Maximum GCD

Given $n$ integers. You have to find the maximum GCD (greatest common divisor) of every possible pair of these integers.

Input

The first line contains the number of test cases $t(1\le t\le 100)$.

The following $t$ lines are the $t$ test cases. Each test case contains $n(1\le n\le 100)$ positive integers.

Output

For each test case, print on a separate line the maximum GCD value among all possible pairs of integers.

Examples

Note

For the first test case, the answer is GCD(20, 40) = 20.

For the third test case, the answer is GCD(125, 25) = 25.