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
t = int(input())

def solve(n):
	res = []
	for i in range(1,int(n**0.5)+1):
		if n % i == 0:
			res.append(i)
			res.append(n//i)
	return sorted(set(res))

for _ in range(t):
	A,B,C = map(int,input().split())
	A = solve(A)
	B = solve(B)
	C = solve(C)
	visited = set()
	res = 0
	for a in A:
		for b in B:
			for c in C:
				x,y,z = sorted([a,b,c])
				if (x,y,z) not in visited:
					res += 1
					visited.add((x,y,z))
	print(res)