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.
import java.io.*;
import java.util.*;

public class Main {

    static BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
    static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) throws IOException {

        int t = Integer.parseInt(r.readLine());
        while(t-- > 0) {
          String sn = r.readLine();
          int n = Integer.parseInt(sn);
          int arr[][] = new int[2][n];
          int diff[] = new int[n+1];
          int topic[] = new int[n+1];

          for(int i = 0; i < n; i++) {
              String sr[] = r.readLine().split(" ");
              arr[0][i] = Integer.parseInt(sr[0]);
              arr[1][i] = Integer.parseInt(sr[1]);
              topic[arr[0][i]]++;
              diff[arr[1][i]]++;
          }


          long ans = n*(n-1L)*(n-2L)/6;
          for(int i = 0; i < n; i++) {
              int a1 = arr[0][i], a2 = arr[1][i];
              ans -= (topic[a1]-1L) * (diff[a2]-1);
          }
          System.out.println(ans);
        }
    }
}


