// SPDX-License-Identifier: MIT

// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/GSN/Context.sol


pragma solidity ^0.6.12;

/*
 * @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.
 */
abstract contract Context {
    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;
    }
}

// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/access/Ownable.sol

pragma solidity ^0.6.12;

/**
 * @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 Ownable is Context {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor () internal {
        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;
    }
}

pragma solidity ^0.6.12;

 /**
 * @title Power function by Bancor
 * @dev https://github.com/bancorprotocol/contracts
 *
 * Modified from the original by Slava Balasanov & Tarrence van As
 *
 * Split Power.sol out from BancorFormula.sol
 * https://github.com/bancorprotocol/contracts/blob/c9adc95e82fdfb3a0ada102514beb8ae00147f5d/solidity/contracts/converter/BancorFormula.sol
 */
contract Power {
  string public version = "0.3";

  uint256 private constant ONE = 1;
  uint8 private constant MIN_PRECISION = 32;
  uint8 private constant MAX_PRECISION = 127;

  /**
    The values below depend on MAX_PRECISION. If you choose to change it:
    Apply the same change in file 'PrintIntScalingFactors.py', run it and paste the results below.
  */
  uint256 private constant FIXED_1 = 0x080000000000000000000000000000000;
  uint256 private constant FIXED_2 = 0x100000000000000000000000000000000;
  uint256 private constant MAX_NUM = 0x200000000000000000000000000000000;

  /**
      Auto-generated via 'PrintLn2ScalingFactors.py'
  */
  uint256 private constant LN2_NUMERATOR   = 0x3f80fe03f80fe03f80fe03f80fe03f8;
  uint256 private constant LN2_DENOMINATOR = 0x5b9de1d10bf4103d647b0955897ba80;

  /**
      Auto-generated via 'PrintFunctionOptimalLog.py' and 'PrintFunctionOptimalExp.py'
  */
  uint256 private constant OPT_LOG_MAX_VAL =
  0x15bf0a8b1457695355fb8ac404e7a79e3;
  uint256 private constant OPT_EXP_MAX_VAL =
  0x800000000000000000000000000000000;

  /**
    The values below depend on MIN_PRECISION and MAX_PRECISION. If you choose to change either one of them:
    Apply the same change in file 'PrintFunctionBancorFormula.py', run it and paste the results below.
  */
  uint256[128] private maxExpArray;
  constructor() public {
//  maxExpArray[0] = 0x6bffffffffffffffffffffffffffffffff;
//  maxExpArray[1] = 0x67ffffffffffffffffffffffffffffffff;
//  maxExpArray[2] = 0x637fffffffffffffffffffffffffffffff;
//  maxExpArray[3] = 0x5f6fffffffffffffffffffffffffffffff;
//  maxExpArray[4] = 0x5b77ffffffffffffffffffffffffffffff;
//  maxExpArray[5] = 0x57b3ffffffffffffffffffffffffffffff;
//  maxExpArray[6] = 0x5419ffffffffffffffffffffffffffffff;
//  maxExpArray[7] = 0x50a2ffffffffffffffffffffffffffffff;
//  maxExpArray[8] = 0x4d517fffffffffffffffffffffffffffff;
//  maxExpArray[9] = 0x4a233fffffffffffffffffffffffffffff;
//  maxExpArray[10] = 0x47165fffffffffffffffffffffffffffff;
//  maxExpArray[11] = 0x4429afffffffffffffffffffffffffffff;
//  maxExpArray[12] = 0x415bc7ffffffffffffffffffffffffffff;
//  maxExpArray[13] = 0x3eab73ffffffffffffffffffffffffffff;
//  maxExpArray[14] = 0x3c1771ffffffffffffffffffffffffffff;
//  maxExpArray[15] = 0x399e96ffffffffffffffffffffffffffff;
//  maxExpArray[16] = 0x373fc47fffffffffffffffffffffffffff;
//  maxExpArray[17] = 0x34f9e8ffffffffffffffffffffffffffff;
//  maxExpArray[18] = 0x32cbfd5fffffffffffffffffffffffffff;
//  maxExpArray[19] = 0x30b5057fffffffffffffffffffffffffff;
//  maxExpArray[20] = 0x2eb40f9fffffffffffffffffffffffffff;
//  maxExpArray[21] = 0x2cc8340fffffffffffffffffffffffffff;
//  maxExpArray[22] = 0x2af09481ffffffffffffffffffffffffff;
//  maxExpArray[23] = 0x292c5bddffffffffffffffffffffffffff;
//  maxExpArray[24] = 0x277abdcdffffffffffffffffffffffffff;
//  maxExpArray[25] = 0x25daf6657fffffffffffffffffffffffff;
//  maxExpArray[26] = 0x244c49c65fffffffffffffffffffffffff;
//  maxExpArray[27] = 0x22ce03cd5fffffffffffffffffffffffff;
//  maxExpArray[28] = 0x215f77c047ffffffffffffffffffffffff;
//  maxExpArray[29] = 0x1fffffffffffffffffffffffffffffffff;
//  maxExpArray[30] = 0x1eaefdbdabffffffffffffffffffffffff;
//  maxExpArray[31] = 0x1d6bd8b2ebffffffffffffffffffffffff;
    maxExpArray[32] = 0x1c35fedd14ffffffffffffffffffffffff;
    maxExpArray[33] = 0x1b0ce43b323fffffffffffffffffffffff;
    maxExpArray[34] = 0x19f0028ec1ffffffffffffffffffffffff;
    maxExpArray[35] = 0x18ded91f0e7fffffffffffffffffffffff;
    maxExpArray[36] = 0x17d8ec7f0417ffffffffffffffffffffff;
    maxExpArray[37] = 0x16ddc6556cdbffffffffffffffffffffff;
    maxExpArray[38] = 0x15ecf52776a1ffffffffffffffffffffff;
    maxExpArray[39] = 0x15060c256cb2ffffffffffffffffffffff;
    maxExpArray[40] = 0x1428a2f98d72ffffffffffffffffffffff;
    maxExpArray[41] = 0x13545598e5c23fffffffffffffffffffff;
    maxExpArray[42] = 0x1288c4161ce1dfffffffffffffffffffff;
    maxExpArray[43] = 0x11c592761c666fffffffffffffffffffff;
    maxExpArray[44] = 0x110a688680a757ffffffffffffffffffff;
    maxExpArray[45] = 0x1056f1b5bedf77ffffffffffffffffffff;
    maxExpArray[46] = 0x0faadceceeff8bffffffffffffffffffff;
    maxExpArray[47] = 0x0f05dc6b27edadffffffffffffffffffff;
    maxExpArray[48] = 0x0e67a5a25da4107fffffffffffffffffff;
    maxExpArray[49] = 0x0dcff115b14eedffffffffffffffffffff;
    maxExpArray[50] = 0x0d3e7a392431239fffffffffffffffffff;
    maxExpArray[51] = 0x0cb2ff529eb71e4fffffffffffffffffff;
    maxExpArray[52] = 0x0c2d415c3db974afffffffffffffffffff;
    maxExpArray[53] = 0x0bad03e7d883f69bffffffffffffffffff;
    maxExpArray[54] = 0x0b320d03b2c343d5ffffffffffffffffff;
    maxExpArray[55] = 0x0abc25204e02828dffffffffffffffffff;
    maxExpArray[56] = 0x0a4b16f74ee4bb207fffffffffffffffff;
    maxExpArray[57] = 0x09deaf736ac1f569ffffffffffffffffff;
    maxExpArray[58] = 0x0976bd9952c7aa957fffffffffffffffff;
    maxExpArray[59] = 0x09131271922eaa606fffffffffffffffff;
    maxExpArray[60] = 0x08b380f3558668c46fffffffffffffffff;
    maxExpArray[61] = 0x0857ddf0117efa215bffffffffffffffff;
    maxExpArray[62] = 0x07ffffffffffffffffffffffffffffffff;
    maxExpArray[63] = 0x07abbf6f6abb9d087fffffffffffffffff;
    maxExpArray[64] = 0x075af62cbac95f7dfa7fffffffffffffff;
    maxExpArray[65] = 0x070d7fb7452e187ac13fffffffffffffff;
    maxExpArray[66] = 0x06c3390ecc8af379295fffffffffffffff;
    maxExpArray[67] = 0x067c00a3b07ffc01fd6fffffffffffffff;
    maxExpArray[68] = 0x0637b647c39cbb9d3d27ffffffffffffff;
    maxExpArray[69] = 0x05f63b1fc104dbd39587ffffffffffffff;
    maxExpArray[70] = 0x05b771955b36e12f7235ffffffffffffff;
    maxExpArray[71] = 0x057b3d49dda84556d6f6ffffffffffffff;
    maxExpArray[72] = 0x054183095b2c8ececf30ffffffffffffff;
    maxExpArray[73] = 0x050a28be635ca2b888f77fffffffffffff;
    maxExpArray[74] = 0x04d5156639708c9db33c3fffffffffffff;
    maxExpArray[75] = 0x04a23105873875bd52dfdfffffffffffff;
    maxExpArray[76] = 0x0471649d87199aa990756fffffffffffff;
    maxExpArray[77] = 0x04429a21a029d4c1457cfbffffffffffff;
    maxExpArray[78] = 0x0415bc6d6fb7dd71af2cb3ffffffffffff;
    maxExpArray[79] = 0x03eab73b3bbfe282243ce1ffffffffffff;
    maxExpArray[80] = 0x03c1771ac9fb6b4c18e229ffffffffffff;
    maxExpArray[81] = 0x0399e96897690418f785257fffffffffff;
    maxExpArray[82] = 0x0373fc456c53bb779bf0ea9fffffffffff;
    maxExpArray[83] = 0x034f9e8e490c48e67e6ab8bfffffffffff;
    maxExpArray[84] = 0x032cbfd4a7adc790560b3337ffffffffff;
    maxExpArray[85] = 0x030b50570f6e5d2acca94613ffffffffff;
    maxExpArray[86] = 0x02eb40f9f620fda6b56c2861ffffffffff;
    maxExpArray[87] = 0x02cc8340ecb0d0f520a6af58ffffffffff;
    maxExpArray[88] = 0x02af09481380a0a35cf1ba02ffffffffff;
    maxExpArray[89] = 0x0292c5bdd3b92ec810287b1b3fffffffff;
    maxExpArray[90] = 0x0277abdcdab07d5a77ac6d6b9fffffffff;
    maxExpArray[91] = 0x025daf6654b1eaa55fd64df5efffffffff;
    maxExpArray[92] = 0x0244c49c648baa98192dce88b7ffffffff;
    maxExpArray[93] = 0x022ce03cd5619a311b2471268bffffffff;
    maxExpArray[94] = 0x0215f77c045fbe885654a44a0fffffffff;
    maxExpArray[95] = 0x01ffffffffffffffffffffffffffffffff;
    maxExpArray[96] = 0x01eaefdbdaaee7421fc4d3ede5ffffffff;
    maxExpArray[97] = 0x01d6bd8b2eb257df7e8ca57b09bfffffff;
    maxExpArray[98] = 0x01c35fedd14b861eb0443f7f133fffffff;
    maxExpArray[99] = 0x01b0ce43b322bcde4a56e8ada5afffffff;
    maxExpArray[100] = 0x019f0028ec1fff007f5a195a39dfffffff;
    maxExpArray[101] = 0x018ded91f0e72ee74f49b15ba527ffffff;
    maxExpArray[102] = 0x017d8ec7f04136f4e5615fd41a63ffffff;
    maxExpArray[103] = 0x016ddc6556cdb84bdc8d12d22e6fffffff;
    maxExpArray[104] = 0x015ecf52776a1155b5bd8395814f7fffff;
    maxExpArray[105] = 0x015060c256cb23b3b3cc3754cf40ffffff;
    maxExpArray[106] = 0x01428a2f98d728ae223ddab715be3fffff;
    maxExpArray[107] = 0x013545598e5c23276ccf0ede68034fffff;
    maxExpArray[108] = 0x01288c4161ce1d6f54b7f61081194fffff;
    maxExpArray[109] = 0x011c592761c666aa641d5a01a40f17ffff;
    maxExpArray[110] = 0x0110a688680a7530515f3e6e6cfdcdffff;
    maxExpArray[111] = 0x01056f1b5bedf75c6bcb2ce8aed428ffff;
    maxExpArray[112] = 0x00faadceceeff8a0890f3875f008277fff;
    maxExpArray[113] = 0x00f05dc6b27edad306388a600f6ba0bfff;
    maxExpArray[114] = 0x00e67a5a25da41063de1495d5b18cdbfff;
    maxExpArray[115] = 0x00dcff115b14eedde6fc3aa5353f2e4fff;
    maxExpArray[116] = 0x00d3e7a3924312399f9aae2e0f868f8fff;
    maxExpArray[117] = 0x00cb2ff529eb71e41582cccd5a1ee26fff;
    maxExpArray[118] = 0x00c2d415c3db974ab32a51840c0b67edff;
    maxExpArray[119] = 0x00bad03e7d883f69ad5b0a186184e06bff;
    maxExpArray[120] = 0x00b320d03b2c343d4829abd6075f0cc5ff;
    maxExpArray[121] = 0x00abc25204e02828d73c6e80bcdb1a95bf;
    maxExpArray[122] = 0x00a4b16f74ee4bb2040a1ec6c15fbbf2df;
    maxExpArray[123] = 0x009deaf736ac1f569deb1b5ae3f36c130f;
    maxExpArray[124] = 0x00976bd9952c7aa957f5937d790ef65037;
    maxExpArray[125] = 0x009131271922eaa6064b73a22d0bd4f2bf;
    maxExpArray[126] = 0x008b380f3558668c46c91c49a2f8e967b9;
    maxExpArray[127] = 0x00857ddf0117efa215952912839f6473e6;
  }

  /**
    General Description:
        Determine a value of precision.
        Calculate an integer approximation of (_baseN / _baseD) ^ (_expN / _expD) * 2 ^ precision.
        Return the result along with the precision used.
     Detailed Description:
        Instead of calculating "base ^ exp", we calculate "e ^ (log(base) * exp)".
        The value of "log(base)" is represented with an integer slightly smaller than "log(base) * 2 ^ precision".
        The larger "precision" is, the more accurately this value represents the real value.
        However, the larger "precision" is, the more bits are required in order to store this value.
        And the exponentiation function, which takes "x" and calculates "e ^ x", is limited to a maximum exponent (maximum value of "x").
        This maximum exponent depends on the "precision" used, and it is given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
        Hence we need to determine the highest precision which can be used for the given input, before calling the exponentiation function.
        This allows us to compute "base ^ exp" with maximum accuracy and without exceeding 256 bits in any of the intermediate computations.
        This functions assumes that "_expN < 2 ^ 256 / log(MAX_NUM - 1)", otherwise the multiplication should be replaced with a "safeMul".
  */
  function power(
    uint256 _baseN,
    uint256 _baseD,
    uint32 _expN,
    uint32 _expD
  ) internal view returns (uint256, uint8)
  {
    assert(_baseN < MAX_NUM);
    require(_baseN >= _baseD, "Bases < 1 are not supported.");

    uint256 baseLog;
    uint256 base = _baseN * FIXED_1 / _baseD;
    if (base < OPT_LOG_MAX_VAL) {
      baseLog = optimalLog(base);
    } else {
      baseLog = generalLog(base);
    }

    uint256 baseLogTimesExp = baseLog * _expN / _expD;
    if (baseLogTimesExp < OPT_EXP_MAX_VAL) {
      return (optimalExp(baseLogTimesExp), MAX_PRECISION);
    } else {
      uint8 precision = findPositionInMaxExpArray(baseLogTimesExp);
      return (generalExp(baseLogTimesExp >> (MAX_PRECISION - precision), precision), precision);
    }
  }

  /**
      Compute log(x / FIXED_1) * FIXED_1.
      This functions assumes that "x >= FIXED_1", because the output would be negative otherwise.
  */
  function generalLog(uint256 _x) internal pure returns (uint256) {
    uint256 res = 0;
    uint256 x = _x;

    // If x >= 2, then we compute the integer part of log2(x), which is larger than 0.
    if (x >= FIXED_2) {
      uint8 count = floorLog2(x / FIXED_1);
      x >>= count; // now x < 2
      res = count * FIXED_1;
    }

    // If x > 1, then we compute the fraction part of log2(x), which is larger than 0.
    if (x > FIXED_1) {
      for (uint8 i = MAX_PRECISION; i > 0; --i) {
        x = (x * x) / FIXED_1; // now 1 < x < 4
        if (x >= FIXED_2) {
          x >>= 1; // now 1 < x < 2
          res += ONE << (i - 1);
        }
      }
    }

    return res * LN2_NUMERATOR / LN2_DENOMINATOR;
  }

  /**
    Compute the largest integer smaller than or equal to the binary logarithm of the input.
  */
  function floorLog2(uint256 _n) internal pure returns (uint8) {
    uint8 res = 0;
    uint256 n = _n;

    if (n < 256) {
      // At most 8 iterations
      while (n > 1) {
        n >>= 1;
        res += 1;
      }
    } else {
      // Exactly 8 iterations
      for (uint8 s = 128; s > 0; s >>= 1) {
        if (n >= (ONE << s)) {
          n >>= s;
          res |= s;
        }
      }
    }

    return res;
  }

  /**
      The global "maxExpArray" is sorted in descending order, and therefore the following statements are equivalent:
      - This function finds the position of [the smallest value in "maxExpArray" larger than or equal to "x"]
      - This function finds the highest position of [a value in "maxExpArray" larger than or equal to "x"]
  */
  function findPositionInMaxExpArray(uint256 _x)
  internal view returns (uint8)
  {
    uint8 lo = MIN_PRECISION;
    uint8 hi = MAX_PRECISION;

    while (lo + 1 < hi) {
      uint8 mid = (lo + hi) / 2;
      if (maxExpArray[mid] >= _x)
        lo = mid;
      else
        hi = mid;
    }

    if (maxExpArray[hi] >= _x)
      return hi;
    if (maxExpArray[lo] >= _x)
      return lo;

    assert(false);
    return 0;
  }

  /* solium-disable */
  /**
       This function can be auto-generated by the script 'PrintFunctionGeneralExp.py'.
       It approximates "e ^ x" via maclaurin summation: "(x^0)/0! + (x^1)/1! + ... + (x^n)/n!".
       It returns "e ^ (x / 2 ^ precision) * 2 ^ precision", that is, the result is upshifted for accuracy.
       The global "maxExpArray" maps each "precision" to "((maximumExponent + 1) << (MAX_PRECISION - precision)) - 1".
       The maximum permitted value for "x" is therefore given by "maxExpArray[precision] >> (MAX_PRECISION - precision)".
   */
   function generalExp(uint256 _x, uint8 _precision) internal pure returns (uint256) {
       uint256 xi = _x;
       uint256 res = 0;

       xi = (xi * _x) >> _precision; res += xi * 0x3442c4e6074a82f1797f72ac0000000; // add x^02 * (33! / 02!)
       xi = (xi * _x) >> _precision; res += xi * 0x116b96f757c380fb287fd0e40000000; // add x^03 * (33! / 03!)
       xi = (xi * _x) >> _precision; res += xi * 0x045ae5bdd5f0e03eca1ff4390000000; // add x^04 * (33! / 04!)
       xi = (xi * _x) >> _precision; res += xi * 0x00defabf91302cd95b9ffda50000000; // add x^05 * (33! / 05!)
       xi = (xi * _x) >> _precision; res += xi * 0x002529ca9832b22439efff9b8000000; // add x^06 * (33! / 06!)
       xi = (xi * _x) >> _precision; res += xi * 0x00054f1cf12bd04e516b6da88000000; // add x^07 * (33! / 07!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000a9e39e257a09ca2d6db51000000; // add x^08 * (33! / 08!)
       xi = (xi * _x) >> _precision; res += xi * 0x000012e066e7b839fa050c309000000; // add x^09 * (33! / 09!)
       xi = (xi * _x) >> _precision; res += xi * 0x000001e33d7d926c329a1ad1a800000; // add x^10 * (33! / 10!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000002bee513bdb4a6b19b5f800000; // add x^11 * (33! / 11!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000003a9316fa79b88eccf2a00000; // add x^12 * (33! / 12!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000048177ebe1fa812375200000; // add x^13 * (33! / 13!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000005263fe90242dcbacf00000; // add x^14 * (33! / 14!)
       xi = (xi * _x) >> _precision; res += xi * 0x000000000057e22099c030d94100000; // add x^15 * (33! / 15!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000057e22099c030d9410000; // add x^16 * (33! / 16!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000052b6b54569976310000; // add x^17 * (33! / 17!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000004985f67696bf748000; // add x^18 * (33! / 18!)
       xi = (xi * _x) >> _precision; res += xi * 0x000000000000003dea12ea99e498000; // add x^19 * (33! / 19!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000000031880f2214b6e000; // add x^20 * (33! / 20!)
       xi = (xi * _x) >> _precision; res += xi * 0x000000000000000025bcff56eb36000; // add x^21 * (33! / 21!)
       xi = (xi * _x) >> _precision; res += xi * 0x000000000000000001b722e10ab1000; // add x^22 * (33! / 22!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000001317c70077000; // add x^23 * (33! / 23!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000000000000cba84aafa00; // add x^24 * (33! / 24!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000000000000082573a0a00; // add x^25 * (33! / 25!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000000000000005035ad900; // add x^26 * (33! / 26!)
       xi = (xi * _x) >> _precision; res += xi * 0x000000000000000000000002f881b00; // add x^27 * (33! / 27!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000000000001b29340; // add x^28 * (33! / 28!)
       xi = (xi * _x) >> _precision; res += xi * 0x00000000000000000000000000efc40; // add x^29 * (33! / 29!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000000000000007fe0; // add x^30 * (33! / 30!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000000000000000420; // add x^31 * (33! / 31!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000000000000000021; // add x^32 * (33! / 32!)
       xi = (xi * _x) >> _precision; res += xi * 0x0000000000000000000000000000001; // add x^33 * (33! / 33!)

       return res / 0x688589cc0e9505e2f2fee5580000000 + _x + (ONE << _precision); // divide by 33! and then add x^1 / 1! + x^0 / 0!
   }

   /**
       Return log(x / FIXED_1) * FIXED_1
       Input range: FIXED_1 <= x <= LOG_EXP_MAX_VAL - 1
       Auto-generated via 'PrintFunctionOptimalLog.py'
   */
   function optimalLog(uint256 x) internal pure returns (uint256) {
       uint256 res = 0;

       uint256 y;
       uint256 z;
       uint256 w;

       if (x >= 0xd3094c70f034de4b96ff7d5b6f99fcd8) {res += 0x40000000000000000000000000000000; x = x * FIXED_1 / 0xd3094c70f034de4b96ff7d5b6f99fcd8;}
       if (x >= 0xa45af1e1f40c333b3de1db4dd55f29a7) {res += 0x20000000000000000000000000000000; x = x * FIXED_1 / 0xa45af1e1f40c333b3de1db4dd55f29a7;}
       if (x >= 0x910b022db7ae67ce76b441c27035c6a1) {res += 0x10000000000000000000000000000000; x = x * FIXED_1 / 0x910b022db7ae67ce76b441c27035c6a1;}
       if (x >= 0x88415abbe9a76bead8d00cf112e4d4a8) {res += 0x08000000000000000000000000000000; x = x * FIXED_1 / 0x88415abbe9a76bead8d00cf112e4d4a8;}
       if (x >= 0x84102b00893f64c705e841d5d4064bd3) {res += 0x04000000000000000000000000000000; x = x * FIXED_1 / 0x84102b00893f64c705e841d5d4064bd3;}
       if (x >= 0x8204055aaef1c8bd5c3259f4822735a2) {res += 0x02000000000000000000000000000000; x = x * FIXED_1 / 0x8204055aaef1c8bd5c3259f4822735a2;}
       if (x >= 0x810100ab00222d861931c15e39b44e99) {res += 0x01000000000000000000000000000000; x = x * FIXED_1 / 0x810100ab00222d861931c15e39b44e99;}
       if (x >= 0x808040155aabbbe9451521693554f733) {res += 0x00800000000000000000000000000000; x = x * FIXED_1 / 0x808040155aabbbe9451521693554f733;}

       z = y = x - FIXED_1;
       w = y * y / FIXED_1;
       res += z * (0x100000000000000000000000000000000 - y) / 0x100000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x0aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa - y) / 0x200000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x099999999999999999999999999999999 - y) / 0x300000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x092492492492492492492492492492492 - y) / 0x400000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x08e38e38e38e38e38e38e38e38e38e38e - y) / 0x500000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x08ba2e8ba2e8ba2e8ba2e8ba2e8ba2e8b - y) / 0x600000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x089d89d89d89d89d89d89d89d89d89d89 - y) / 0x700000000000000000000000000000000; z = z * w / FIXED_1;
       res += z * (0x088888888888888888888888888888888 - y) / 0x800000000000000000000000000000000;

       return res;
   }

   /**
       Return e ^ (x / FIXED_1) * FIXED_1
       Input range: 0 <= x <= OPT_EXP_MAX_VAL - 1
       Auto-generated via 'PrintFunctionOptimalExp.py'
   */
   function optimalExp(uint256 x) internal pure returns (uint256) {
       uint256 res = 0;

       uint256 y;
       uint256 z;

       z = y = x % 0x10000000000000000000000000000000;
       z = z * y / FIXED_1; res += z * 0x10e1b3be415a0000; // add y^02 * (20! / 02!)
       z = z * y / FIXED_1; res += z * 0x05a0913f6b1e0000; // add y^03 * (20! / 03!)
       z = z * y / FIXED_1; res += z * 0x0168244fdac78000; // add y^04 * (20! / 04!)
       z = z * y / FIXED_1; res += z * 0x004807432bc18000; // add y^05 * (20! / 05!)
       z = z * y / FIXED_1; res += z * 0x000c0135dca04000; // add y^06 * (20! / 06!)
       z = z * y / FIXED_1; res += z * 0x0001b707b1cdc000; // add y^07 * (20! / 07!)
       z = z * y / FIXED_1; res += z * 0x000036e0f639b800; // add y^08 * (20! / 08!)
       z = z * y / FIXED_1; res += z * 0x00000618fee9f800; // add y^09 * (20! / 09!)
       z = z * y / FIXED_1; res += z * 0x0000009c197dcc00; // add y^10 * (20! / 10!)
       z = z * y / FIXED_1; res += z * 0x0000000e30dce400; // add y^11 * (20! / 11!)
       z = z * y / FIXED_1; res += z * 0x000000012ebd1300; // add y^12 * (20! / 12!)
       z = z * y / FIXED_1; res += z * 0x0000000017499f00; // add y^13 * (20! / 13!)
       z = z * y / FIXED_1; res += z * 0x0000000001a9d480; // add y^14 * (20! / 14!)
       z = z * y / FIXED_1; res += z * 0x00000000001c6380; // add y^15 * (20! / 15!)
       z = z * y / FIXED_1; res += z * 0x000000000001c638; // add y^16 * (20! / 16!)
       z = z * y / FIXED_1; res += z * 0x0000000000001ab8; // add y^17 * (20! / 17!)
       z = z * y / FIXED_1; res += z * 0x000000000000017c; // add y^18 * (20! / 18!)
       z = z * y / FIXED_1; res += z * 0x0000000000000014; // add y^19 * (20! / 19!)
       z = z * y / FIXED_1; res += z * 0x0000000000000001; // add y^20 * (20! / 20!)
       res = res / 0x21c3677c82b40000 + y + FIXED_1; // divide by 20! and then add y^1 / 1! + y^0 / 0!

       if ((x & 0x010000000000000000000000000000000) != 0) res = res * 0x1c3d6a24ed82218787d624d3e5eba95f9 / 0x18ebef9eac820ae8682b9793ac6d1e776;
       if ((x & 0x020000000000000000000000000000000) != 0) res = res * 0x18ebef9eac820ae8682b9793ac6d1e778 / 0x1368b2fc6f9609fe7aceb46aa619baed4;
       if ((x & 0x040000000000000000000000000000000) != 0) res = res * 0x1368b2fc6f9609fe7aceb46aa619baed5 / 0x0bc5ab1b16779be3575bd8f0520a9f21f;
       if ((x & 0x080000000000000000000000000000000) != 0) res = res * 0x0bc5ab1b16779be3575bd8f0520a9f21e / 0x0454aaa8efe072e7f6ddbab84b40a55c9;
       if ((x & 0x100000000000000000000000000000000) != 0) res = res * 0x0454aaa8efe072e7f6ddbab84b40a55c5 / 0x00960aadc109e7a3bf4578099615711ea;
       if ((x & 0x200000000000000000000000000000000) != 0) res = res * 0x00960aadc109e7a3bf4578099615711d7 / 0x0002bf84208204f5977f9a8cf01fdce3d;
       if ((x & 0x400000000000000000000000000000000) != 0) res = res * 0x0002bf84208204f5977f9a8cf01fdc307 / 0x0000003c6ab775dd0b95b4cbee7e65d11;

       return res;
   }
   /* solium-enable */
}
// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/utils/Address.sol


pragma solidity ^0.6.12;

/**
 * @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 on 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");
        require(isContract(target), "Address: call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.call{ value: value }(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data, string memory errorMessage) internal view returns (bytes memory) {
        require(isContract(target), "Address: static call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.staticcall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.3._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.3._
     */
    function functionDelegateCall(address target, bytes memory data, string memory errorMessage) internal returns (bytes memory) {
        require(isContract(target), "Address: delegate call to non-contract");

        // solhint-disable-next-line avoid-low-level-calls
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return _verifyCallResult(success, returndata, errorMessage);
    }

    function _verifyCallResult(bool success, bytes memory returndata, string memory errorMessage) private pure returns(bytes memory) {
        if (success) {
            return returndata;
        } else {
            // Look for revert reason and bubble it up if present
            if (returndata.length > 0) {
                // The easiest way to bubble the revert reason is using memory via assembly

                // solhint-disable-next-line no-inline-assembly
                assembly {
                    let returndata_size := mload(returndata)
                    revert(add(32, returndata), returndata_size)
                }
            } else {
                revert(errorMessage);
            }
        }
    }
}

// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/payment/escrow/Escrow.sol


pragma solidity ^0.6.12;




 /**
  * @title Escrow
  * @dev Base escrow contract, holds funds designated for a payee until they
  * withdraw them.
  *
  * Intended usage: This contract (and derived escrow contracts) should be a
  * standalone contract, that only interacts with the contract that instantiated
  * it. That way, it is guaranteed that all Ether will be handled according to
  * the `Escrow` rules, and there is no need to check for payable functions or
  * transfers in the inheritance tree. The contract that uses the escrow as its
  * payment method should be its owner, and provide public methods redirecting
  * to the escrow's deposit and withdraw.
  */
contract Escrow is Ownable {
    using SafeMath for uint256;
    using Address for address payable;

    event Deposited(address indexed payee, uint256 weiAmount);
    event Withdrawn(address indexed payee, uint256 weiAmount);

    mapping(address => uint256) private _deposits;

    function depositsOf(address payee) public view returns (uint256) {
        return _deposits[payee];
    }

    /**
     * @dev Stores the sent amount as credit to be withdrawn.
     * @param payee The destination address of the funds.
     */
    function deposit(address payee) public virtual payable onlyOwner {
        uint256 amount = msg.value;
        _deposits[payee] = _deposits[payee].add(amount);

        emit Deposited(payee, amount);
    }

    /**
     * @dev Withdraw accumulated balance for a payee, forwarding all gas to the
     * recipient.
     *
     * WARNING: Forwarding all gas opens the door to reentrancy vulnerabilities.
     * Make sure you trust the recipient, or are either following the
     * checks-effects-interactions pattern or using {ReentrancyGuard}.
     *
     * @param payee The address whose funds will be withdrawn and transferred to.
     */
    function withdraw(address payable payee) public virtual onlyOwner {
        uint256 payment = _deposits[payee];

        _deposits[payee] = 0;

        payee.sendValue(payment);

        emit Withdrawn(payee, payment);
    }
}

// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/payment/PullPayment.sol


pragma solidity ^0.6.12;


/**
 * @dev Simple implementation of a
 * https://consensys.github.io/smart-contract-best-practices/recommendations/#favor-pull-over-push-for-external-calls[pull-payment]
 * strategy, where the paying contract doesn't interact directly with the
 * receiver account, which must withdraw its payments itself.
 *
 * Pull-payments are often considered the best practice when it comes to sending
 * Ether, security-wise. It prevents recipients from blocking execution, and
 * eliminates reentrancy concerns.
 *
 * 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].
 *
 * To use, derive from the `PullPayment` contract, and use {_asyncTransfer}
 * instead of Solidity's `transfer` function. Payees can query their due
 * payments with {payments}, and retrieve them with {withdrawPayments}.
 */
contract PullPayment {
    Escrow private _escrow;

    constructor () internal {
        _escrow = new Escrow();
    }

    /**
     * @dev Withdraw accumulated payments, forwarding all gas to the recipient.
     *
     * Note that _any_ account can call this function, not just the `payee`.
     * This means that contracts unaware of the `PullPayment` protocol can still
     * receive funds this way, by having a separate account call
     * {withdrawPayments}.
     *
     * WARNING: Forwarding all gas opens the door to reentrancy vulnerabilities.
     * Make sure you trust the recipient, or are either following the
     * checks-effects-interactions pattern or using {ReentrancyGuard}.
     *
     * @param payee Whose payments will be withdrawn.
     */
    function withdrawPayments(address payable payee) public virtual {
        _escrow.withdraw(payee);
    }

    /**
     * @dev Returns the payments owed to an address.
     * @param dest The creditor's address.
     */
    function payments(address dest) public view returns (uint256) {
        return _escrow.depositsOf(dest);
    }

    /**
     * @dev Called by the payer to store the sent amount as credit to be pulled.
     * Funds sent in this way are stored in an intermediate {Escrow} contract, so
     * there is no danger of them being spent before withdrawal.
     *
     * @param dest The destination address of the funds.
     * @param amount The amount to transfer.
     */
    function _asyncTransfer(address dest, uint256 amount) internal virtual {
        _escrow.deposit{ value: amount }(dest);
    }
}

// File: https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/math/SafeMath.sol


pragma solidity ^0.6.12;

/**
 * @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;
    }
}

// File: browser/AutomaticMarketMaker.sol

//Be name khoda


pragma solidity ^0.6.12;





interface DEUSToken {
	function totalSupply() external view returns (uint256);

	function mint(address to, uint256 amount) external;
	function burn(address from, uint256 amount) external;
} 

contract AutomaticMarketMaker is Ownable, PullPayment, Power{

	using SafeMath for uint256;
	using SafeMath for uint32;

	DEUSToken public deusToken;
	uint256 public reserve;
	uint256 public firstSupply;
	uint256 public firstReserve;
	uint256 public reserveShiftAmount;
	address payable public daoWallet;

	uint32 public scale = 10**6;
	uint32 public cw = 0.4 * 10**6; 
	uint256 public daoShareScale = 10**18;
	uint256 public maxDaoShare = 0.15 * 10**18; // 15% * scale
	uint256 public daoTargetBalance = 500 * 10**18;

	function setDaoWallet(address payable _daoWallet) external onlyOwner{
		daoWallet = _daoWallet;
	}

	function withdraw(uint256 amount) external onlyOwner{
		daoWallet.transfer(amount);
	}

	function init(uint256 _firstReserve, uint256 _firstSupply) external onlyOwner{
		reserve = _firstReserve;
		firstReserve = _firstReserve;
		firstSupply = _firstSupply;
		reserveShiftAmount = reserve.mul(scale.sub(cw)).div(scale);
	}

	function setDaoShare(uint256 _maxDaoShare, uint256 _daoTargetBalance) external onlyOwner{
		maxDaoShare = _maxDaoShare;
		daoTargetBalance = _daoTargetBalance;
	}

	receive() external payable {
		// receive ether
	}

	constructor(address _deusToken) public{
		daoWallet = msg.sender;
		deusToken = DEUSToken(_deusToken);
	}

	function daoShare() public view returns (uint256){
		return maxDaoShare.sub(maxDaoShare.mul(daoWallet.balance).div(daoTargetBalance));
	}

	function _bancorCalculatePurchaseReturn(
		uint256 _supply,
		uint256 _connectorBalance,
		uint32 _connectorWeight,
		uint256 _depositAmount) internal view returns (uint256){
		// validate input
		require(_supply > 0 && _connectorBalance > 0 && _connectorWeight > 0 && _connectorWeight <= scale);

		// special case for 0 deposit amount
		if (_depositAmount == 0) {
			return 0;
		}

		uint256 result;
		uint8 precision;
		uint256 baseN = _depositAmount.add(_connectorBalance);
		(result, precision) = power(
		baseN, _connectorBalance, _connectorWeight, scale
		);
		uint256 newTokenSupply = _supply.mul(result) >> precision;
		return newTokenSupply - _supply;
	}

	function calculatePurchaseReturn(uint256 etherAmount) public view returns (uint256) {

		etherAmount = etherAmount.mul(daoShareScale.sub(daoShare())).div(daoShareScale);

		uint256 supply = deusToken.totalSupply();
		
		if (supply < firstSupply){
			if  (reserve.add(etherAmount) > firstReserve){
				uint256 exteraEtherAmount = reserve.add(etherAmount).sub(firstReserve);
				uint256 tokenAmount = firstSupply.sub(supply);

				tokenAmount = tokenAmount.add(_bancorCalculatePurchaseReturn(firstSupply, firstReserve.sub(reserveShiftAmount), cw, exteraEtherAmount));
				return tokenAmount;
			}
			else{
				return supply.mul(etherAmount).div(reserve);
			}
		}else{
			return _bancorCalculatePurchaseReturn(supply, reserve.sub(reserveShiftAmount), cw, etherAmount);
		}
	}

	function buy(uint256 _tokenAmount) external payable{
		uint256 tokenAmount = calculatePurchaseReturn(msg.value);
		require(tokenAmount >= _tokenAmount, 'price changed');

		uint256 daoEtherAmount = msg.value.mul(daoShare()).div(daoShareScale);
		reserve = reserve.add(msg.value.sub(daoEtherAmount));

		daoWallet.transfer(daoEtherAmount);
		deusToken.mint(msg.sender, tokenAmount);
	}

	function _bancorCalculateSaleReturn(
		uint256 _supply,
		uint256 _connectorBalance,
		uint32 _connectorWeight,
		uint256 _sellAmount) internal view returns (uint256){

		// validate input
		require(_supply > 0 && _connectorBalance > 0 && _connectorWeight > 0 && _connectorWeight <= scale && _sellAmount <= _supply);
		// special case for 0 sell amount
		if (_sellAmount == 0) {
			return 0;
		}
		// special case for selling the entire supply
		if (_sellAmount == _supply) {
			return _connectorBalance;
		}

		uint256 result;
		uint8 precision;
		uint256 baseD = _supply - _sellAmount;
		(result, precision) = power(
			_supply, baseD, scale, _connectorWeight
		);
		uint256 oldBalance = _connectorBalance.mul(result);
		uint256 newBalance = _connectorBalance << precision;
		return oldBalance.sub(newBalance).div(result);
	}

	function calculateSaleReturn(uint256 tokenAmount) public view returns (uint256) {
		uint256 supply = deusToken.totalSupply();
		if (supply > firstSupply){
			if (firstSupply > supply.sub(tokenAmount)){
				uint256 exteraTokenAmount = firstSupply.sub(supply.sub(tokenAmount));
				uint256 etherAmount = reserve.sub(firstReserve);

				return etherAmount.add(firstReserve.mul(exteraTokenAmount).div(firstSupply));

			}else{
				return _bancorCalculateSaleReturn(supply, reserve.sub(reserveShiftAmount), cw, tokenAmount);
			}
		}else{
			return reserve.mul(tokenAmount).div(supply);
		}
	}

	function sell(uint256 tokenAmount, uint256 _etherAmount) external{
		uint256 etherAmount = calculateSaleReturn(tokenAmount);

		require(etherAmount >= _etherAmount, 'price changed');

		_asyncTransfer(msg.sender, etherAmount);
		reserve = reserve.sub(etherAmount);
		deusToken.burn(msg.sender, tokenAmount);
	}
}