library SafeMath {
    
    /**
    * @dev Multiplies two numbers, throws on overflow.
    */
    
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a * b;
    assert(a == 0 || c / a == b);
    return c;
    }
    
    /**
    * @dev Integer division of two numbers, truncating the quotient.
    */
    
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a / b;
    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 div(uint256 a, uint256 b) internal pure returns (uint256) {
uint256 c = a / b;
return c;
}

/**
 * @dev Integer division of two numbers, truncating the quotient.
 */