P7009 [CERC2013] Magical GCD

The Magical GCD of a nonempty sequence of positive integers is defined as the product of its length and the greatest common divisor of all its elements. Given a sequence $(a_1, \ldots , a_ n)$, find the largest possible Magical GCD of its connected subsequences.

The first line of input contains the number of test cases $T$. The descriptions of the test cases follow: The description of each test case starts with a line containing a single integer $n$, $1 \leq n \leq 100\, 000$. The next line contains the sequence $a_1, a_2 , \ldots , a _ n$, $1 \leq a_ i \leq 10^{12}$.

For each test case output one line containing a single integer: the largest Magical GCD of a connected subsequence of the input sequence.

Time limit: 8000 ms, Memory limit: 1048576 kB. Central Europe Regional Contest (CERC) 2013