library SafeMath {




	/**
	* @dev Multiplies two numbers, reverts on overflow.
	*/
	function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
		// Gas optimization: this is cheaper than requiring '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;
		}




		uint256 c = _a * _b;
		require(c / _a == _b);




		return c;
	}




	/**
	* @dev Integer division of two numbers truncating the quotient, reverts on division by zero.
	*/
	function div(uint256 _a, uint256 _b) internal pure returns (uint256) {
		require(_b > 0); // Solidity only automatically asserts 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 Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
	*/
	function sub(uint256 _a, uint256 _b) internal pure returns (uint256) {
		require(_b <= _a);
		uint256 c = _a - _b;




		return c;
	}




	/**
	* @dev Adds two numbers, reverts on overflow.
	*/
	function add(uint256 _a, uint256 _b) internal pure returns (uint256) {
		uint256 c = _a + _b;
		require(c >= _a);




		return c;
	}
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that revert on error
 */
function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
	// Gas optimization: this is cheaper than requiring '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;
	}




	uint256 c = _a * _b;
	require(c / _a == _b);




	return c;
}

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