library SafeMath {

  /**
  * @dev Multiplies two numbers, throws on overflow.
  */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
      if (a == 0) {
          return 0;
      }
      uint256 c = a * b;
      require(c / a == b);
      return c;
  }

  /**
  * @dev Integer division of two numbers, truncating the quotient.
  */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
      uint256 c = a / b;
      return c;
  }

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

  /**
  * @dev Adds two numbers, throws on overflow.
  */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
      uint256 c = a + b;
      require(c >= a);
      return c;
  }
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
      require(b <= a);
      return a - b;
  }
/**
 * @dev Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
 */