional interface id that will be supported. For example:
 *
 * ```solidity
 * function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
 *     return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
 * }
 * ```
 *
 * Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.
 */
abstract contract ERC165 is IERC165 {
    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
        return interfaceId == type(IERC165).interfaceId;
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC20/ERC20.sol)

pragma solidity ^0.8.0;

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

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

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC20/extensions/ERC20Capped.sol)

pragma solidity ^0.8.0;

import "../ERC20.sol";

/**
 * @dev Extension of {ERC20} that adds a cap to the supply of tokens.
 */
abstract contract ERC20Capped is ERC20 {
    uint256 private immutable _cap;

    /**
     * @dev Sets the value of the `cap`. This value is immutable, it can only be
     * set once during construction.
     */
    constructor(uint256 cap_) {
        require(cap_ > 0, "ERC20Capped: cap is 0");
        _cap = cap_;
    }

    /**
     * @dev Returns the cap on the token's total supply.
     */
    function cap() public view virtual returns (uint256) {
        return _cap;
    }

    /**
     * @dev See {ERC20-_mint}.
     */
    function _mint(address account, uint256 amount) internal virtual override {
        require(ERC20.totalSupply() + amount <= cap(), "ERC20Capped: cap exceeded");
        super._mint(account, amount);
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (metatx/ERC2771Context.sol)

pragma solidity ^0.8.10;

import "@openzeppelin/contracts/utils/Context.sol";

/**
 * @dev Context variant with ERC2771 support.
 */
abstract contract ERC2771Context is Context {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable
    // one-time settable var
    address internal _trustedForwarder;

    /// @custom:oz-upgrades-unsafe-allow constructor
    constructor(address trustedForwarder) {
        _trustedForwarder = trustedForwarder;
    }

    function isTrustedForwarder(address forwarder) public view virtual returns (bool) {
        return forwarder == _trustedForwarder;
    }

    function _msgSender() internal view virtual override returns (address sender) {
        if (isTrustedForwarder(msg.sender)) {
            // The assembly code is more direct than the Solidity version using `abi.decode`.
            /// @solidity memory-safe-assembly
            assembly {
                sender := shr(96, calldataload(sub(calldatasize(), 20)))
            }
        } else {
            return super._msgSender();
        }
    }

    function _msgData() internal view virtual override returns (bytes calldata) {
        if (isTrustedForwarder(msg.sender)) {
            return msg.data[:msg.data.length - 20];
        } else {
            return super._msgData();
        }
    }
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC721/ERC721.sol)

pragma solidity ^0.8.0;

import "./IERC721.sol";
import "./IERC721Receiver.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/Address.sol";
import "../../utils/Context.sol";
import "../../utils/Strings.sol";
import "../../utils/introspection/ERC165.sol";

/**
 * @dev Implementation of https://eips.ethereum.org/EIPS/eip-721[ERC721] Non-Fungible Token Standard, including
 * the Metadata extension, but not including the Enumerable extension, which is available separately as
 * {ERC721Enumerable}.
 */
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
    using Address for address;
    using Strings for uint256;

    // Token name
    string private _name;

    // Token symbol
    string private _symbol;

    // Mapping from token ID to owner address
    mapping(uint256 => address) private _owners;

    // Mapping owner address to token count
    mapping(address => uint256) private _balances;

    // Mapping from token ID to approved address
    mapping(uint256 => address) private _tokenApprovals;

    // Mapping from owner to operator approvals
    mapping(address => mapping(address => bool)) private _operatorApprovals;

    /**
     * @dev Initializes the contract by setting a `name` and a `symbol` to the token collection.
     */
    constructor(string memory name_, string memory symbol_) {
        _name = name_;
        _symbol = symbol_;
    }

    /**
     * @dev See {IERC165-supportsInterface}.
     */
    function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
        return
            interfaceId == type(IERC721).interfaceId ||
            interfaceId == type(IERC721Metadata).interfaceId ||
            super.supportsInterface(interfaceId);
    }

    /**
     * @dev See {IERC721-balanceOf}.
     */
    function balanceOf(address owner) public view virtual override returns (uint256) {
        require(owner != address(0), "ERC721: address zero is not a valid owner");
        return _balances[owner];
    }

    /**
     * @dev See {IERC721-ownerOf}.
     */
    function ownerOf(uint256 tokenId) public view virtual override returns (address) {
        address owner = _owners[tokenId];
        require(owner != address(0), "ERC721: invalid token ID");
        return owner;
    }

    /**
     * @dev See {IERC721Metadata-name}.
     */
    function name() public view virtual override returns (string memory) {
        return _name;
    }

    /**
     * @dev See {IERC721Metadata-symbol}.
     */
    function symbol() public view virtual override returns (string memory) {
        return _symbol;
    }

    /**
     * @dev See {IERC721Metadata-tokenURI}.
     */
    function tokenURI(uint256 tokenId) public view virtual override returns (string memory) {
        _requireMinted(tokenId);

        string memory baseURI = _baseURI();
        return bytes(baseURI).length > 0 ? string(abi.encodePacked(baseURI, tokenId.toString())) : "";
    }

    /**
     * @dev Base URI for computing {tokenURI}. If set, the resulting URI for each
     * token will be the concatenation of the `baseURI` and the `tokenId`. Empty
     * by default, can be overridden in child contracts.
     */
    function _baseURI() internal view virtual returns (string memory) {
        return "";
    }

    /**
     * @dev See {IERC721-approve}.
     */
    function approve(address to, uint256 tokenId) public virtual override {
        address owner = ERC721.ownerOf(tokenId);
        require(to != owner, "ERC721: approval to current owner");

        require(
            _msgSender() == owner || isApprovedForAll(owner, _msgSender()),
            "ERC721: approve caller is not token owner nor approved for all"
        );

        _approve(to, tokenId);
    }

    /**
     * @dev See {IERC721-getApproved}.
     */
    function getApproved(uint256 tokenId) public view virtual override returns (address) {
        _requireMinted(tokenId);

        return _tokenApprovals[tokenId];
    }

    /**
     * @dev See {IERC721-setApprovalForAll}.
     */
    function setApprovalForAll(address operator, bool approved) public virtual override {
        _setApprovalForAll(_msgSender(), operator, approved);
    }

    /**
     * @dev See {IERC721-isApprovedForAll}.
     */
    function isApprovedForAll(address owner, address operator) public view virtual override returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev See {IERC721-transferFrom}.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        //solhint-disable-next-line max-line-length
        require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: caller is not token owner nor approved");

        _transfer(from, to, tokenId);
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) public virtual override {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev See {IERC721-safeTransferFrom}.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) public virtual override {
        require(_isApprovedOrOwner(_msgSender(), tokenId), "ERC721: caller is not token owner nor approved");
        _safeTransfer(from, to, tokenId, data);
    }

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * `data` is additional data, it has no specified format and it is sent in call to `to`.
     *
     * This internal function is equivalent to {safeTransferFrom}, and can be used to e.g.
     * implement alternative mechanisms to perform token transfer, such as signature-based.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeTransfer(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) internal virtual {
        _transfer(from, to, tokenId);
        require(_checkOnERC721Received(from, to, tokenId, data), "ERC721: transfer to non ERC721Receiver implementer");
    }

    /**
     * @dev Returns whether `tokenId` exists.
     *
     * Tokens can be managed by their owner or approved accounts via {approve} or {setApprovalForAll}.
     *
     * Tokens start existing when they are minted (`_mint`),
     * and stop existing when they are burned (`_burn`).
     */
    function _exists(uint256 tokenId) internal view virtual returns (bool) {
        return _owners[tokenId] != address(0);
    }

    /**
     * @dev Returns whether `spender` is allowed to manage `tokenId`.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId) internal view virtual returns (bool) {
        address owner = ERC721.ownerOf(tokenId);
        return (spender == owner || isApprovedForAll(owner, spender) || getApproved(tokenId) == spender);
    }

    /**
     * @dev Safely mints `tokenId` and transfers it to `to`.
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function _safeMint(address to, uint256 tokenId) internal virtual {
        _safeMint(to, tokenId, "");
    }

    /**
     * @dev Same as {xref-ERC721-_safeMint-address-uint256-}[`_safeMint`], with an additional `data` parameter which is
     * forwarded in {IERC721Receiver-onERC721Received} to contract recipients.
     */
    function _safeMint(
        address to,
        uint256 tokenId,
        bytes memory data
    ) internal virtual {
        _mint(to, tokenId);
        require(
            _checkOnERC721Received(address(0), to, tokenId, data),
            "ERC721: transfer to non ERC721Receiver implementer"
        );
    }

    /**
     * @dev Mints `tokenId` and transfers it to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {_safeMint} whenever possible
     *
     * Requirements:
     *
     * - `tokenId` must not exist.
     * - `to` cannot be the zero address.
     *
     * Emits a {Transfer} event.
     */
    function _mint(address to, uint256 tokenId) internal virtual {
        require(to != address(0), "ERC721: mint to the zero address");
        require(!_exists(tokenId), "ERC721: token already minted");

        _beforeTokenTransfer(address(0), to, tokenId);

        _balances[to] += 1;
        _owners[tokenId] = to;

        emit Transfer(address(0), to, tokenId);

        _afterTokenTransfer(address(0), to, tokenId);
    }

    /**
     * @dev Destroys `tokenId`.
     * The approval is cleared when the token is burned.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     *
     * Emits a {Transfer} event.
     */
    function _burn(uint256 tokenId) internal virtual {
        address owner = ERC721.ownerOf(tokenId);

        _beforeTokenTransfer(owner, address(0), tokenId);

        // Clear approvals
        _approve(address(0), tokenId);

        _balances[owner] -= 1;
        delete _owners[tokenId];

        emit Transfer(owner, address(0), tokenId);

        _afterTokenTransfer(owner, address(0), tokenId);
    }

    /**
     * @dev Transfers `tokenId` from `from` to `to`.
     *  As opposed to {transferFrom}, this imposes no restrictions on msg.sender.
     *
     * Requirements:
     *
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     *
     * Emits a {Transfer} event.
     */
    function _transfer(
        address from,
        address to,
        uint256 tokenId
    ) internal virtual {
        require(ERC721.ownerOf(tokenId) == from, "ERC721: transfer from incorrect owner");
        require(to != address(0), "ERC721: transfer to the zero address");

        _beforeTokenTransfer(from, to, tokenId);

        // Clear approvals from the previous owner
        _approve(address(0), tokenId);

        _balances[from] -= 1;
        _balances[to] += 1;
        _owners[tokenId] = to;

        emit Transfer(from, to, tokenId);

        _afterTokenTransfer(from, to, tokenId);
    }

    /**
     * @dev Approve `to` to operate on `tokenId`
     *
     * Emits an {Approval} event.
     */
    function _approve(address to, uint256 tokenId) internal virtual {
        _tokenApprovals[tokenId] = to;
        emit Approval(ERC721.ownerOf(tokenId), to, tokenId);
    }

    /**
     * @dev Approve `operator` to operate on all of `owner` tokens
     *
     * Emits an {ApprovalForAll} event.
     */
    function _setApprovalForAll(
        address owner,
        address operator,
        bool approved
    ) internal virtual {
        require(owner != operator, "ERC721: approve to caller");
        _operatorApprovals[owner][operator] = approved;
        emit ApprovalForAll(owner, operator, approved);
    }

    /**
     * @dev Reverts if the `tokenId` has not been minted yet.
     */
    function _requireMinted(uint256 tokenId) internal view virtual {
        require(_exists(tokenId), "ERC721: invalid token ID");
    }

    /**
     * @dev Internal function to invoke {IERC721Receiver-onERC721Received} on a target address.
     * The call is not executed if the target address is not a contract.
     *
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param data bytes optional data to send along with the call
     * @return bool whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(
        address from,
        address to,
        uint256 tokenId,
        bytes memory data
    ) private returns (bool) {
        if (to.isContract()) {
            try IERC721Receiver(to).onERC721Received(_msgSender(), from, tokenId, data) returns (bytes4 retval) {
                return retval == IERC721Receiver.onERC721Received.selector;
            } catch (bytes memory reason) {
                if (reason.length == 0) {
                    revert("ERC721: transfer to non ERC721Receiver implementer");
                } else {
                    /// @solidity memory-safe-assembly
                    assembly {
                        revert(add(32, reason), mload(reason))
                    }
                }
            }
        } else {
            return true;
        }
    }

    /**
     * @dev Hook that is called before any token transfer. This includes minting
     * and burning.
     *
     * Calling conditions:
     *
     * - When `from` and `to` are both non-zero, ``from``'s `tokenId` will be
     * transferred to `to`.
     * - When `from` is zero, `tokenId` will be minted for `to`.
     * - When `to` is zero, ``from``'s `tokenId` 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 tokenId
    ) 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.
     * - `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 tokenId
    ) internal virtual {}
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

library FormattedStrings {
    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
            Base on OpenZeppelin `toString` method from `String` library
     */
    function toFormattedString(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;
        }
        uint256 pos;
        uint256 comas = digits / 3;
        digits = digits + (digits % 3 == 0 ? comas - 1 : comas);
        bytes memory buffer = new bytes(digits);
        while (value != 0) {
            digits -= 1;
            if (pos == 3) {
                buffer[digits] = ",";
                pos = 0;
            } else {
                buffer[digits] = bytes1(uint8(48 + uint256(value % 10)));
                value /= 10;
                pos++;
            }
        }
        return string(buffer);
    }
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IBurnRedeemable {
    event Redeemed(
        address indexed user,
        address indexed xenContract,
        address indexed tokenContract,
        uint256 xenAmount,
        uint256 tokenAmount
    );

    function onTokenBurned(address user, uint256 amount) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IBurnableToken {
    function burn(address user, uint256 amount) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (utils/introspection/IERC165.sol)

pragma solidity ^0.8.0;

/**
 * @dev Interface of the ERC165 standard, as defined in the
 * https://eips.ethereum.org/EIPS/eip-165[EIP].
 *
 * Implementers can declare support of contract interfaces, which can then be
 * queried by others ({ERC165Checker}).
 *
 * For an implementation, see {ERC165}.
 */
interface IERC165 {
    /**
     * @dev Returns true if this contract implements the interface defined by
     * `interfaceId`. See the corresponding
     * https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
     * to learn more about how these ids are created.
     *
     * This function call must use less than 30 000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}

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

pragma solidity ^0.8.0;

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

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

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

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

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

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

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

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

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

pragma solidity ^0.8.0;

import "../IERC20.sol";

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

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

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

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IERC2771 {
    function isTrustedForwarder(address forwarder) external;
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (interfaces/IERC2981.sol)

pragma solidity ^0.8.0;

import "../utils/introspection/IERC165.sol";

/**
 * @dev Interface for the NFT Royalty Standard.
 *
 * A standardized way to retrieve royalty payment information for non-fungible tokens (NFTs) to enable universal
 * support for royalty payments across all NFT marketplaces and ecosystem participants.
 *
 * _Available since v4.5._
 */
interface IERC2981 is IERC165 {
    /**
     * @dev Returns how much royalty is owed and to whom, based on a sale price that may be denominated in any unit of
     * exchange. The royalty amount is denominated and should be paid in that same unit of exchange.
     */
    function royaltyInfo(uint256 tokenId, uint256 salePrice)
        external
        view
        returns (address receiver, uint256 royaltyAmount);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.7.0) (token/ERC721/IERC721.sol)

pragma solidity ^0.8.0;

import "../../utils/introspection/IERC165.sol";

/**
 * @dev Required interface of an ERC721 compliant contract.
 */
interface IERC721 is IERC165 {
    /**
     * @dev Emitted when `tokenId` token is transferred from `from` to `to`.
     */
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables `approved` to manage the `tokenId` token.
     */
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);

    /**
     * @dev Emitted when `owner` enables or disables (`approved`) `operator` to manage all of its assets.
     */
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    /**
     * @dev Returns the number of tokens in ``owner``'s account.
     */
    function balanceOf(address owner) external view returns (uint256 balance);

    /**
     * @dev Returns the owner of the `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function ownerOf(uint256 tokenId) external view returns (address owner);

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId,
        bytes calldata data
    ) external;

    /**
     * @dev Safely transfers `tokenId` token from `from` to `to`, checking first that contract recipients
     * are aware of the ERC721 protocol to prevent tokens from being forever locked.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must exist and be owned by `from`.
     * - If the caller is not `from`, it must have been allowed to move this token by either {approve} or {setApprovalForAll}.
     * - If `to` refers to a smart contract, it must implement {IERC721Receiver-onERC721Received}, which is called upon a safe transfer.
     *
     * Emits a {Transfer} event.
     */
    function safeTransferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Transfers `tokenId` token from `from` to `to`.
     *
     * WARNING: Usage of this method is discouraged, use {safeTransferFrom} whenever possible.
     *
     * Requirements:
     *
     * - `from` cannot be the zero address.
     * - `to` cannot be the zero address.
     * - `tokenId` token must be owned by `from`.
     * - If the caller is not `from`, it must be approved to move this token by either {approve} or {setApprovalForAll}.
     *
     * Emits a {Transfer} event.
     */
    function transferFrom(
        address from,
        address to,
        uint256 tokenId
    ) external;

    /**
     * @dev Gives permission to `to` to transfer `tokenId` token to another account.
     * The approval is cleared when the token is transferred.
     *
     * Only a single account can be approved at a time, so approving the zero address clears previous approvals.
     *
     * Requirements:
     *
     * - The caller must own the token or be an approved operator.
     * - `tokenId` must exist.
     *
     * Emits an {Approval} event.
     */
    function approve(address to, uint256 tokenId) external;

    /**
     * @dev Approve or remove `operator` as an operator for the caller.
     * Operators can call {transferFrom} or {safeTransferFrom} for any token owned by the caller.
     *
     * Requirements:
     *
     * - The `operator` cannot be the caller.
     *
     * Emits an {ApprovalForAll} event.
     */
    function setApprovalForAll(address operator, bool _approved) external;

    /**
     * @dev Returns the account approved for `tokenId` token.
     *
     * Requirements:
     *
     * - `tokenId` must exist.
     */
    function getApproved(uint256 tokenId) external view returns (address operator);

    /**
     * @dev Returns if the `operator` is allowed to manage all of the assets of `owner`.
     *
     * See {setApprovalForAll}
     */
    function isApprovedForAll(address owner, address operator) external view returns (bool);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (token/ERC721/extensions/IERC721Metadata.sol)

pragma solidity ^0.8.0;

import "../IERC721.sol";

/**
 * @title ERC-721 Non-Fungible Token Standard, optional metadata extension
 * @dev See https://eips.ethereum.org/EIPS/eip-721
 */
interface IERC721Metadata is IERC721 {
    /**
     * @dev Returns the token collection name.
     */
    function name() external view returns (string memory);

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

    /**
     * @dev Returns the Uniform Resource Identifier (URI) for `tokenId` token.
     */
    function tokenURI(uint256 tokenId) external view returns (string memory);
}

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.6.0) (token/ERC721/IERC721Receiver.sol)

pragma solidity ^0.8.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
interface IERC721Receiver {
    /**
     * @dev Whenever an {IERC721} `tokenId` token is transferred to this contract via {IERC721-safeTransferFrom}
     * by `operator` from `from`, this function is called.
     *
     * It must return its Solidity selector to confirm the token transfer.
     * If any other value is returned or the interface is not implemented by the recipient, the transfer will be reverted.
     *
     * The selector can be obtained in Solidity with `IERC721Receiver.onERC721Received.selector`.
     */
    function onERC721Received(
        address operator,
        address from,
        uint256 tokenId,
        bytes calldata data
    ) external returns (bytes4);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.13;

interface IOperatorFilterRegistry {
    /**
     * @notice Returns true if operator is not filtered for a given token, either by address or codeHash. Also returns
     *         true if supplied registrant address is not registered.
     */
    function isOperatorAllowed(address registrant, address operator) external view returns (bool);

    /**
     * @notice Registers an address with the registry. May be called by address itself or by EIP-173 owner.
     */
    function register(address registrant) external;

    /**
     * @notice Registers an address with the registry and "subscribes" to another address's filtered operators and codeHashes.
     */
    function registerAndSubscribe(address registrant, address subscription) external;

    /**
     * @notice Registers an address with the registry and copies the filtered operators and codeHashes from another
     *         address without subscribing.
     */
    function registerAndCopyEntries(address registrant, address registrantToCopy) external;

    /**
     * @notice Unregisters an address with the registry and removes its subscription. May be called by address itself or by EIP-173 owner.
     *         Note that this does not remove any filtered addresses or codeHashes.
     *         Also note that any subscriptions to this registrant will still be active and follow the existing filtered addresses and codehashes.
     */
    function unregister(address addr) external;

    /**
     * @notice Update an operator address for a registered address - when filtered is true, the operator is filtered.
     */
    function updateOperator(address registrant, address operator, bool filtered) external;

    /**
     * @notice Update multiple operators for a registered address - when filtered is true, the operators will be filtered. Reverts on duplicates.
     */
    function updateOperators(address registrant, address[] calldata operators, bool filtered) external;

    /**
     * @notice Update a codeHash for a registered address - when filtered is true, the codeHash is filtered.
     */
    function updateCodeHash(address registrant, bytes32 codehash, bool filtered) external;

    /**
     * @notice Update multiple codeHashes for a registered address - when filtered is true, the codeHashes will be filtered. Reverts on duplicates.
     */
    function updateCodeHashes(address registrant, bytes32[] calldata codeHashes, bool filtered) external;

    /**
     * @notice Subscribe an address to another registrant's filtered operators and codeHashes. Will remove previous
     *         subscription if present.
     *         Note that accounts with subscriptions may go on to subscribe to other accounts - in this case,
     *         subscriptions will not be forwarded. Instead the former subscription's existing entries will still be
     *         used.
     */
    function subscribe(address registrant, address registrantToSubscribe) external;

    /**
     * @notice Unsubscribe an address from its current subscribed registrant, and optionally copy its filtered operators and codeHashes.
     */
    function unsubscribe(address registrant, bool copyExistingEntries) external;

    /**
     * @notice Get the subscription address of a given registrant, if any.
     */
    function subscriptionOf(address addr) external returns (address registrant);

    /**
     * @notice Get the set of addresses subscribed to a given registrant.
     *         Note that order is not guaranteed as updates are made.
     */
    function subscribers(address registrant) external returns (address[] memory);

    /**
     * @notice Get the subscriber at a given index in the set of addresses subscribed to a given registrant.
     *         Note that order is not guaranteed as updates are made.
     */
    function subscriberAt(address registrant, uint256 index) external returns (address);

    /**
     * @notice Copy filtered operators and codeHashes from a different registrantToCopy to addr.
     */
    function copyEntriesOf(address registrant, address registrantToCopy) external;

    /**
     * @notice Returns true if operator is filtered by a given address or its subscription.
     */
    function isOperatorFiltered(address registrant, address operator) external returns (bool);

    /**
     * @notice Returns true if the hash of an address's code is filtered by a given address or its subscription.
     */
    function isCodeHashOfFiltered(address registrant, address operatorWithCode) external returns (bool);

    /**
     * @notice Returns true if a codeHash is filtered by a given address or its subscription.
     */
    function isCodeHashFiltered(address registrant, bytes32 codeHash) external returns (bool);

    /**
     * @notice Returns a list of filtered operators for a given address or its subscription.
     */
    function filteredOperators(address addr) external returns (address[] memory);

    /**
     * @notice Returns the set of filtered codeHashes for a given address or its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredCodeHashes(address addr) external returns (bytes32[] memory);

    /**
     * @notice Returns the filtered operator at the given index of the set of filtered operators for a given address or
     *         its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredOperatorAt(address registrant, uint256 index) external returns (address);

    /**
     * @notice Returns the filtered codeHash at the given index of the list of filtered codeHashes for a given address or
     *         its subscription.
     *         Note that order is not guaranteed as updates are made.
     */
    function filteredCodeHashAt(address registrant, uint256 index) external returns (bytes32);

    /**
     * @notice Returns true if an address has registered
     */
    function isRegistered(address addr) external returns (bool);

    /**
     * @dev Convenience method to compute the code hash of an arbitrary contract
     */
    function codeHashOf(address addr) external returns (bytes32);
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IRankedMintingToken {
    event RankClaimed(address indexed user, uint256 term, uint256 rank);

    event MintClaimed(address indexed user, uint256 rewardAmount);

    function claimRank(uint256 term) external;

    function claimMintReward() external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IStakingToken {
    event Staked(address indexed user, uint256 amount, uint256 term);

    event Withdrawn(address indexed user, uint256 amount, uint256 reward);

    function stake(uint256 amount, uint256 term) external;

    function withdraw() external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IXENProxying {
    function callClaimRank(uint256 term) external;

    function callClaimMintReward(address to) external;

    function powerDown() external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IXENStake {
    event CreateStake(address indexed user, uint256 indexed tokenId, uint256 amount, uint256 term);
    event EndStake(address indexed user, uint256 indexed tokenId);

    function createStake(uint256 amount, uint256 term) external returns (uint256);

    function endStake(uint256 tokenId) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IXENStakeProxying {
    function callStake(uint256 amount, uint256 term) external;

    function callTransfer(address to) external;

    function callWithdraw() external;

    function powerDown() external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

interface IXENTorrent {
    event StartTorrent(address indexed user, uint256 count, uint256 term);
    event EndTorrent(address indexed user, uint256 tokenId, address to);

    function bulkClaimRank(uint256 count, uint256 term) external returns (uint256);

    function bulkClaimMintReward(uint256 tokenId, address to) external;
}

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

/*

        \\      //   |||||||||||   |\      ||       A CRYPTOCURRENCY FOR THE MASSES
         \\    //    ||            |\\     ||
          \\  //     ||            ||\\    ||       PRINCIPLES OF XEN:
           \\//      ||            || \\   ||       - No pre-mint; starts with zero supply
            XX       ||||||||      ||  \\  ||       - No admin keys
           //\\      ||            ||   \\ ||       - Immutable contract
          //  \\     ||            ||    \\||
         //    \\    ||            ||     \\|
        //      \\   |||||||||||   ||      \|       Copyright (C) FairCrypto Foundation 2022-2023

 */

library MagicNumbers {

    uint256 constant VERSION = 1;
    string public constant AUTHORS = "@MrJackLevin @lbelyaev faircrypto.org";

    // There's 370 fibs that fit in uint256 number
    uint256 constant MAX_UINT256_FIB_IDX = 370;
    // Max fib number that fits into uint256 size
    uint256 constant MAX_UINT256_FIB = 94611056096305838013295371573764256526437182762229865607320618320601813254535;
    // Max fib index supported by this Library
    uint256 constant MAX_FIB_IDX = 90;
    // Max number that could be safely tested by this Library
    uint256 constant MAX_SUPPORTED_FIB_CANDIDATE = 2 ** 62 - 1;

    /**
        @dev First 60 Fibonacci numbers, which fit into uint64
    */
    function fibs64() internal pure returns (uint64[60] memory) {
        return [
            uint64(0),            1,                     1,
            2,                    3,                     5,
            8,                    13,                    21,
            34,                   55,                    89,
            144,                  233,                   377,
            610,                  987,                   1597,
            2584,                 4181,                  6765,
            10946,                17711,                 28657,
            46368,                75025,                 121393,
            196418,               317811,                514229,
            832040,               1346269,               2178309,
            3524578,              5702887,               9227465,
            14930352,             24157817,              39088169,
            63245986,             102334155,             165580141,
            267914296,            433494437,             701408733,
            1134903170,           1836311903,            2971215073,
            4807526976,           7778742049,            12586269025,
            20365011074,          32951280099,           53316291173,
            86267571272,          139583862445,          225851433717,
            365435296162,         591286729879,          956722026041
        ];
    }

    /**
        @dev Tests if number is a fib via a linear lookup in the table above
    */
    function isFibs64(uint256 n) internal pure returns (bool) {
        for(uint i = 0; i < 60; i++) if (fibs64()[i] == n) return true;
        return false;
    }

    /**
        @dev Next 38 Fibonacci numbers, which fit into uint128
    */
    function fibs128() internal pure returns (uint128[39] memory) {
        return [
            uint128(1548008755920),2504730781961,        4052739537881,
            6557470319842,        10610209857723,        17167680177565,
            27777890035288,       44945570212853,        72723460248141,
            117669030460994,      190392490709135,       308061521170129,
            498454011879264,      806515533049393,       1304969544928657,
            2111485077978050,     3416454622906707,      5527939700884757,
            8944394323791464,     14472334024676221,     23416728348467685,
            37889062373143906,    61305790721611591,     99194853094755497,
            160500643816367088,   259695496911122585,    420196140727489673,
            679891637638612258,   1100087778366101931,   1779979416004714189,
            2880067194370816120,  4660046610375530309,   7540113804746346429,
            12200160415121876738, 19740274219868223167,  31940434634990099905,
            51680708854858323072, 83621143489848422977,  135301852344706746049
        ];
    }

    /**
        @dev Tests if number is a fib via a linear lookup in the table above
    */
    function isFibs128(uint256 n) internal pure returns (bool) {
        for(uint i = 0; i < 39; i++) if (fibs128()[i] == n) return true;
        return false;
    }

    /**
        @dev Helper for Miller-Rabin probabilistic primality test
    */
    // Write (n - 1) as 2^s * d
    function getValues(uint256 n) internal pure returns (uint256[2] memory) {
        uint256 s = 0;
        uint256 d = n - 1;
        while (d % 2 == 0) {
            d = d / 2;
            s++;
        }
        uint256[2] memory ret;
        ret[0] = s;
        ret[1] = d;
        return ret;
    }

    /**
        @dev Wrapper around EVM precompiled function for modular exponentiation, deployed at 0x05 address
    */
    function modExp(uint256 base, uint256 e, uint256 m) internal view returns (uint o) {
        assembly {
        // define pointer
            let p := mload(0x40)
        // store data assembly-favouring ways
            mstore(p, 0x20)             // Length of Base
            mstore(add(p, 0x20), 0x20)  // Length of Exponent
            mstore(add(p, 0x40), 0x20)  // Length of Modulus
            mstore(add(p, 0x60), base)  // Base
            mstore(add(p, 0x80), e)     // Exponent
            mstore(add(p, 0xa0), m)     // Modulus
        if iszero(staticcall(sub(gas(), 2000), 0x05, p, 0xc0, p, 0x20)) {
           revert(0, 0)
        }
        // data
            o := mload(p)
        }
    }

    /**
      @dev  Miller-Rabin test probabilistic primality test
            see https://en.wikipedia.org/wiki/Miller–Rabin_primality_test
    */
    function probablyPrime(uint256 n, uint256 prime) internal view returns (bool) {
        if (n == 2 || n == 3) {
            return true;
        }

        if (n % 2 == 0 || n < 2) {
            return false;
        }

        uint256[2] memory values = getValues(n);
        uint256 s = values[0];
        uint256 d = values[1];

        uint256 x = modExp(prime, d, n);

        if (x == 1 || x == n - 1) {
            return true;
        }

        for (uint256 i = s - 1; i > 0; i--) {
            x = modExp(x, 2, n);
            if (x == 1) {
                return false;
            }
            if (x == n - 1) {
                return true;
            }
        }
        return false;
    }

    /**
      @dev  Determines if a number is prime, using Miller-Rabin test probabilistic primality test
            plus deterministic checking to sift out pseudo-primes
            see https://en.wikipedia.org/wiki/Miller–Rabin_primality_test
    */
    function isPrime(uint256 n) public view returns (bool) {
        if (n < 2_047)
            return probablyPrime(n, 2);
        else if (n < 1_373_653)
            return probablyPrime(n, 2) && probablyPrime(n, 3);
        else if (n < 9_080_191)
            return probablyPrime(n, 31) && probablyPrime(n, 73);
        else if (n < 25_326_001)
            return probablyPrime(n, 2) && probablyPrime(n, 3)
            && probablyPrime(n, 5);
        else if (n < 3_215_031_751)
            return probablyPrime(n, 2) && probablyPrime(n, 3)
            && probablyPrime(n, 5) && probablyPrime(n, 7);
        else if (n < 4_759_123_141)
            return probablyPrime(n, 2) && probablyPrime(n, 7)
            && probablyPrime(n, 61);
        else if (n < 1_122_004_669_633)
            return probablyPrime(n, 2) && probablyPrime(n, 13)
            && probablyPrime(n, 23) && probablyPrime(n, 1662803);
        else if (n < 2_152_302_898_747)
            return probablyPrime(n, 2) && probablyPrime(n, 3)
            && probablyPrime(n, 5) && probablyPrime(n, 7)
            && probablyPrime(n, 11);
        else if (n < 3_474_749_660_383)
            return probablyPrime(n, 2) && probablyPrime(n, 3)
            && probablyPrime(n, 5) && probablyPrime(n, 7)
            && probablyPrime(n, 11) && probablyPrime(n, 13);
        else if (n < 341_550_071_728_321)
            return probablyPrime(n, 2) && probablyPrime(n, 3)
            && probablyPrime(n, 5) && probablyPrime(n, 7)
            && probablyPrime(n, 11) && probablyPrime(n, 13)
            && probablyPrime(n, 17);
        return false;
        // TODO: consider reverting ???
        // revert('number too big');
    }

    /**
        @dev Count prime numbers occurring between `from` and `to` numbers
    */
    function findPrimes(uint256 from, uint256 to) external view returns (uint256 count) {
        require(to > 0, "findPrimes: to should be natural");
        require(to > from, "findPrimes: to should be larger than from");
        count = 0;
        for(uint i = from; i < to; i++) {
            if (isPrime(i)) count++;
        }
    }

    /**
        @dev Helper to get N-th Fibonacci number (0 returns 0)
    */
    function getFib(uint256 n) internal pure returns (uint256 a) {
        if (n == 0) {
            return 0;
        }
        uint256 h = n / 2;
        uint256 mask = 1;
        // find highest set bit in n
        while(mask <= h) {
            mask <<= 1;
        }
        mask >>= 1;
        a = 1;
        uint256 b = 1;
        uint256 c;
        while(mask > 0) {
            c = a * a+b * b;
            if (n & mask > 0) {
                b = b * (b + 2 * a);
                a = c;
            } else {
                a = a * (2 * b - a);
                b = c;
            }
            mask >>= 1;
        }
        return a;
    }

    /**
        @dev Helper to check if a number is a perfect square
    */
    function isPerfectSquare(uint256 n) internal pure returns (bool) {
       uint256 low = 0;
       uint256 high = n;
       while (low <= high) {
           uint mid = (low + high) / 2;
           uint square = mid * mid;
           if (square == n) {
               return true;
           } else if (square > n) {
               high = mid - 1;
           } else {
               low = mid + 1;
           }
       }
       return false;
   }

    /**
        @dev Test if the number is a fib
        note the upper limit of 2 ** 62 - 1, to avoid overflow while preforming tests
    */
   function isFib(uint256 n) public pure returns (bool) {
       if (n == 0) return false;
       require(n < MAX_SUPPORTED_FIB_CANDIDATE, 'isFib: number too big');
       uint256 base = n * n * 5;
       uint256 p1 = base + 4;
       uint256 p2 = base - 4;
       return (isPerfectSquare(p1) || isPerfectSquare(p2));
    }
}