Problem

You are given an array $A$ consisting of $N$ integers. You are allowed to rearrange the elements of the array in any order.

A segment $[l,r]$ of the array is considered beautiful if, for every pair $(i,j)$ where $l\le i\le j\le r$, either ��mod  ��=0Ai​modAj​=0 or ��mod  ��=0Aj​modAi​=0. Note that mod denotes the modulo operation.

The score of a beautiful segment $[l,r]$ is calculated as follows:

• score([�,�])=min⁡(��,��+1,…,��)⋅(�−�+1)([l,r])=min(Al​,Al+1​,…,Ar​)⋅(r−l+1)

Your task is to determine the maximum possible score of a beautiful segment within the given array $A$.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first line of each test case contains an integer $N$ – the length of the array $A$.
• The second line of each test case contains $N$ space-separated integers �1,�2,…,��A1​,A2​,…,AN​, denoting the array.

Output Format

For each test case, output on a new line, the maximum possible score of a beautiful segment.

Constraints

Sample 1:

2
4
2 3 4 6
5
4 4 8 10 4

6
16

Explanation:

Test case $1$: The array elements can be rearranged as $[3,6,2,4]$.
The beautiful segments are $[1,1],[2,2],[3,3],[4,4],[1,2],[2,3],[3,4]$.
score([1,2])=min⁡(�1,�2)⋅2=6([1,2])=min(A1​,A2​)⋅2=6, which is the maximum possible score.

Test case $2$: The array elements can be rearranged as $[4,4,8,4,10]$.
The beautiful segment $[1,4]$ has the maximum score of $16$.