Handsome GCD

Every sequence whose length is a positive integer has a value called its handsome GCD. The handsome GCD is the greatest common divisor of all elements of the sequence, multiplied by the length of the sequence.

Given a sequence $a_1, a_2, \dots, a_n$, find the largest handsome GCD among all contiguous subsequences of that sequence.

The input holds several test cases. The first line contains $T$, the number of test cases.

Each test case takes two lines. The first line contains the length of the sequence $n$ ($1 \le n \le 100\,000$). The second line contains the elements $a_1, a_2, \dots, a_n$ separated by single spaces. Every element satisfies $1 \le a_i \le 10^{12}$.

For each test case, print on one line the largest handsome GCD over all contiguous subsequences of the given sequence. The answer is a single integer and it is unique.