Prime divisors

Let's denote $S(x)$ by the sum of prime numbers that divides $x$. You are given an array $a_1, a_2, \ldots, a_n$ of $n$ numbers, find the number of pairs $i, j$ such that $i \neq j$, $a_i$ divides $a_j$ and $S(a_i)$ divides $S(a_j)$. ###Input: - First line will contain $T$, number of testcases. Then the testcases follow. - First line of each testcase contains one integer $n$ — number of