1007_B. Pave the Parallelepiped
You are given a rectangular parallelepiped with sides of positive integer lengths A, B and C. 

Find the number of different groups of three integers (a, b, c) such that 1≤ a≤ b≤ c and parallelepiped A× B× C can be paved with parallelepipeds a× b× c. Note, that all small parallelepipeds have to be rotated in the same direction.

For example, parallelepiped 1× 5× 6 can be divided into parallelepipeds 1× 3× 5, but can not be divided into parallelepipeds 1× 2× 3.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each of the next t lines contains three integers A, B and C (1 ≤ A, B, C ≤ 10^5) — the sizes of the parallelepiped.

Output

For each test case, print the number of different groups of three points that satisfy all given conditions.

Example

Input

4
1 1 1
1 6 1
2 2 2
100 100 100


Output

1
4
4
165

Note

In the first test case, rectangular parallelepiped (1, 1, 1) can be only divided into rectangular parallelepiped with sizes (1, 1, 1).

In the second test case, rectangular parallelepiped (1, 6, 1) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 1, 3) and (1, 1, 6).

In the third test case, rectangular parallelepiped (2, 2, 2) can be divided into rectangular parallelepipeds with sizes (1, 1, 1), (1, 1, 2), (1, 2, 2) and (2, 2, 2). 
```python
from sys import stdin
from math import gcd


def main():
    input()
    l = stdin.read().splitlines()
    d = [3., 1., 2., 2., 2., 1.] * 16667
    for i in range(4, 100001):
        for j in range(i, 100001, i):
            d[j] += 1.
    for i, s in enumerate(l):
        a, b, c = map(int, s.split())
        k = gcd(b, c)
        ab = d[gcd(a, b)]
        ac = d[gcd(a, c)]
        bc = d[k]
        abc = d[gcd(a, k)]
        asz = d[a] - ab - ac + abc
        bsz = d[b] - bc - ab + abc
        csz = d[c] - ac - bc + abc
        absz = ab - abc
        bcsz = bc - abc
        acsz = ac - abc
        l[i] = '%d' % (asz * bsz * csz +
                       (absz * (asz + bsz) * csz) +
                       (bcsz * (bsz + csz) * asz) +
                       (acsz * (asz + csz) * bsz) +
                       (abc * (asz * bsz + asz * csz + bsz * csz)) +
                       (abc * (absz + bcsz + acsz) * (asz + bsz + csz)) +
                       ((asz + bsz + csz + absz + bcsz + acsz) * (abc * (abc + 1) * .5)) +
                       (absz * bcsz * acsz) +
                       ((absz * (absz + 1.) * d[c]) +
                        (bcsz * (bcsz + 1.) * d[a]) +
                        (acsz * (acsz + 1.) * d[b])) * .5 +
                       ((asz + bsz + csz + abc) * (absz * acsz + absz * bcsz + bcsz * acsz)) +
                       (abc + (abc * (abc - 1.)) + (abc * (abc - 1.) * (abc - 2.) / 6.)))
    print('\n'.join(map(str, l)))


if __name__ == '__main__':
    main()




# Made By Mostafa_Khaled
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