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.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.StringTokenizer;

public class D {

    static FastScanner sc = new FastScanner();
    static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    static void solve(){
        int n = sc.nextInt();
        long[]left = new long[n + 1];
        long[]right = new long[n + 1];
        int[][]arr = new int[n][2];
        for (int i = 1; i <= n; i++) {
            int l = sc.nextInt();
            int r = sc.nextInt();
            arr[i - 1][0] = l;
            arr[i - 1][1] = r;
            left[l]++;
            right[r]++;
        }
        long ans = (long)n * (n - 1) * (n - 2) / 6;
        for(int i = 0;i < n;i++){
            long rest = right[arr[i][1]] - 1;
            long mul = left[arr[i][0]] - 1;
            if(rest != 0 || mul != 0){
                ans -= mul * rest;
            }
        }
        System.out.println(ans);
    }


    public static void main(String[] args) {
        int n = sc.nextInt();
        for(int i = 0;i < n;i++){
            solve();
        }
    }


    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
