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B. Pave the Parallelepiped
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$1\times 2\times 3$$$.

Input

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.

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 $$$(2, 2, 2)$$$.