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

public class TrainingSession {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int T = scanner.nextInt();
        while(T-->0) {
            int n = scanner.nextInt();
            HashMap<Long, Long> a = new HashMap<>();
            HashMap<Long, Long> b = new HashMap<>();
            ArrayList<Integer>[] lists = new ArrayList[n+1];
            for(int i = 0; i <= n; i++) lists[i]=new ArrayList<>();
            for(int i = 0; i < n; i++) {
                long ai = scanner.nextLong();
                long bi = scanner.nextLong();
                lists[(int)ai].add((int)bi);
                Long aa = a.get(ai);
                if (aa == null) a.put(ai, 1L);
                else a.put(ai, aa + 1);
                Long bb = b.get(bi);
                if (bb == null) b.put(bi, 1L);
                else b.put(bi, bb + 1);
            }
            long ans = (long)n * (n-1) * (n-2);
            ans /= 6;
            for(long key: a.keySet()) {
                long val = a.get(key)-1;
                for(long diff: lists[(int)key]) {
                    long other = b.get(diff)-1;
                    ans -= other * val;
                }
            }
            out.println(ans);
        }
        out.flush();
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
