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 tank {

    static final FastScanner fs = new FastScanner();

    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int t = fs.nextInt();
        while(t-- > 0) run_case();

        out.close();
    }

    static void run_case() {
        int n = fs.nextInt();
        int[][] top = new int[n + 1][2];
        int[][] a = new int[n][];

        for (int i = 0; i < n; i++) {
            a[i] = fs.readArray(2);

            top[a[i][0]][0]++;
            top[a[i][1]][1]++;
        }

        long ans = 0, cur, c1, c2;

        for (int i = 0; i < n; i++) {
            cur = 0;
            c1 = (top[a[i][0]][0] - 1);
            c2 = (top[a[i][1]][1] - 1);

            cur += (c1 * c2);

            //top[a[i][0]][0]--;
            //top[a[i][1]][1]--;

            ans += cur;
        }

        cur = n;

        cur = (cur * (cur - 1) * (cur - 2));

        cur /= 6;

        out.println(cur - ans);
    }

    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();
        }

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

            return "";
        }

        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());
        }

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