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.
 */