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 $1\leq a\leq b\leq c$ and parallelepiped $A\times B\times C$ can be paved with parallelepipeds $a\times b\times c$. Note, that all small parallelepipeds have to be rotated in the same direction.

For example, parallelepiped $1\times 5\times 6$ can be divided into parallelepipeds $1\times 3\times 5$, but can not be divided into parallelepipeds $1\times 2\times 3$.
The first line contains a single integer $t$ ($1 \leq t \leq 10^5$) — the number of test cases.

Each of the next $t$ lines contains three integers $A$, $B$ and $C$ ($1 \leq A, B, C \leq 10^5$) — the sizes of the parallelepiped.
4
1 1 1
1 6 1
2 2 2
100 100 100
1
4
4
165
10
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1
1
1
1
1
1
1
1
1
1
10
9 6 8
5 5 2
8 9 2
2 7 9
6 4 10
1 1 8
2 8 1
10 6 3
7 5 2
9 5 4
41
6
21
12
39
4
7
26
8
18
1
100000 100000 100000
8436
from math import gcd

N = 100001
divisor_count = [0 for i in range(N)]

for i in range(1, N):
    for j in range(i, N, i):
        divisor_count[j] += 1

for _ in range(int(input())):
    A, B, C = map(int, input().split())
    a = divisor_count[A]
    b = divisor_count[B]
    c = divisor_count[C]
    ab = divisor_count[gcd(A, B)]
    bc = divisor_count[gcd(B, C)]
    ca = divisor_count[gcd(C, A)]
    abc = divisor_count[gcd(gcd(A, B), C)]
    answer = a * b * c - ab * bc * ca + abc * (ab * bc + bc * ca + ca * ab) - a * bc * (bc - 1) // 2 - b * ca * (ca - 1) // 2 - c * ab * (ab - 1) // 2 - abc * (abc + 1) * (ab + bc + ca) // 2 + abc * (abc + 1) * (abc + 2) // 6
    print(answer)
