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;
  	assert(c / a == b);
  	return c;
  }

  /**
  * @dev Integer division of two numbers, truncating the quotient.
  */
 // we don't need "div"
/*  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 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) {
  	assert(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;
  	assert(c >= a);
  	return c;
  }
}
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
	if (a == 0) {
		return 0;
	}
	uint256 c = a * b;
	assert(c / a == b);
	return c;
}

/**
 * @dev Multiplies two numbers, throws on overflow.
 */