library SafeMath {

	  /**
	  * @dev Multiplies two numbers, throws on overflow.
	  */
	  function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
		// Gas optimization: this is cheaper than asserting 'a' not being zero, but the
		// benefit is lost if 'b' is also tested.
		// See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
		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 sub(uint256 a, uint256 b) internal pure returns (uint256) {
		assert(b <= a);
		return a - b;
	  }
/**
 	  * @dev Subtracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
 	  */