// SPDX-License-Identifier: MIT

pragma solidity 0.6.12;
pragma experimental ABIEncoderV2;



// Part: ABDKMath64x64

/**
 * 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) {
    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) {
    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) {
    require (x <= 0x7FFFFFFFFFFFFFFF);
    return int128 (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) {
    require (x >= 0);
    return uint64 (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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    if (y == 0) return 0;

    require (x >= 0);

    uint256 lo = (uint256 (x) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
    uint256 hi = uint256 (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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    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) {
    uint256 absoluteResult;
    bool negativeResult = false;
    if (x >= 0) {
      absoluteResult = powu (uint256 (x) << 63, y);
    } else {
      // We rely on overflow behavior here
      absoluteResult = powu (uint256 (uint128 (-x)) << 63, y);
      negativeResult = y & 1 > 0;
    }

    absoluteResult >>= 63;

    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 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) {
    require (x >= 0);
    return int128 (sqrtu (uint256 (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) {
    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 (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) {
    require (x > 0);

    return int128 (
        uint256 (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) {
    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 (63 - (x >> 64));
    require (result <= uint256 (MAX_64x64));

    return int128 (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) {
    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) {
    require (y != 0);

    uint256 result;

    if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
      result = (x << 64) / y;
    else {
      uint256 msb = 192;
      uint256 xc = x >> 192;
      if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
      if (xc >= 0x10000) { xc >>= 16; msb += 16; }
      if (xc >= 0x100) { xc >>= 8; msb += 8; }
      if (xc >= 0x10) { xc >>= 4; msb += 4; }
      if (xc >= 0x4) { xc >>= 2; msb += 2; }
      if (xc >= 0x2) msb += 1;  // No need to shift xc anymore

      result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
      require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

      uint256 hi = result * (y >> 128);
      uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);

      uint256 xh = x >> 192;
      uint256 xl = x << 64;

      if (xl < lo) xh -= 1;
      xl -= lo; // We rely on overflow behavior here
      lo = hi << 128;
      if (xl < lo) xh -= 1;
      xl -= lo; // We rely on overflow behavior here

      assert (xh == hi >> 128);

      result += xl / y;
    }

    require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
    return uint128 (result);
  }

  /**
   * Calculate x^y assuming 0^0 is 1, where x is unsigned 129.127 fixed point
   * number and y is unsigned 256-bit integer number.  Revert on overflow.
   *
   * @param x unsigned 129.127-bit fixed point number
   * @param y uint256 value
   * @return unsigned 129.127-bit fixed point number
   */
  function powu (uint256 x, uint256 y) private pure returns (uint256) {
    if (y == 0) return 0x80000000000000000000000000000000;
    else if (x == 0) return 0;
    else {
      int256 msb = 0;
      uint256 xc = x;
      if (xc >= 0x100000000000000000000000000000000) { xc >>= 128; msb += 128; }
      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 xe = msb - 127;
      if (xe > 0) x >>= uint256 (xe);
      else x <<= uint256 (-xe);

      uint256 result = 0x80000000000000000000000000000000;
      int256 re = 0;

      while (y > 0) {
        if (y & 1 > 0) {
          result = result * x;
          y -= 1;
          re += xe;
          if (result >=
            0x8000000000000000000000000000000000000000000000000000000000000000) {
            result >>= 128;
            re += 1;
          } else result >>= 127;
          if (re < -127) return 0; // Underflow
          require (re < 128); // Overflow
        } else {
          x = x * x;
          y >>= 1;
          xe <<= 1;
          if (x >=
            0x8000000000000000000000000000000000000000000000000000000000000000) {
            x >>= 128;
            xe += 1;
          } else x >>= 127;
          if (xe < -127) return 0; // Underflow
          require (xe < 128); // Overflow
        }
      }

      if (re > 0) result <<= uint256 (re);
      else if (re < 0) result >>= uint256 (-re);

      return 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) {
    if (x == 0) return 0;
    else {
      uint256 xx = x;
      uint256 r = 1;
      if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }
      if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }
      if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }
      if (xx >= 0x10000) { xx >>= 16; r <<= 8; }
      if (xx >= 0x100) { xx >>= 8; r <<= 4; }
      if (xx >= 0x10) { xx >>= 4; r <<= 2; }
      if (xx >= 0x8) { r <<= 1; }
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1;
      r = (r + x / r) >> 1; // Seven iterations should be enough
      uint256 r1 = x / r;
      return uint128 (r < r1 ? r : r1);
    }
  }
}

// Part: BokkyPooBahsDateTimeLibrary

// ----------------------------------------------------------------------------
// 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 {

    uint constant SECONDS_PER_DAY = 24 * 60 * 60;
    uint constant SECONDS_PER_HOUR = 60 * 60;
    uint constant SECONDS_PER_MINUTE = 60;
    int constant OFFSET19700101 = 2440588;

    uint constant DOW_MON = 1;
    uint constant DOW_TUE = 2;
    uint constant DOW_WED = 3;
    uint constant DOW_THU = 4;
    uint constant DOW_FRI = 5;
    uint constant DOW_SAT = 6;
    uint constant DOW_SUN = 7;

    // ------------------------------------------------------------------------
    // Calculate the number of days from 1970/01/01 to year/month/day using
    // the date conversion algorithm from
    //   http://aa.usno.navy.mil/faq/docs/JD_Formula.php
    // 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(uint year, uint month, uint day) internal pure returns (uint _days) {
        require(year >= 1970);
        int _year = int(year);
        int _month = int(month);
        int _day = int(day);

        int __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 = uint(__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(uint _days) internal pure returns (uint year, uint month, uint day) {
        int __days = int(_days);

        int L = __days + 68569 + OFFSET19700101;
        int N = 4 * L / 146097;
        L = L - (146097 * N + 3) / 4;
        int _year = 4000 * (L + 1) / 1461001;
        L = L - 1461 * _year / 4 + 31;
        int _month = 80 * L / 2447;
        int _day = L - 2447 * _month / 80;
        L = _month / 11;
        _month = _month + 2 - 12 * L;
        _year = 100 * (N - 49) + _year + L;

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

    function timestampFromDate(uint year, uint month, uint day) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY;
    }
    function timestampFromDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (uint timestamp) {
        timestamp = _daysFromDate(year, month, day) * SECONDS_PER_DAY + hour * SECONDS_PER_HOUR + minute * SECONDS_PER_MINUTE + second;
    }
    function timestampToDate(uint timestamp) internal pure returns (uint year, uint month, uint day) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function timestampToDateTime(uint timestamp) internal pure returns (uint year, uint month, uint day, uint hour, uint minute, uint second) {
        (year, month, day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint 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(uint year, uint month, uint day) internal pure returns (bool valid) {
        if (year >= 1970 && month > 0 && month <= 12) {
            uint daysInMonth = _getDaysInMonth(year, month);
            if (day > 0 && day <= daysInMonth) {
                valid = true;
            }
        }
    }
    function isValidDateTime(uint year, uint month, uint day, uint hour, uint minute, uint second) internal pure returns (bool valid) {
        if (isValidDate(year, month, day)) {
            if (hour < 24 && minute < 60 && second < 60) {
                valid = true;
            }
        }
    }
    function isLeapYear(uint timestamp) internal pure returns (bool leapYear) {
        (uint year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        leapYear = _isLeapYear(year);
    }
    function _isLeapYear(uint year) internal pure returns (bool leapYear) {
        leapYear = ((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0);
    }
    function isWeekDay(uint timestamp) internal pure returns (bool weekDay) {
        weekDay = getDayOfWeek(timestamp) <= DOW_FRI;
    }
    function isWeekEnd(uint timestamp) internal pure returns (bool weekEnd) {
        weekEnd = getDayOfWeek(timestamp) >= DOW_SAT;
    }
    function getDaysInMonth(uint timestamp) internal pure returns (uint daysInMonth) {
        (uint year, uint month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
        daysInMonth = _getDaysInMonth(year, month);
    }
    function _getDaysInMonth(uint year, uint month) internal pure returns (uint 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(uint timestamp) internal pure returns (uint dayOfWeek) {
        uint _days = timestamp / SECONDS_PER_DAY;
        dayOfWeek = (_days + 3) % 7 + 1;
    }

    function getYear(uint timestamp) internal pure returns (uint year) {
        (year,,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getMonth(uint timestamp) internal pure returns (uint month) {
        (,month,) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getDay(uint timestamp) internal pure returns (uint day) {
        (,,day) = _daysToDate(timestamp / SECONDS_PER_DAY);
    }
    function getHour(uint timestamp) internal pure returns (uint hour) {
        uint secs = timestamp % SECONDS_PER_DAY;
        hour = secs / SECONDS_PER_HOUR;
    }
    function getMinute(uint timestamp) internal pure returns (uint minute) {
        uint secs = timestamp % SECONDS_PER_HOUR;
        minute = secs / SECONDS_PER_MINUTE;
    }
    function getSecond(uint timestamp) internal pure returns (uint second) {
        second = timestamp % SECONDS_PER_MINUTE;
    }

    function addYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year += _years;
        uint 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(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        month += _months;
        year += (month - 1) / 12;
        month = (month - 1) % 12 + 1;
        uint 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(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _days * SECONDS_PER_DAY;
        require(newTimestamp >= timestamp);
    }
    function addHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _hours * SECONDS_PER_HOUR;
        require(newTimestamp >= timestamp);
    }
    function addMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp >= timestamp);
    }
    function addSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp + _seconds;
        require(newTimestamp >= timestamp);
    }

    function subYears(uint timestamp, uint _years) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        year -= _years;
        uint 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(uint timestamp, uint _months) internal pure returns (uint newTimestamp) {
        (uint year, uint month, uint day) = _daysToDate(timestamp / SECONDS_PER_DAY);
        uint yearMonth = year * 12 + (month - 1) - _months;
        year = yearMonth / 12;
        month = yearMonth % 12 + 1;
        uint 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(uint timestamp, uint _days) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _days * SECONDS_PER_DAY;
        require(newTimestamp <= timestamp);
    }
    function subHours(uint timestamp, uint _hours) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _hours * SECONDS_PER_HOUR;
        require(newTimestamp <= timestamp);
    }
    function subMinutes(uint timestamp, uint _minutes) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _minutes * SECONDS_PER_MINUTE;
        require(newTimestamp <= timestamp);
    }
    function subSeconds(uint timestamp, uint _seconds) internal pure returns (uint newTimestamp) {
        newTimestamp = timestamp - _seconds;
        require(newTimestamp <= timestamp);
    }

    function diffYears(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _years) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear,,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear,,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _years = toYear - fromYear;
    }
    function diffMonths(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _months) {
        require(fromTimestamp <= toTimestamp);
        (uint fromYear, uint fromMonth,) = _daysToDate(fromTimestamp / SECONDS_PER_DAY);
        (uint toYear, uint toMonth,) = _daysToDate(toTimestamp / SECONDS_PER_DAY);
        _months = toYear * 12 + toMonth - fromYear * 12 - fromMonth;
    }
    function diffDays(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _days) {
        require(fromTimestamp <= toTimestamp);
        _days = (toTimestamp - fromTimestamp) / SECONDS_PER_DAY;
    }
    function diffHours(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _hours) {
        require(fromTimestamp <= toTimestamp);
        _hours = (toTimestamp - fromTimestamp) / SECONDS_PER_HOUR;
    }
    function diffMinutes(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _minutes) {
        require(fromTimestamp <= toTimestamp);
        _minutes = (toTimestamp - fromTimestamp) / SECONDS_PER_MINUTE;
    }
    function diffSeconds(uint fromTimestamp, uint toTimestamp) internal pure returns (uint _seconds) {
        require(fromTimestamp <= toTimestamp);
        _seconds = toTimestamp - fromTimestamp;
    }
}

// Part: CloneFactory

/*
The MIT License (MIT)

Copyright (c) 2018 Murray Software, LLC.

Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
//solhint-disable max-line-length
//solhint-disable no-inline-assembly

contract CloneFactory {

  function createClone(address target) internal returns (address result) {
    bytes20 targetBytes = bytes20(target);
    assembly {
      let clone := mload(0x40)
      mstore(clone, 0x3d602d80600a3d3981f3363d3d373d3d3d363d73000000000000000000000000)
      mstore(add(clone, 0x14), targetBytes)
      mstore(add(clone, 0x28), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)
      result := create(0, clone, 0x37)
    }
  }

  function isClone(address target, address query) internal view returns (bool result) {
    bytes20 targetBytes = bytes20(target);
    assembly {
      let clone := mload(0x40)
      mstore(clone, 0x363d3d373d3d3d363d7300000000000000000000000000000000000000000000)
      mstore(add(clone, 0xa), targetBytes)
      mstore(add(clone, 0x1e), 0x5af43d82803e903d91602b57fd5bf30000000000000000000000000000000000)

      let other := add(clone, 0x40)
      extcodecopy(query, other, 0, 0x2d)
      result := and(
        eq(mload(clone), mload(other)),
        eq(mload(add(clone, 0xd)), mload(add(other, 0xd)))
      )
    }
  }
}

// Part: IOracle

interface IOracle {
    function getPrice() external view returns (uint256);
}

// Part: Initializable

/**
 * @title Initializable
 *
 * @dev Helper contract to support initializer functions. To use it, replace
 * the constructor with a function that has the `initializer` modifier.
 * WARNING: Unlike constructors, initializer functions must be manually
 * invoked. This applies both to deploying an Initializable contract, as well
 * as extending an Initializable contract via inheritance.
 * WARNING: When used with inheritance, manual care must be taken to not invoke
 * a parent initializer twice, or ensure that all initializers are idempotent,
 * because this is not dealt with automatically as with constructors.
 */
contract Initializable {

  /**
   * @dev Indicates that the contract has been initialized.
   */
  bool private initialized;

  /**
   * @dev Indicates that the contract is in the process of being initialized.
   */
  bool private initializing;

  /**
   * @dev Modifier to use in the initializer function of a contract.
   */
  modifier initializer() {
    require(initializing || isConstructor() || !initialized, "Contract instance has already been initialized");

    bool isTopLevelCall = !initializing;
    if (isTopLevelCall) {
      initializing = true;
      initialized = true;
    }

    _;

    if (isTopLevelCall) {
      initializing = false;
    }
  }

  /// @dev Returns true if and only if the function is running in the constructor
  function isConstructor() private view returns (bool) {
    // extcodesize checks the size of the code stored in an address, and
    // address returns the current address. Since the code is still not
    // deployed when running a constructor, any checks on its code size will
    // yield zero, making it an effective way to detect if a contract is
    // under construction or not.
    address self = address(this);
    uint256 cs;
    assembly { cs := extcodesize(self) }
    return cs == 0;
  }

  // Reserved storage space to allow for layout changes in the future.
  uint256[50] private ______gap;
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/Address

/**
 * @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
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies in extcodesize, which returns 0 for contracts in
        // construction, since the code is only stored at the end of the
        // constructor execution.

        uint256 size;
        // solhint-disable-next-line no-inline-assembly
        assembly { size := extcodesize(account) }
        return size > 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");

        // solhint-disable-next-line avoid-low-level-calls, avoid-call-value
        (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");
        return _functionCallWithValue(target, data, value, errorMessage);
    }

    function _functionCallWithValue(address target, bytes memory data, uint256 weiValue, string memory errorMessage) private returns (bytes memory) {
        require(isContract(target), "Address: call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.call{ value: weiValue }(data);
        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

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/IERC20

/**
 * @dev Interface of the ERC20 standard as defined in the EIP.
 */
interface IERC20 {
    /**
     * @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 `recipient`.
     *
     * Returns a boolean value indicating whether the operation succeeded.
     *
     * Emits a {Transfer} event.
     */
    function transfer(address recipient, 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 `sender` to `recipient` 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 sender, address recipient, uint256 amount) external returns (bool);

    /**
     * @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);
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/Math

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a >= b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow, so we distribute
        return (a / 2) + (b / 2) + ((a % 2 + b % 2) / 2);
    }
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/ReentrancyGuard

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
contract ReentrancyGuard {
    // Booleans are more expensive than uint256 or any type that takes up a full
    // word because each write operation emits an extra SLOAD to first read the
    // slot's contents, replace the bits taken up by the boolean, and then write
    // back. This is the compiler's defense against contract upgrades and
    // pointer aliasing, and it cannot be disabled.

    // The values being non-zero value makes deployment a bit more expensive,
    // but in exchange the refund on every call to nonReentrant will be lower in
    // amount. Since refunds are capped to a percentage of the total
    // transaction's gas, it is best to keep them low in cases like this one, to
    // increase the likelihood of the full refund coming into effect.
    uint256 private constant _NOT_ENTERED = 1;
    uint256 private constant _ENTERED = 2;

    uint256 private _status;

    constructor () internal {
        _status = _NOT_ENTERED;
    }

    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_status != _ENTERED, "ReentrancyGuard: reentrant call");

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

        _;

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

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/SafeMath

/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 */
library SafeMath {
    /**
     * @dev Returns the addition of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `+` operator.
     *
     * Requirements:
     *
     * - Addition cannot overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");

        return c;
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction overflow");
    }

    /**
     * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
     * overflow (when the result is negative).
     *
     * Counterpart to Solidity's `-` operator.
     *
     * Requirements:
     *
     * - Subtraction cannot overflow.
     */
    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Returns the multiplication of two unsigned integers, reverting on
     * overflow.
     *
     * Counterpart to Solidity's `*` operator.
     *
     * Requirements:
     *
     * - Multiplication cannot overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "SafeMath: multiplication overflow");

        return c;
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    /**
     * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
     * division by zero. The result is rounded towards zero.
     *
     * Counterpart to Solidity's `/` operator. Note: this function uses a
     * `revert` opcode (which leaves remaining gas untouched) while Solidity
     * uses an invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b > 0, errorMessage);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    /**
     * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
     * Reverts with custom message when dividing by zero.
     *
     * Counterpart to Solidity's `%` operator. This function uses a `revert`
     * opcode (which leaves remaining gas untouched) while Solidity uses an
     * invalid opcode to revert (consuming all remaining gas).
     *
     * Requirements:
     *
     * - The divisor cannot be zero.
     */
    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/Strings

/**
 * @dev String operations.
 */
library Strings {
    /**
     * @dev Converts a `uint256` to its ASCII `string` representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        // Inspired by OraclizeAPI's implementation - MIT licence
        // https://github.com/oraclize/ethereum-api/blob/b42146b063c7d6ee1358846c198246239e9360e8/oraclizeAPI_0.4.25.sol

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

// Part: ContextUpgradeSafe

/*
 * @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 GSN 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.
 */
contract ContextUpgradeSafe is Initializable {
    // Empty internal constructor, to prevent people from mistakenly deploying
    // an instance of this contract, which should be used via inheritance.

    function __Context_init() internal initializer {
        __Context_init_unchained();
    }

    function __Context_init_unchained() internal initializer {


    }


    function _msgSender() internal view virtual returns (address payable) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes memory) {
        this; // silence state mutability warning without generating bytecode - see https://github.com/ethereum/solidity/issues/2691
        return msg.data;
    }

    uint256[50] private __gap;
}

// Part: OpenZeppelin/openzeppelin-contracts@3.2.0/SafeERC20

/**
 * @title SafeERC20
 * @dev Wrappers around ERC20 operations that throw on failure (when the token
 * contract returns false). Tokens that return no value (and instead revert or
 * throw on failure) are also supported, non-reverting calls are assumed to be
 * successful.
 * To use this library you can add a `using SafeERC20 for IERC20;` statement to your contract,
 * which allows you to call the safe operations as `token.safeTransfer(...)`, etc.
 */
library SafeERC20 {
    using SafeMath for uint256;
    using Address for address;

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

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

    /**
     * @dev Deprecated. This function has issues similar to the ones found in
     * {IERC20-approve}, and its usage is discouraged.
     *
     * Whenever possible, use {safeIncreaseAllowance} and
     * {safeDecreaseAllowance} instead.
     */
    function safeApprove(IERC20 token, address spender, uint256 value) internal {
        // safeApprove should only be called when setting an initial allowance,
        // or when resetting it to zero. To increase and decrease it, use
        // 'safeIncreaseAllowance' and 'safeDecreaseAllowance'
        // solhint-disable-next-line max-line-length
        require((value == 0) || (token.allowance(address(this), spender) == 0),
            "SafeERC20: approve from non-zero to non-zero allowance"
        );
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, value));
    }

    function safeIncreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).add(value);
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    function safeDecreaseAllowance(IERC20 token, address spender, uint256 value) internal {
        uint256 newAllowance = token.allowance(address(this), spender).sub(value, "SafeERC20: decreased allowance below zero");
        _callOptionalReturn(token, abi.encodeWithSelector(token.approve.selector, spender, newAllowance));
    }

    /**
     * @dev Imitates a Solidity high-level call (i.e. a regular function call to a contract), relaxing the requirement
     * on the return value: the return value is optional (but if data is returned, it must not be false).
     * @param token The token targeted by the call.
     * @param data The call data (encoded using abi.encode or one of its variants).
     */
    function _callOptionalReturn(IERC20 token, bytes memory data) private {
        // We need to perform a low level call here, to bypass Solidity's return data size checking mechanism, since
        // we're implementing it ourselves. We use {Address.functionCall} to perform this call, which verifies that
        // the target address contains contract code and also asserts for success in the low-level call.

        bytes memory returndata = address(token).functionCall(data, "SafeERC20: low-level call failed");
        if (returndata.length > 0) { // Return data is optional
            // solhint-disable-next-line max-line-length
            require(abi.decode(returndata, (bool)), "SafeERC20: ERC20 operation did not succeed");
        }
    }
}

// Part: OptionMath

library OptionMath {
    using SafeMath for uint256;

    uint256 public constant SCALE = 1e18;

    /**
     * Converts total supplies of options into the tokenized payoff quantities used
     * by the LMSR
     *
     * For puts, multiply by strike price since option quantity is in terms of the
     * underlying, but lmsr quantities should be in terms of the strike currency
     */
    function calcQuantities(
        uint256[] memory strikePrices,
        bool isPut,
        uint256[] memory longSupplies,
        uint256[] memory shortSupplies
    ) internal pure returns (uint256[] memory) {
        uint256 n = strikePrices.length;
        require(longSupplies.length == n, "Lengths do not match");
        require(shortSupplies.length == n, "Lengths do not match");

        // this mutates the method arguments, but costs less gas
        if (isPut) {
            for (uint256 i = 0; i < n; i++) {
                longSupplies[i] = longSupplies[i].mul(strikePrices[i]).div(SCALE);
                shortSupplies[i] = shortSupplies[i].mul(strikePrices[i]).div(SCALE);
            }
        }

        // swap shortSupplies and longSupplies for puts
        uint256[] memory leftSupplies = isPut ? shortSupplies : longSupplies;
        uint256[] memory rightSupplies = isPut ? longSupplies : shortSupplies;

        uint256[] memory quantities = new uint256[](n + 1);

        // set quantities[0] = sum(rightSupplies)
        for (uint256 i = 0; i < n; i++) {
            quantities[0] = quantities[0].add(rightSupplies[i]);
        }

        // set quantities[i] = leftSupplies[:i] + rightSupplies[i:]
        for (uint256 i = 0; i < n; i++) {
            quantities[i + 1] = quantities[i].add(leftSupplies[i]).sub(rightSupplies[i]);
        }
        return quantities;
    }

    /**
     * Calculates the LMSR cost function
     *
     *   C(q_1, ..., q_n) = b * log(exp(q_1 / b) + ... + exp(q_n / b))
     *
     * where
     *
     *   q_i = total supply of ith tokenized payoff
     *   b = liquidity parameter
     *
     * An equivalent expression for C is used to avoid overflow when calculating exponentials
     *
     *   C(q_1, ..., q_n) = m + b * log(exp((q_1 - m) / b) + ... + exp((q_n - m) / b))
     *
     * where
     *
     *   m = max(q_1, ..., q_n)
     */
    function calcLmsrCost(uint256[] memory quantities, uint256 b) internal pure returns (uint256) {
        uint256 maxQuantity = quantities[0];
        for (uint256 i = 1; i < quantities.length; i++) {
            maxQuantity = Math.max(maxQuantity, quantities[i]);
        }

        // cost converges to max(q) as b tends to 0
        if (b == 0) {
            return maxQuantity;
        }

        int128 sumExp;
        for (uint256 i = 0; i < quantities.length; i++) {
            // max(q) - q_i
            uint256 diff = maxQuantity.sub(quantities[i]);

            // (max(q) - q_i) / b
            int128 div = ABDKMath64x64.divu(diff, b);

            // exp((q_i - max(q)) / b)
            int128 exp = ABDKMath64x64.exp(ABDKMath64x64.neg(div));
            sumExp = ABDKMath64x64.add(sumExp, exp);
        }

        // log(sumExp)
        int128 log = ABDKMath64x64.ln(sumExp);

        // b * log(sumExp) + max(q)
        return ABDKMath64x64.mulu(log, b).add(maxQuantity);
    }

    /**
     * Calculate total payoff of all outstanding options
     *
     * This value will decrease as options are redeemed
     *
     * For calls, divide by expiry price since payoff should be in terms of the
     * `baseToken`
     */
    function calcPayoff(
        uint256[] memory strikePrices,
        uint256 expiryPrice,
        bool isPut,
        uint256[] memory longSupplies,
        uint256[] memory shortSupplies
    ) internal pure returns (uint256) {
        require(longSupplies.length == strikePrices.length, "Lengths do not match");
        require(shortSupplies.length == strikePrices.length, "Lengths do not match");

        if (expiryPrice == 0) {
            return 0;
        }

        uint256 payoff;
        for (uint256 i = 0; i < strikePrices.length; i++) {
            uint256 strikePrice = strikePrices[i];

            if (isPut && expiryPrice < strikePrice) {
                // put payoff = max(K - S, 0)
                payoff = payoff.add(longSupplies[i].mul(strikePrice.sub(expiryPrice)));
            } else if (!isPut && expiryPrice > strikePrice) {
                // call payoff = max(S - K, 0)
                payoff = payoff.add(longSupplies[i].mul(expiryPrice.sub(strikePrice)));
            }

            // short payoff = min(S, K)
            payoff = payoff.add(shortSupplies[i].mul(Math.min(expiryPrice, strikePrice)));
        }
        return payoff.div(isPut ? SCALE : expiryPrice);
    }
}

// Part: OptionSymbol

contract OptionSymbol {
    using SafeMath for uint256;

    uint256 private constant STRIKE_PRICE_SCALE = 1e18;
    uint256 private constant STRIKE_PRICE_DIGITS = 18;

    // example symbol: Charm LP ETH 04DEC2020 C
    function getMarketSymbol(
        string memory underlying,
        uint256 expiryTime,
        bool isPut
    ) public pure returns (string memory) {
        (uint256 year, uint256 month, uint256 day) = BokkyPooBahsDateTimeLibrary.timestampToDate(expiryTime);
        (string memory monthSymbol, ) = _getMonth(month);

        string memory suffix = isPut ? "P" : "C";

        return
            string(
                abi.encodePacked(
                    "Charm LP ",
                    underlying,
                    " ",
                    _uintTo2Chars(day),
                    monthSymbol,
                    Strings.toString(year),
                    " ",
                    suffix
                )
            );
    }

    // example symbol: Charm ETH 04DEC2020 500 C
    function getOptionSymbol(
        string memory underlying,
        uint256 strikePrice,
        uint256 expiryTime,
        bool isPut,
        bool isLong
    ) public pure returns (string memory) {
        string memory displayStrikePrice = _getDisplayedStrikePrice(strikePrice);

        (uint256 year, uint256 month, uint256 day) = BokkyPooBahsDateTimeLibrary.timestampToDate(expiryTime);
        (string memory monthSymbol, ) = _getMonth(month);

        string memory suffix = isPut ? (isLong ? "P" : "SP") : (isLong ? "C" : "SC");

        return
            string(
                abi.encodePacked(
                    "Charm ",
                    underlying,
                    " ",
                    _uintTo2Chars(day),
                    monthSymbol,
                    Strings.toString(year),
                    " ",
                    displayStrikePrice,
                    " ",
                    suffix
                )
            );
    }

    /**
     * @dev convert strike price scaled by 1e8 to human readable number string
     * @param _strikePrice strike price scaled by 1e8
     * @return strike price string
     */
    function _getDisplayedStrikePrice(uint256 _strikePrice) internal pure returns (string memory) {
        uint256 remainder = _strikePrice.mod(STRIKE_PRICE_SCALE);
        uint256 quotient = _strikePrice.div(STRIKE_PRICE_SCALE);
        string memory quotientStr = Strings.toString(quotient);

        if (remainder == 0) return quotientStr;

        uint256 trailingZeroes = 0;
        while (remainder.mod(10) == 0) {
            remainder = remainder / 10;
            trailingZeroes += 1;
        }

        // pad the number with "1 + starting zeroes"
        remainder += 10**(STRIKE_PRICE_DIGITS - trailingZeroes);

        string memory tmpStr = Strings.toString(remainder);
        tmpStr = _slice(tmpStr, 1, 1 + STRIKE_PRICE_DIGITS - trailingZeroes);

        string memory completeStr = string(abi.encodePacked(quotientStr, ".", tmpStr));
        return completeStr;
    }

    /**
     * @dev return a representation of a number using 2 characters, adds a leading 0 if one digit, uses two trailing digits if a 3 digit number
     * @return 2 characters that corresponds to a number
     */
    function _uintTo2Chars(uint256 number) internal pure returns (string memory) {
        if (number > 99) number = number % 100;
        string memory str = Strings.toString(number);
        if (number < 10) {
            return string(abi.encodePacked("0", str));
        }
        return str;
    }

    /**
     * @dev cut string s into s[start:end]
     * @param _s the string to cut
     * @param _start the starting index
     * @param _end the ending index (excluded in the substring)
     */
    function _slice(
        string memory _s,
        uint256 _start,
        uint256 _end
    ) internal pure returns (string memory) {
        bytes memory a = new bytes(_end - _start);
        for (uint256 i = 0; i < _end - _start; i++) {
            a[i] = bytes(_s)[_start + i];
        }
        return string(a);
    }

    /**
     * @dev return string representation of a month
     * @return shortString a 3 character representation of a month (ex: SEP, DEC, etc)
     * @return longString a full length string of a month (ex: September, December, etc)
     */
    function _getMonth(uint256 _month) internal pure returns (string memory shortString, string memory longString) {
        if (_month == 1) {
            return ("JAN", "January");
        } else if (_month == 2) {
            return ("FEB", "February");
        } else if (_month == 3) {
            return ("MAR", "March");
        } else if (_month == 4) {
            return ("APR", "April");
        } else if (_month == 5) {
            return ("MAY", "May");
        } else if (_month == 6) {
            return ("JUN", "June");
        } else if (_month == 7) {
            return ("JUL", "July");
        } else if (_month == 8) {
            return ("AUG", "August");
        } else if (_month == 9) {
            return ("SEP", "September");
        } else if (_month == 10) {
            return ("OCT", "October");
        } else if (_month == 11) {
            return ("NOV", "November");
        } else {
            return ("DEC", "December");
        }
    }
}

// Part: ReentrancyGuardUpgradeSafe

/**
 * @dev Contract module that helps prevent reentrant calls to a function.
 *
 * Inheriting from `ReentrancyGuard` will make the {nonReentrant} modifier
 * available, which can be applied to functions to make sure there are no nested
 * (reentrant) calls to them.
 *
 * Note that because there is a single `nonReentrant` guard, functions marked as
 * `nonReentrant` may not call one another. This can be worked around by making
 * those functions `private`, and then adding `external` `nonReentrant` entry
 * points to them.
 *
 * TIP: If you would like to learn more about reentrancy and alternative ways
 * to protect against it, check out our blog post
 * https://blog.openzeppelin.com/reentrancy-after-istanbul/[Reentrancy After Istanbul].
 */
contract ReentrancyGuardUpgradeSafe is Initializable {
    bool private _notEntered;


    function __ReentrancyGuard_init() internal initializer {
        __ReentrancyGuard_init_unchained();
    }

    function __ReentrancyGuard_init_unchained() internal initializer {


        // Storing an initial non-zero value makes deployment a bit more
        // expensive, but in exchange the refund on every call to nonReentrant
        // will be lower in amount. Since refunds are capped to a percetange of
        // the total transaction's gas, it is best to keep them low in cases
        // like this one, to increase the likelihood of the full refund coming
        // into effect.
        _notEntered = true;

    }


    /**
     * @dev Prevents a contract from calling itself, directly or indirectly.
     * Calling a `nonReentrant` function from another `nonReentrant`
     * function is not supported. It is possible to prevent this from happening
     * by making the `nonReentrant` function external, and make it call a
     * `private` function that does the actual work.
     */
    modifier nonReentrant() {
        // On the first call to nonReentrant, _notEntered will be true
        require(_notEntered, "ReentrancyGuard: reentrant call");

        // Any calls to nonReentrant after this point will fail
        _notEntered = false;

        _;

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

    uint256[49] private __gap;
}

// Part: ERC20UpgradeSafe

/**
 * @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 {ERC20MinterPauser}.
 *
 * 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 guidelines: functions revert instead
 * of 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 ERC20UpgradeSafe is Initializable, ContextUpgradeSafe, IERC20 {
    using SafeMath for uint256;
    using Address for address;

    mapping (address => uint256) private _balances;

    mapping (address => mapping (address => uint256)) private _allowances;

    uint256 private _totalSupply;

    string private _name;
    string private _symbol;
    uint8 private _decimals;

    /**
     * @dev Sets the values for {name} and {symbol}, initializes {decimals} with
     * a default value of 18.
     *
     * To select a different value for {decimals}, use {_setupDecimals}.
     *
     * All three of these values are immutable: they can only be set once during
     * construction.
     */

    function __ERC20_init(string memory name, string memory symbol) internal initializer {
        __Context_init_unchained();
        __ERC20_init_unchained(name, symbol);
    }

    function __ERC20_init_unchained(string memory name, string memory symbol) internal initializer {


        _name = name;
        _symbol = symbol;
        _decimals = 18;

    }


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

    /**
     * @dev Returns the symbol of the token, usually a shorter version of the
     * name.
     */
    function symbol() public view 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 {_setupDecimals} is
     * called.
     *
     * 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 returns (uint8) {
        return _decimals;
    }

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

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

    /**
     * @dev See {IERC20-transfer}.
     *
     * Requirements:
     *
     * - `recipient` cannot be the zero address.
     * - the caller must have a balance of at least `amount`.
     */
    function transfer(address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(_msgSender(), recipient, 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}.
     *
     * Requirements:
     *
     * - `spender` cannot be the zero address.
     */
    function approve(address spender, uint256 amount) public virtual override returns (bool) {
        _approve(_msgSender(), 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};
     *
     * Requirements:
     * - `sender` and `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     * - the caller must have allowance for ``sender``'s tokens of at least
     * `amount`.
     */
    function transferFrom(address sender, address recipient, uint256 amount) public virtual override returns (bool) {
        _transfer(sender, recipient, amount);
        _approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance"));
        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) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].add(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) {
        _approve(_msgSender(), spender, _allowances[_msgSender()][spender].sub(subtractedValue, "ERC20: decreased allowance below zero"));
        return true;
    }

    /**
     * @dev Moves tokens `amount` from `sender` to `recipient`.
     *
     * This is 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:
     *
     * - `sender` cannot be the zero address.
     * - `recipient` cannot be the zero address.
     * - `sender` must have a balance of at least `amount`.
     */
    function _transfer(address sender, address recipient, uint256 amount) internal virtual {
        require(sender != address(0), "ERC20: transfer from the zero address");
        require(recipient != address(0), "ERC20: transfer to the zero address");

        _beforeTokenTransfer(sender, recipient, amount);

        _balances[sender] = _balances[sender].sub(amount, "ERC20: transfer amount exceeds balance");
        _balances[recipient] = _balances[recipient].add(amount);
        emit Transfer(sender, recipient, 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
     *
     * - `to` 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 = _totalSupply.add(amount);
        _balances[account] = _balances[account].add(amount);
        emit Transfer(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);

        _balances[account] = _balances[account].sub(amount, "ERC20: burn amount exceeds balance");
        _totalSupply = _totalSupply.sub(amount);
        emit Transfer(account, address(0), amount);
    }

    /**
     * @dev Sets `amount` as the allowance of `spender` over the `owner`s tokens.
     *
     * This is 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 Sets {decimals} to a value other than the default one of 18.
     *
     * WARNING: This function should only be called from the constructor. Most
     * applications that interact with token contracts will not expect
     * {decimals} to ever change, and may work incorrectly if it does.
     */
    function _setupDecimals(uint8 decimals_) internal {
        _decimals = decimals_;
    }

    /**
     * @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 to 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 { }

    uint256[44] private __gap;
}

// Part: OwnableUpgradeSafe

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
contract OwnableUpgradeSafe is Initializable, ContextUpgradeSafe {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */

    function __Ownable_init() internal initializer {
        __Context_init_unchained();
        __Ownable_init_unchained();
    }

    function __Ownable_init_unchained() internal initializer {


        address msgSender = _msgSender();
        _owner = msgSender;
        emit OwnershipTransferred(address(0), msgSender);

    }


    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(_owner == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions anymore. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        emit OwnershipTransferred(_owner, address(0));
        _owner = address(0);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        emit OwnershipTransferred(_owner, newOwner);
        _owner = newOwner;
    }

    uint256[49] private __gap;
}

// Part: UniERC20

library UniERC20 {
    using SafeMath for uint256;
    using SafeERC20 for IERC20;

    function isETH(IERC20 token) internal pure returns (bool) {
        return (address(token) == address(0));
    }

    function uniBalanceOf(IERC20 token, address account) internal view returns (uint256) {
        if (isETH(token)) {
            return account.balance;
        } else {
            return token.balanceOf(account);
        }
    }

    function uniTransfer(
        IERC20 token,
        address payable to,
        uint256 amount
    ) internal {
        if (amount > 0) {
            if (isETH(token)) {
                (bool success, ) = to.call{value: amount}("");
                require(success, "Transfer failed");
            } else {
                token.safeTransfer(to, amount);
            }
        }
    }

    function uniTransferFromSenderToThis(IERC20 token, uint256 amount) internal {
        if (amount > 0) {
            if (isETH(token)) {
                require(msg.value >= amount, "UniERC20: not enough value");
                if (msg.value > amount) {
                    // Return remainder if exist
                    uint256 refundAmount = msg.value.sub(amount);
                    (bool success, ) = msg.sender.call{value: refundAmount}("");
                    require(success, "Transfer failed");
                }
            } else {
                token.safeTransferFrom(msg.sender, address(this), amount);
            }
        }
    }

    function uniSymbol(IERC20 token) internal view returns (string memory) {
        if (isETH(token)) {
            return "ETH";
        }

        (bool success, bytes memory data) = address(token).staticcall{gas: 20000}(abi.encodeWithSignature("symbol()"));
        if (!success) {
            (success, data) = address(token).staticcall{gas: 20000}(abi.encodeWithSignature("SYMBOL()"));
        }

        if (success && data.length >= 96) {
            (uint256 offset, uint256 len) = abi.decode(data, (uint256, uint256));
            if (offset == 0x20 && len > 0 && len <= 256) {
                return string(abi.decode(data, (bytes)));
            }
        }

        if (success && data.length == 32) {
            uint256 len = 0;
            while (len < data.length && data[len] >= 0x20 && data[len] <= 0x7E) {
                len++;
            }

            if (len > 0) {
                bytes memory result = new bytes(len);
                for (uint256 i = 0; i < len; i++) {
                    result[i] = data[i];
                }
                return string(result);
            }
        }

        return _toHex(address(token));
    }

    function _toHex(address account) private pure returns (string memory) {
        return _toHex(abi.encodePacked(account));
    }

    function _toHex(bytes memory data) private pure returns (string memory) {
        bytes memory str = new bytes(2 + data.length * 2);
        str[0] = "0";
        str[1] = "x";
        uint256 j = 2;
        for (uint256 i = 0; i < data.length; i++) {
            uint256 a = uint8(data[i]) >> 4;
            uint256 b = uint8(data[i]) & 0x0f;
            str[j++] = bytes1(uint8(a + 48 + (a / 10) * 39));
            str[j++] = bytes1(uint8(b + 48 + (b / 10) * 39));
        }

        return string(str);
    }
}

// Part: OptionToken

/**
 * ERC20 token representing a long or short option position. It is intended to be
 * used by `OptionMarket`, which mints/burns these tokens when users buy/sell options
 *
 * Note that `decimals` should match the decimals of the `baseToken` in `OptionMarket`
 */
contract OptionToken is ERC20UpgradeSafe {
    using Address for address;
    using SafeERC20 for IERC20;
    using SafeMath for uint256;

    address public market;

    function initialize(
        address _market,
        string memory name,
        string memory symbol,
        uint8 decimals
    ) public initializer {
        __ERC20_init(name, symbol);
        _setupDecimals(decimals);
        market = _market;
    }

    function mint(address account, uint256 amount) external {
        require(msg.sender == market, "!market");
        _mint(account, amount);
    }

    function burn(address account, uint256 amount) external {
        require(msg.sender == market, "!market");
        _burn(account, amount);
    }
}

// Part: OptionMarket

/**
 * Automated market-maker for options
 *
 * This contract allows an asset to be split up into tokenized payoffs such that
 * different combinations of payoffs sum up to different call/put option payoffs.
 * An LMSR (Hanson's market-maker) is used to provide liquidity for the tokenized
 * payoffs.
 *
 * The parameter `b` in the LMSR represents the market depth. `b` is increased when
 * users provide liquidity by depositing funds and it is decreased when they withdraw
 * liquidity. Trading fees are distributed proportionally to liquidity providers
 * at the time of the trade.
 *
 * Call and put option with any of the supported strikes are provided. Short options
 * (equivalent to owning 1 underlying + sell 1 option) are provided, which let users
 * take on short option exposure
 *
 * `buy`, `sell`, `deposit` and `withdraw` are the main methods used to interact with
 * this contract.
 *
 * After expiration, `settle` can be called to fetch the expiry price from a
 * price oracle. `buy` and `deposit` cannot be called after expiration, but `sell`
 * can be called to redeem options for their corresponding payouts and `withdraw`
 * can be called to redeem LP tokens for a stake of the remaining funds left
 * in the contract.
 *
 * Methods to calculate the LMSR cost and option payoffs can be found in `OptionMath`.
 * `OptionToken` is an ERC20 token representing a long or short option position
 * that's minted or burned when users buy or sell options.
 *
 * This contract is also an ERC20 token itself representing shares in the liquidity
 * pool.
 *
 * The intended way to deploy this contract is to call `createMarket` in `OptionFactory`
 * Then liquidity has to be provided using `deposit` before trades can occur.
 *
 * Please note that the deployer of this contract is highly privileged and has
 * permissions such as withdrawing all funds from the contract, being able to pause
 * trading, modify the market parameters and override the settlement price. These
 * permissions will be removed in future versions.
 */
contract OptionMarket is ERC20UpgradeSafe, ReentrancyGuardUpgradeSafe, OwnableUpgradeSafe {
    using Address for address;
    using SafeERC20 for IERC20;
    using UniERC20 for IERC20;
    using SafeMath for uint256;

    event Buy(
        address indexed account,
        bool isLongToken,
        uint256 strikeIndex,
        uint256 optionsOut,
        uint256 amountIn,
        uint256 newSupply
    );

    event Sell(
        address indexed account,
        bool isLongToken,
        uint256 strikeIndex,
        uint256 optionsIn,
        uint256 amountOut,
        uint256 newSupply,
        bool isSettled
    );

    event Deposit(address indexed account, uint256 sharesOut, uint256 amountIn, uint256 newSupply);
    event Withdraw(address indexed account, uint256 sharesIn, uint256 amountOut, uint256 newSupply, bool isSettled);
    event Settle(uint256 expiryPrice);

    uint256 public constant SCALE = 1e18;
    uint256 public constant SCALE_SCALE = 1e36;

    IERC20 public baseToken;
    IOracle public oracle;
    OptionToken[] public longTokens;
    OptionToken[] public shortTokens;
    uint256[] public strikePrices;
    uint256 public expiryTime;
    bool public isPut;
    uint256 public tradingFee;
    uint256 public balanceCap;
    uint256 public totalSupplyCap;
    uint256 public disputePeriod;

    bool public isPaused;
    bool public isSettled;
    uint256 public expiryPrice;

    // cache getCurrentCost and getCurrentPayoff between trades to save gas
    uint256 public lastCost;
    uint256 public lastPayoff;

    // total value of fees owed to LPs
    uint256 public poolValue;

    /**
     * @param _baseToken        Underlying asset if call. Strike currency if put
     *                          Represents ETH if equal to 0x0
     * @param _oracle           Oracle from which settlement price is obtained
     * @param _longTokens       Tokens representing long calls/puts
     * @param _shortTokens      Tokens representing short calls/puts
     * @param _strikePrices     Strike prices expressed in wei. Must be in increasing order
     * @param _expiryTime       Expiration time as a unix timestamp
     * @param _isPut            Whether this market provides calls or puts
     * @param _tradingFee       Trading fee as fraction of underlying expressed in wei
     * @param _symbol           Name and symbol of LP tokens
     */
    function initialize(
        address _baseToken,
        address _oracle,
        address[] memory _longTokens,
        address[] memory _shortTokens,
        uint256[] memory _strikePrices,
        uint256 _expiryTime,
        bool _isPut,
        uint256 _tradingFee,
        string memory _symbol
    ) public payable initializer {
        // this contract is also an ERC20 token, representing shares in the liquidity pool
        __ERC20_init(_symbol, _symbol);
        __ReentrancyGuard_init();
        __Ownable_init();

        // use same decimals as base token
        uint8 decimals = IERC20(_baseToken).isETH() ? 18 : ERC20UpgradeSafe(_baseToken).decimals();
        _setupDecimals(decimals);

        require(_longTokens.length == _strikePrices.length, "Lengths do not match");
        require(_shortTokens.length == _strikePrices.length, "Lengths do not match");

        require(_strikePrices.length > 0, "Strike prices must not be empty");
        require(_strikePrices[0] > 0, "Strike prices must be > 0");

        // check strike prices are increasing
        for (uint256 i = 0; i < _strikePrices.length - 1; i++) {
            require(_strikePrices[i] < _strikePrices[i + 1], "Strike prices must be increasing");
        }

        // check trading fee is less than 100%
        // note trading fee can be 0
        require(_tradingFee < SCALE, "Trading fee must be < 1");

        baseToken = IERC20(_baseToken);
        oracle = IOracle(_oracle);
        strikePrices = _strikePrices;
        expiryTime = _expiryTime;
        isPut = _isPut;
        tradingFee = _tradingFee;

        for (uint256 i = 0; i < _strikePrices.length; i++) {
            longTokens.push(OptionToken(_longTokens[i]));
            shortTokens.push(OptionToken(_shortTokens[i]));
        }

        require(!isExpired(), "Already expired");
    }

    /**
     * Buy options
     *
     * The option bought is specified by `isLongToken` and `strikeIndex` and the
     * amount by `optionsOut`
     *
     * This method reverts if the resulting cost is greater than `maxAmountIn`
     */
    function buy(
        bool isLongToken,
        uint256 strikeIndex,
        uint256 optionsOut,
        uint256 maxAmountIn
    ) external payable nonReentrant returns (uint256 amountIn) {
        require(totalSupply() > 0, "No liquidity");
        require(!isExpired(), "Already expired");
        require(msg.sender == owner() || !isPaused, "Paused");
        require(strikeIndex < strikePrices.length, "Index too large");
        require(optionsOut > 0, "Options out must be > 0");

        // mint options to user
        OptionToken option = isLongToken ? longTokens[strikeIndex] : shortTokens[strikeIndex];
        option.mint(msg.sender, optionsOut);

        // calculate trading fee and allocate it to the LP pool
        // like LMSR cost, fees have to be multiplied by strike price
        uint256 fee = optionsOut.mul(tradingFee);
        fee = isPut ? fee.mul(strikePrices[strikeIndex]).div(SCALE_SCALE) : fee.div(SCALE);
        poolValue = poolValue.add(fee);

        // calculate amount that needs to be paid by user to buy these options
        // it's equal to the increase in LMSR cost after minting the options
        uint256 costAfter = getCurrentCost();
        amountIn = costAfter.sub(lastCost).add(fee); // do sub first as a check since should not fail
        lastCost = costAfter;
        require(amountIn > 0, "Amount in must be > 0");
        require(amountIn <= maxAmountIn, "Max slippage exceeded");

        // transfer in amount from user
        _transferIn(amountIn);
        emit Buy(msg.sender, isLongToken, strikeIndex, optionsOut, amountIn, option.totalSupply());
    }

    /**
     * Sell options
     *
     * The option sold is specified by `isLongToken` and `strikeIndex` and the
     * amount by `optionsIn`
     *
     * This method reverts if the resulting amount returned is less than `minAmountOut`
     */
    function sell(
        bool isLongToken,
        uint256 strikeIndex,
        uint256 optionsIn,
        uint256 minAmountOut
    ) external nonReentrant returns (uint256 amountOut) {
        require(!isExpired() || isSettled, "Must be called before expiry or after settlement");
        require(!isDisputePeriod(), "Dispute period");
        require(msg.sender == owner() || !isPaused, "Paused");
        require(strikeIndex < strikePrices.length, "Index too large");
        require(optionsIn > 0, "Options in must be > 0");

        // burn user's options
        OptionToken option = isLongToken ? longTokens[strikeIndex] : shortTokens[strikeIndex];
        option.burn(msg.sender, optionsIn);

        // calculate amount that needs to be returned to user
        if (isSettled) {
            // if after settlement, amount is the option payoff
            uint256 payoffAfter = getCurrentPayoff();
            amountOut = lastPayoff.sub(payoffAfter);
            lastPayoff = payoffAfter;
        } else {
            // if before expiry, amount is the decrease in LMSR cost after burning the options
            uint256 costAfter = getCurrentCost();
            amountOut = lastCost.sub(costAfter);
            lastCost = costAfter;
        }
        require(amountOut > 0, "Amount out must be > 0");
        require(amountOut >= minAmountOut, "Max slippage exceeded");

        // transfer amount to user
        baseToken.uniTransfer(msg.sender, amountOut);
        emit Sell(msg.sender, isLongToken, strikeIndex, optionsIn, amountOut, option.totalSupply(), isSettled);
    }

    /**
     * Deposit liquidity
     *
     * `sharesOut` is the intended increase in the parameter `b`
     *
     * This method reverts if the resulting cost is greater than `maxAmountIn`
     */
    function deposit(uint256 sharesOut, uint256 maxAmountIn) external payable nonReentrant returns (uint256 amountIn) {
        require(!isExpired(), "Already expired");
        require(msg.sender == owner() || !isPaused, "Paused");
        require(sharesOut > 0, "Shares out must be > 0");

        // user needs to contribute proportional amount of fees to pool, which
        // ensures they are only earning fees generated after they have deposited
        if (totalSupply() > 0) {
            // add 1 to round up
            amountIn = poolValue.mul(sharesOut).div(totalSupply()).add(1);
            poolValue = poolValue.add(amountIn);
        }
        _mint(msg.sender, sharesOut);
        require(totalSupplyCap == 0 || totalSupply() <= totalSupplyCap, "Total supply cap exceeded");

        // need to add increase in LMSR cost after increasing b
        uint256 costAfter = getCurrentCost();
        amountIn = costAfter.sub(lastCost).add(amountIn); // do sub first as a check since should not fail
        lastCost = costAfter;
        require(amountIn > 0, "Amount in must be > 0");
        require(amountIn <= maxAmountIn, "Max slippage exceeded");

        // transfer in amount from user
        _transferIn(amountIn);
        emit Deposit(msg.sender, sharesOut, amountIn, totalSupply());
    }

    /**
     * Withdraw liquidity
     *
     * `sharesIn` is the intended decrease in the parameter `b`
     *
     * This method reverts if the resulting amount returned is less than `minAmountOut`
     */
    function withdraw(uint256 sharesIn, uint256 minAmountOut) external nonReentrant returns (uint256 amountOut) {
        require(!isExpired() || isSettled, "Must be called before expiry or after settlement");
        require(!isDisputePeriod(), "Dispute period");
        require(msg.sender == owner() || !isPaused, "Paused");
        require(sharesIn > 0, "Shares in must be > 0");

        // calculate cut of fees earned by user
        amountOut = poolValue.mul(sharesIn).div(totalSupply());
        poolValue = poolValue.sub(amountOut);
        _burn(msg.sender, sharesIn);

        // if before expiry, add decrease in LMSR cost after decreasing b
        if (!isSettled) {
            uint256 costAfter = getCurrentCost();
            amountOut = lastCost.sub(costAfter).add(amountOut); // do sub first as a check since should not fail
            lastCost = costAfter;
        }
        require(amountOut > 0, "Amount out must be > 0");
        require(amountOut >= minAmountOut, "Max slippage exceeded");

        // return amount to user
        baseToken.uniTransfer(msg.sender, amountOut);
        emit Withdraw(msg.sender, sharesIn, amountOut, totalSupply(), isSettled);
    }

    /**
     * Retrieve and store the underlying price from the oracle
     *
     * This method can be called by anyone after expiration but cannot be called
     * more than once. In practice it should be called as soon as possible after the
     * expiration time.
     */
    function settle() external nonReentrant {
        require(isExpired(), "Cannot be called before expiry");
        require(!isSettled, "Already settled");

        // fetch expiry price from oracle
        isSettled = true;
        expiryPrice = oracle.getPrice();
        require(expiryPrice > 0, "Price from oracle must be > 0");

        // update cached payoff and pool value
        lastPayoff = getCurrentPayoff();
        poolValue = baseToken.uniBalanceOf(address(this)).sub(lastPayoff);
        emit Settle(expiryPrice);
    }

    /**
     * Calculate LMSR cost
     *
     * Represents total amount locked in the LMSR
     *
     * This value will increase as options are bought and decrease as options
     * are sold. The change in value corresponds to the total cost of a purchase
     * or the amount returned from a sale.
     *
     * This method is only used before expiry. Before expiry, the `baseToken`
     * balance of this contract is always at least current cost + pool value.
     * Current cost is maximum possible amount that needs to be paid out to
     * option holders. Pool value is the fees earned by LPs.
     */
    function getCurrentCost() public view returns (uint256) {
        uint256[] memory longSupplies = getTotalSupplies(longTokens);
        uint256[] memory shortSupplies = getTotalSupplies(shortTokens);
        uint256[] memory quantities = OptionMath.calcQuantities(strikePrices, isPut, longSupplies, shortSupplies);
        return OptionMath.calcLmsrCost(quantities, totalSupply());
    }

    /**
     * Calculate option payoff
     *
     * Represents total payoff to option holders
     *
     * This value will decrease as options are redeemed. The change in value
     * corresponds to the payoff returned from a redemption.
     *
     * This method is only used after expiry. After expiry, the `baseToken` balance
     * of this contract is always at least current payoff + pool value. Current
     * payoff is the amount owed to option holders and pool value is the amount
     * owed to LPs.
     */
    function getCurrentPayoff() public view returns (uint256) {
        uint256[] memory longSupplies = getTotalSupplies(longTokens);
        uint256[] memory shortSupplies = getTotalSupplies(shortTokens);
        return OptionMath.calcPayoff(strikePrices, expiryPrice, isPut, longSupplies, shortSupplies);
    }

    function getTotalSupplies(OptionToken[] memory optionTokens) public view returns (uint256[] memory totalSupplies) {
        totalSupplies = new uint256[](optionTokens.length);
        for (uint256 i = 0; i < optionTokens.length; i++) {
            totalSupplies[i] = optionTokens[i].totalSupply();
        }
    }

    function isExpired() public view returns (bool) {
        return block.timestamp >= expiryTime;
    }

    function isDisputePeriod() public view returns (bool) {
        return block.timestamp >= expiryTime && block.timestamp < expiryTime.add(disputePeriod);
    }

    function numStrikes() external view returns (uint256) {
        return strikePrices.length;
    }

    /**
     * Transfer amount from sender and do additional checks
     */
    function _transferIn(uint256 amountIn) private {
        // save gas
        IERC20 _baseToken = baseToken;
        uint256 balanceBefore = _baseToken.uniBalanceOf(address(this));
        _baseToken.uniTransferFromSenderToThis(amountIn);
        uint256 balanceAfter = _baseToken.uniBalanceOf(address(this));
        require(_baseToken.isETH() || balanceAfter.sub(balanceBefore) == amountIn, "Deflationary tokens not supported");
        require(balanceCap == 0 || _baseToken.uniBalanceOf(address(this)) <= balanceCap, "Balance cap exceeded");
    }

    // used for guarded launch
    function setBalanceCap(uint256 _balanceCap) external onlyOwner {
        balanceCap = _balanceCap;
    }

    // used for guarded launch
    function setTotalSupplyCap(uint256 _totalSupplyCap) external onlyOwner {
        totalSupplyCap = _totalSupplyCap;
    }

    // emergency use only. to be removed in future versions
    function pause() external onlyOwner {
        isPaused = true;
    }

    // emergency use only. to be removed in future versions
    function unpause() external onlyOwner {
        isPaused = false;
    }

    // emergency use only. to be removed in future versions
    function setOracle(IOracle _oracle) external onlyOwner {
        oracle = _oracle;
    }

    // emergency use only. to be removed in future versions
    function setExpiryTime(uint256 _expiryTime) external onlyOwner {
        expiryTime = _expiryTime;
    }

    // emergency use only. to be removed in future versions
    function setDisputePeriod(uint256 _disputePeriod) external onlyOwner {
        disputePeriod = _disputePeriod;
    }

    // emergency use only. to be removed in future versions
    function disputeExpiryPrice(uint256 _expiryPrice) external onlyOwner {
        require(isDisputePeriod(), "Not dispute period");
        require(isSettled, "Cannot be called before settlement");
        expiryPrice = _expiryPrice;

        // update cached payoff and pool value
        lastPayoff = getCurrentPayoff();
        poolValue = baseToken.uniBalanceOf(address(this)).sub(lastPayoff);
        emit Settle(_expiryPrice);
    }

    // emergency use only. to be removed in future versions
    function emergencyWithdraw() external onlyOwner {
        baseToken.uniTransfer(msg.sender, baseToken.uniBalanceOf(address(this)));
    }
}

// Part: OptionFactory

contract OptionFactory is CloneFactory, OptionSymbol, ReentrancyGuard {
    using Address for address;
    using SafeERC20 for IERC20;
    using UniERC20 for IERC20;
    using SafeMath for uint256;

    address public optionMarketLibrary;
    address public optionTokenLibrary;
    address[] public markets;

    constructor(address _optionMarketLibrary, address _optionTokenLibrary) public {
        require(_optionMarketLibrary != address(0), "optionMarketLibrary should not be address 0");
        require(_optionTokenLibrary != address(0), "optionTokenLibrary should not be address 0");
        optionMarketLibrary = _optionMarketLibrary;
        optionTokenLibrary = _optionTokenLibrary;
    }

    function createMarket(
        address baseAsset,
        address quoteAsset,
        address oracle,
        uint256[] memory strikePrices,
        uint256 expiryTime,
        bool isPut,
        uint256 tradingFee
    ) external nonReentrant returns (address marketAddress) {
        marketAddress = createClone(optionMarketLibrary);
        markets.push(marketAddress);

        string memory underlyingSymbol = IERC20(baseAsset).uniSymbol();
        string memory lpSymbol = getMarketSymbol(underlyingSymbol, expiryTime, isPut);
        address baseToken = isPut ? quoteAsset : baseAsset;

        address[] memory longTokens = new address[](strikePrices.length);
        address[] memory shortTokens = new address[](strikePrices.length);

        // use scoping to avoid stack too deep error
        {
            uint8 decimals = IERC20(baseToken).isETH() ? 18 : ERC20UpgradeSafe(baseToken).decimals();

            for (uint256 i = 0; i < strikePrices.length; i++) {
                longTokens[i] = createClone(optionTokenLibrary);
                string memory optionSymbol = getOptionSymbol(
                    underlyingSymbol,
                    strikePrices[i],
                    expiryTime,
                    isPut,
                    true
                );
                OptionToken(longTokens[i]).initialize(marketAddress, optionSymbol, optionSymbol, decimals);
            }

            for (uint256 i = 0; i < strikePrices.length; i++) {
                shortTokens[i] = createClone(optionTokenLibrary);
                string memory optionSymbol = getOptionSymbol(
                    underlyingSymbol,
                    strikePrices[i],
                    expiryTime,
                    isPut,
                    false
                );
                OptionToken(shortTokens[i]).initialize(marketAddress, optionSymbol, optionSymbol, decimals);
            }
        }

        OptionMarket(marketAddress).initialize(
            baseToken,
            oracle,
            longTokens,
            shortTokens,
            strikePrices,
            expiryTime,
            isPut,
            tradingFee,
            lpSymbol
        );

        // transfer ownership to sender
        OptionMarket(marketAddress).transferOwnership(msg.sender);
    }

    function numMarkets() external view returns (uint256) {
        return markets.length;
    }
}

// File: OptionRegistry.sol

contract OptionRegistry is OptionSymbol {
    using Address for address;
    using SafeERC20 for IERC20;
    using UniERC20 for IERC20;
    using SafeMath for uint256;

    struct OptionDetails {
        bool isLong;
        uint256 strikeIndex;
        uint256 strikePrice;
    }

    OptionFactory public immutable factory;
    uint256 public lastIndex;

    mapping(string => OptionMarket) internal markets;
    mapping(string => OptionToken) internal options;
    mapping(OptionToken => OptionDetails) internal optionDetails;

    /**
     * @param _factory {OptionFactory} instance from which markets are retrieved
     * @param _lastIndex Don't add markets with this index or smaller. This saves
     * gas when `populateMarkets()` is initially called
     */
    constructor(address _factory, uint256 _lastIndex) public {
        factory = OptionFactory(_factory);
        lastIndex = _lastIndex;
    }

    /**
     * @dev Fetch option market
     * @param underlying Address of underlying token. Equal to 0x0 for ETH
     * @param expiryTime Expiry time as timestamp
     * @param isPut True if put, false if call
     */
    function getMarket(IERC20 underlying, uint256 expiryTime, bool isPut) external view returns (OptionMarket) {
        string memory symbol = getMarketSymbol(underlying.uniSymbol(), expiryTime, isPut);
        return markets[symbol];
    }

    /**
     * @dev Fetch option token
     * @param underlying Address of underlying token. Equal to 0x0 for ETH
     * @param expiryTime Expiry time as timestamp
     * @param isPut True if put, false if call
     * @param strikePrice Strike price in USDC multiplied by 1e18
     * @param isLong True if long position, false if short position
     */
    function getOption(IERC20 underlying, uint256 expiryTime, bool isPut, uint256 strikePrice, bool isLong) external view returns (OptionToken) {
        string memory symbol = getOptionSymbol(underlying.uniSymbol(), strikePrice, expiryTime, isPut, isLong);
        return options[symbol];
    }

    /**
     * @dev Fetch option details
     * @param optionToken Option token
     */
    function getOptionDetails(OptionToken optionToken) external view returns (OptionDetails memory) {
        return optionDetails[optionToken];
    }

    /**
     * @dev Add mappings for any new markets that have been added to factory
     * since the last time this method was called
     */
    function populateMarkets() external {
        populateMarketsUntil(factory.numMarkets());
    }

    /**
     * @dev Same as {populateMarkets} but only adds markets up to a given index
     */
    function populateMarketsUntil(uint256 index) public {
        require(index > lastIndex, "OptionRegistry: No new markets to add");
        require(index <= factory.numMarkets(), "OptionRegistry: index out of bounds");

        for (uint256 i = lastIndex; i < index; i = i.add(1)) {
            OptionMarket market = OptionMarket(factory.markets(i));
            _populateMarket(market);
        }
        lastIndex = index;
    }

    function _populateMarket(OptionMarket market) internal {
        markets[market.symbol()] = market;

        uint256 numStrikes = market.numStrikes();
        for (uint256 i = 0; i < numStrikes; i = i.add(1)) {
            OptionToken longToken = market.longTokens(i);
            OptionToken shortToken = market.shortTokens(i);
            uint256 strikePrice = market.strikePrices(i);

            options[longToken.symbol()] = longToken;
            options[shortToken.symbol()] = shortToken;
            optionDetails[longToken] = OptionDetails(true, i, strikePrice);
            optionDetails[shortToken] = OptionDetails(false, i, strikePrice);
        }
    }
}