The BOSS Can Count Pairs
Description
You are given two arrays $a$ and $b$, both of length $n$.
Your task is to count the number of pairs of integers $(i,j)$ such that $1 \leq i < j \leq n$ and $a_i \cdot a_j = b_i+b_j$.
Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the length of the arrays.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$) — the elements of array $a$.
The third line of each test case contains $n$ integers $b_1,b_2,\ldots,b_n$ ($1 \le b_i \le n$) — the elements of array $b$.
It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$.
For each test case, output the number of good pairs.
Input
Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the length of the arrays.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le n$) — the elements of array $a$.
The third line of each test case contains $n$ integers $b_1,b_2,\ldots,b_n$ ($1 \le b_i \le n$) — the elements of array $b$.
It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output the number of good pairs.
3
3
2 3 2
3 3 1
8
4 2 8 2 1 2 7 5
3 5 8 8 1 1 6 5
8
4 4 8 8 8 8 8 8
8 8 8 8 8 8 8 8
2
7
1
Note
In the first sample, there are $2$ good pairs:
- $(1,2)$,
- $(1,3)$.
In the second sample, there are $7$ good pairs:
- $(1,2)$,
- $(1,5)$,
- $(2,8)$,
- $(3,4)$,
- $(4,7)$,
- $(5,6)$,
- $(5,7)$.