library SafeMath {

    /**
    * @dev Multiplies two numbers, reverts on overflow.
    */
    function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
        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 sub(uint256 _a, uint256 _b) internal pure returns (uint256) {
        require(_b <= _a);
        uint256 c = _a - _b;

        return c;
    }
/**
 * @dev Subtracts two numbers, reverts on overflow (i.e. if subtrahend is greater than minuend).
 */