Problem: 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

Solution (in PYTHON):

Solution:
def factors(n):    
    return list(set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, long(n**0.5) + 1) if n % i == 0))))
for t in range(input()):
    num=sorted(map(long,raw_input().split()))
    fact=sorted(factors(num[0]),reverse=True)
    flag=False
    for d in fact:
        flag=True
        for n in num:
            if n%d!=0:
                flag=False
                break
        if flag==True:
            print len(factors(d))
            break