library SafeMath {

/**
* @dev Multiplies two unsigned integers, 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 unsigned integers truncating the quotient, reverts on division by zero.
*/

    function div(uint256 _a, uint256 _b) internal pure returns (uint256) {
    // Solidity only automatically asserts when dividing by 0
        require(_b > 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 unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
*/

    function sub(uint256 _a, uint256 _b) internal pure returns (uint256) {
        require(_b <= _a);
        return _a - _b;
    }

/**
* @dev Adds two unsigned integers, reverts on overflow.
*/

    function add(uint256 _a, uint256 _b) internal pure returns (uint256) {
        uint256 c = _a + _b;
        require(c >= _a);
        return c;
    }

/**
* @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo),
* reverts when dividing by zero.
*/

    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0);
        return a % b;
    }

}
function mod(uint256 a, uint256 b) internal pure returns (uint256) {
    require(b != 0);
    return a % b;
}

/**
 * @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo),
 * reverts when dividing by zero.
 */