Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha\,(\alpha > 0)$, and the mean and standard deviation of marks of class B of $n$ students be respectively $55$ and $30 - \alpha$. If the mean and variance of the marks of the combined class of $100 + n$ students are respectively $50$ and $350$, then the sum of variances of classes A and B is