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 $1 \leq i \lt j \leq n$ and $a_i \cdot a_j = b_i+b_j$.

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.

Note

In the first sample, there are $2$ good pairs:

• $(1,2)$,
• $(1,3)$.

In the second sample, there are $7$ good pairs:

• $(1,2)$,
• $(1,5)$,
• $(2,8)$,
• $(3,4)$,
• $(4,7)$,
• $(5,6)$,
• $(5,7)$.