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.
//  D. Training Session

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

public class Main {
    void solve(FastScanner in, PrintWriter out) {
        int n = in.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        HashMap<Integer,Integer> X = new HashMap<>();
        HashMap<Integer,Integer> Y = new HashMap<>();
        for (int i = 0;i < n;i++) {
            a[i] = in.nextInt();
            b[i] = in.nextInt();
            int x = X.getOrDefault(a[i],0);
            int y = Y.getOrDefault(b[i],0);
            X.put(a[i],x+1);
            Y.put(b[i],y+1);
        }

        long ans = (long) n*(n-1)*(n-2)/6;
        for (int i = 0;i < n;i++) {
            long c1 = X.getOrDefault(a[i],0);
            long c2 = Y.getOrDefault(b[i],0);
            ans -= (c1-1)*(c2-1);
        }
        out.println(ans);

    }

    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        FastScanner in = new FastScanner(System.in);
        Main solver = new Main();
        int t;
        t = in.nextInt();
        for (int i = 0;i < t;i++) {
            solver.solve(in, out);
        }
        out.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        FastScanner(InputStream input) {
            br = new BufferedReader(new InputStreamReader(input));
        }

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

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

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