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