library SafeMath {
  /**
  * @dev Multiplies two numbers, reverts on 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-solidity/pull/522
      if (a == 0) {
          return 0;
      }

      uint256 c = a * b;
      require(c / a == b);

      return c;
  }

  /**
  * @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
  */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
      // Solidity only automatically asserts when dividing by 0
      require(b > 0);
      uint256 c = a / b;
      // assert(a == b * c + a % b); // There is no case in which this doesn't hold

      return c;
  }

  /**
  * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
  */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
      require(b <= a);
      uint256 c = a - b;

      return c;
  }

  /**
  * @dev Adds two numbers, reverts on overflow.
  */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
      uint256 c = a + b;
      require(c >= a);

      return c;
  }

  /**
  * @dev Divides two numbers and returns the remainder (unsigned integer modulo),
  * reverts when dividing by zero.
  */
  function mod(uint256 a, uint256 b) internal pure returns (uint256) {
      require(b != 0);
      return a % b;
  }
 

  function uint2str(uint i) internal pure returns (string){
      if (i == 0) return "0";
      uint j = i;
      uint length;
      while (j != 0){
          length++;
          j /= 10;
      }
      bytes memory bstr = new bytes(length);
      uint k = length - 1;
      while (i != 0){
          bstr[k--] = byte(48 + i % 10);
          i /= 10;
      }
      return string(bstr);
  }
 
  
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that revert on error
 */
function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    require(c >= a);

    return c;
}

/**
 * @dev Adds two numbers, reverts on overflow.
 */