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.nio.charset.StandardCharsets;
        import java.util.*;
        import java.io.BufferedReader;
        import java.io.IOException;
        import java.io.InputStreamReader;

public class Solution {

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(
                    new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

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

        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new
                FileOutputStream(java.io.FileDescriptor.out), StandardCharsets.US_ASCII), 512);
        FastReader sc = new FastReader();
        int z = sc.nextInt();
        while (z-- > 0) {
           int n = sc.nextInt();
           int[][] arr = new int[n][2];
            Map<Integer,Integer> xa = new HashMap<>();
            Map<Integer, Integer> ya = new HashMap<>();

            for(int i =0;i<n;i++){
               arr[i][0]=sc.nextInt();
               xa.put(arr[i][0],xa.getOrDefault(arr[i][0],0)+1);
               arr[i][1]=sc.nextInt();
               ya.put(arr[i][1],ya.getOrDefault(arr[i][1],0)+1);
           }
            long ans =((long) n *(n-1)*(n-2))/6;
            for(int i=0;i<n;i++){
                int ca= xa.get(arr[i][0]);
                int cb = ya.get(arr[i][1]);
                ans-= (long) (ca - 1) *(cb-1);
            }
            out.write(ans+"\n");
        }
        out.flush();
    }
}


