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

    function mul(uint256 _a, uint256 _b) internal pure returns (uint256) {
    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 Substracts 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);
    return _a - _b;
    }
    
    /**
    * @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) {
if (_a == 0) {
return 0;
}
uint256 c = _a * _b;
assert(c / _a == _b);
return c;
}

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