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 q4 {

    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        
        int tests = Integer.parseInt(br.readLine());

        for (int test = 1;test <= tests;test++) {
            String[] parts = br.readLine().split(" ");
            int n = Integer.parseInt(parts[0]);

            int[] a = new int[n];
            int[] b = new int[n];
            
            HashMap<Integer,Long> m1 = new HashMap<>();
            HashMap<Integer,Long> m2 = new HashMap<>();
            for(int i = 0;i < n;i++){
                parts = br.readLine().split(" ");

                a[i] = Integer.parseInt(parts[0]);
                m1.put(a[i],m1.getOrDefault(a[i],0L) + 1);

                b[i] = Integer.parseInt(parts[1]);
                m2.put(b[i],m2.getOrDefault(b[i],0L) + 1);
            }

            long ans = (n * (n - 1) * (n - 2) / 6);

            for(int i = 0;i < n;i++){
                long v1 = m1.get(a[i]) - 1;
                long v2 = m2.get(b[i]) - 1;

                if(v1 >= 0 && v2 >= 0) ans -= (v1 * v2);
            }
            
            System.out.println(ans);
        }
    }
}
