library SafeMath {

  	/**
  	 * @dev Multiplies two numbers, throws on overflow.
  	*/
  	function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
    	// 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;
    	}

    	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 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);
    	uint256 c = _a - _b;

    	return c;
  	}

  	/**
  	 * @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;
  	}
}
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
 	// 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;
 	}

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

 	return c;
}

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