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
import sys
import math


def divisor(n):
    if n == 1:
        return [1]
    res = [1, n]
    for i in range(2, 1 + math.floor(n ** (0.5))):
        if n % i == 0:
            res.append(i)
            if i != n // i:
                res.append(n // i)
    res.sort()
    return res


read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
t = int(input())
for case in range(t):
    a, b, c = map(int, input().split())
    # print(a, b, c, divisor(a), divisor(b), divisor(c))
    ans = 0
    visit = []
    for i in divisor(a):
        for j in divisor(b):
            for k in divisor(c):
                tmp = [i, j, k]
                tmp.sort()
                if tmp not in visit:
                    visit.append(tmp)
                    # print(visit)
                    ans += 1
    print(ans)
