# Pave the Parallelepiped

## 题意翻译

$t$ 组询问，每组输入 $A,B,C$，输出满足以下条件的有序数组 $(a,b,c)$ 的个数。 - $1 \le a \le b \le c$ - 存在一个 $a, b, c$ 的排列 $a', b', c'$，使 $a'|A, b'|B, c'|C$。 $t, A, B, C \le 10^5$

## 题目描述

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 $1\times 2\times 3$ .

## 输入输出格式

### 输入格式

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.

### 输出格式

For each test case, print the number of different groups of three points that satisfy all given conditions.

## 输入输出样例

### 输入样例 #1

4
1 1 1
1 6 1
2 2 2
100 100 100


### 输出样例 #1

1
4
4
165


## 说明

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 $(2, 2, 2)$ .