M. Synchronized Arrays
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

It is 5 AM, and $$$WisdomCasual$$$ is exhausted. He has been setting problems all night, and all he wants to do right now is get into bed and sleep. However, the problemset is still missing a problem.

In a desperate attempt to finish the problem and finally get some rest, he quickly writes down two arrays, $$$a$$$ and $$$b$$$, both of size $$$n$$$, and writes a random condition on a napkin.

He defines a pair of indices $$$(i, j)$$$ as synchronized if it satisfies the following conditions:

  1. $$$1 \le i \lt j \le n$$$
  2. The absolute difference between the elements in array $$$a$$$ is exactly equal to the absolute difference between the corresponding elements in array $$$b$$$. Formally: $$$\vert{}a_i - a_j\vert{} = \vert{}b_i - b_j\vert{}$$$

Since $$$WisdomCasual$$$ is already half-asleep, he leaves the task of actually counting the pairs to you. Help him find the total number of synchronized pairs so he can finally close his eyes and go to sleep...

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$)  — the length of the arrays.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$)  — the elements of array $$$a$$$.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^9$$$)  — the elements of array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the total number of synchronized pairs.

Example
Input
3
4
1 3 5 2
2 4 2 2
3
10 10 10
5 5 5
5
1 2 3 4 5
1 2 3 4 5
Output
2
3
10