github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span>###Read problems statements [Mandarin](http://www.codechef.com/download/translated/LTIME66/mandarin/USF.pdf) , [Bengali](http://www.codechef.com/download/translated/LTIME66/bengali/USF.pdf) , [Hindi](http://www.codechef.com/download/translated/LTIME66/hindi/USF.pdf) , [Russian](http://www.codechef.com/download/translated/LTIME66/russian/USF.pdf) and [Vietnamese](http://www.codechef.com/download/translated/LTIME66/vietnamese/USF.pdf) as well.

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
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^5$ for each valid $i$

### Subtasks
**Subtask #1 (30 points):**
- $1 \le N \le 15$
- $1 \le A_i \le 100$ for each valid $i$

**Subtask #2 (70 points):** original constraints

### Example Input
```
1
5
2 2 4 17 8
```

### Example Output
```
4
```
	
### Explanation
**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 $1\cdot 4 = 4$.