While Omar was studying for Math lectures, he found the following problem.
Given 3 Integers \(N_1\), \(N_2\), \(N_3\), count the number of common divisors which divide all of them.

Can you please help Omar in solving this problem, because he usually sleeps in lectures.

Input:

Given an integer T, which indicates the number of test cases.
For each test case: given 3 separated integers \(N_1, N_2, N_3\).

Output:

For each test case: print the number of common divisors which divide \(N_1, N_2, N_3\). Print each case in a separate line.

** Constraints:**

\(1 \le T \le 50\)
\(1 \le minimum\; (N_1, N_2 , N_3) \le 10 ^ {12}\)
\(1 \le maximum\; (N_1, N_2 , N_3) \le 10 ^ {18}\)