library SafeMath {

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

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

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

    /**
    * @dev Adds two numbers, throws on overflow.
    */
    function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
      c = a + b;
      assert(c >= a);
      return c;
    }
  }
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
      c = a + b;
      assert(c >= a);
      return c;
    }
/**
 * @dev Adds two numbers, throws on overflow.
 */