B. The BOSS Can Count Pairs
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 $$$a_i \cdot a_j = b_i+b_j$$$.

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.

Example
Input
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
Output
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:

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