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.
  	*/
  	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.
 	*/