Solve the programming task below in a Python markdown code block.
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You are given an integer sequence $A_{1}, A_{2}, \dots, A_{N}$. Let's define the *useful number* of a subsequence of $A$ as the number of distinct primes $p$ such that $p$ divides each member of the subsequence, multiplied by the length of the subsequence. Find the maximum of useful numbers of all subsequences of $A$.

------  Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-seperated integers $A_{1}, A_{2}, \dots, A_{N}$.

------  Output ------
Print a single line containing one integer — the maximum useful number.

------  Constraints ------
$1 ≤ T ≤ 10$
$1 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{5}$ for each valid $i$

------  Subtasks ------
Subtask #1 (30 points):
$1 ≤ N ≤ 15$
$1 ≤ A_{i} ≤ 100$ for each valid $i$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------ 
1
5
2 2 4 17 8
----- Sample Output 1 ------ 
4
----- explanation 1 ------ 
Example case 1: The subsequence $[2, 2, 4, 8]$ has the maximum useful number. The number of distinct primes that divide each member of the subsequence is $1$ (only the prime $2$) and the length of the subsequence is $4$, so the useful number of this subsequence is $1\cdot 4 = 4$.