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
d = [0 for i in range(N)]
for i in range(1, N):
    for j in range(i, N, i):
        d[j] += 1
 
n = int(input())
for _ in range(n):
    a, b, c = map(int, input().split())
    A, B, C = d[a], d[b], d[c]
    AB, BC, CA = d[gcd(a, b)], d[gcd(b, c)], d[gcd(c, a)]
    ABC = d[gcd(gcd(a, b), c)]
    print(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)