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

SAMPLE INPUT
1
2 4 6

SAMPLE OUTPUT
2

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