There is an integer $a$ and $n$ integers $b_1, \ldots, b_n$. After selecting some numbers from $b_1, \ldots, b_n$ in any order, say $c_1, \ldots, c_r$, we want to make sure that $a \ mod \ c_1 \ mod \ c_2 \ mod \ldots \ mod \ c_r = 0$ (i.e., $a$ will become the remainder divided by $c_i$ each time, and at the end, we want $a$ to become $0$). Please determine the minimum value of $r$. If the goal cannot be achieved, print $-1$ instead.