#include <bits/stdc++.h>
using namespace std;
void solve() {
  int n;
  cin >> n;
  vector<long long> freq_a(n + 1), freq_b(n + 1);
  vector<pair<int, int>> arr(n + 1);
  for (int i = 1; i <= n; i++) {
    int l, r;
    cin >> l >> r;
    freq_a[l]++;
    freq_b[r]++;
    arr[i] = {l, r};
  }
  long long sub = 0;
  for (int i = 1; i <= n; i++)
    sub += (freq_a[arr[i].first] - 1) * (freq_b[arr[i].second] - 1);
  long long all = n;
  all = (all * (all - 1) * (all - 2)) / 6;
  cout << all - sub << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

Monocarp is the coach of the Berland State University programming teams. He decided to compose a problemset for a training session for his teams.

Monocarp has n problems that none of his students have seen yet. The i-th problem has a topic a_i (an integer from 1 to n) and a difficulty b_i (an integer from 1 to n). All problems are different, that is, there are no two tasks that have the same topic and difficulty at the same time.

Monocarp decided to select exactly 3 problems from n problems for the problemset. The problems should satisfy at least one of two conditions (possibly, both):

  * the topics of all three selected problems are different; 
  * the difficulties of all three selected problems are different. 



Your task is to determine the number of ways to select three problems for the problemset.

Input

The first line contains a single integer t (1 ≤ t ≤ 50000) — the number of testcases.

The first line of each testcase contains an integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of problems that Monocarp have.

In the i-th of the following n lines, there are two integers a_i and b_i (1 ≤ a_i, b_i ≤ n) — the topic and the difficulty of the i-th problem.

It is guaranteed that there are no two problems that have the same topic and difficulty at the same time.

The sum of n over all testcases doesn't exceed 2 ⋅ 10^5.

Output

Print the number of ways to select three training problems that meet either of the requirements described in the statement.

Example

Input


2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1


Output


3
10

Note

In the first example, you can take the following sets of three problems:

  * problems 1, 2, 4; 
  * problems 1, 3, 4; 
  * problems 2, 3, 4. 



Thus, the number of ways is equal to three.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void solve() {
  int n;
  cin >> n;
  vector<long long> freq_a(n + 1), freq_b(n + 1);
  vector<pair<int, int>> arr(n + 1);
  for (int i = 1; i <= n; i++) {
    int l, r;
    cin >> l >> r;
    freq_a[l]++;
    freq_b[r]++;
    arr[i] = {l, r};
  }
  long long sub = 0;
  for (int i = 1; i <= n; i++)
    sub += (freq_a[arr[i].first] - 1) * (freq_b[arr[i].second] - 1);
  long long all = n;
  all = (all * (all - 1) * (all - 2)) / 6;
  cout << all - sub << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) solve();
  return 0;
}

```