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 codeforces_Edu115_D {

    private static void solve(FastIOAdapter io) {
        int n = io.nextInt();
        long all = (long) n * (n - 1) * (n - 2) / 6;
        HashMap<Integer, ArrayList<Integer>> themesToComplex = new HashMap<>();
        int[] complexToThemes = new int[n + 1];
        for (int i = 0; i < n; i++) {
            int a = io.nextInt();
            int b = io.nextInt();
            complexToThemes[b]++;
            themesToComplex.putIfAbsent(a, new ArrayList<>());
			themesToComplex.get(a).add(b);
        }
        long minus = 0;
        for (Map.Entry<Integer, ArrayList<Integer>> entry : themesToComplex.entrySet()) {
            if (entry.getValue().size() >= 2) {
                for (Integer complex : entry.getValue()) {
                    int themes = complexToThemes[complex];
                    minus += (long) (entry.getValue().size() - 1) * (themes - 1);
                }
            }
        }

        io.out.println(all - minus);
    }

    public static void main(String[] args) throws Exception {
        try (FastIOAdapter ioAdapter = new FastIOAdapter()) {
            int count = 1;
            count = ioAdapter.nextInt();
            while (count-- > 0) {
                solve(ioAdapter);
            }
        }
    }

    static void ruffleSort(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
    }

    static void ruffleSort(long[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            long tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
    }

    static class FastIOAdapter implements AutoCloseable {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        public PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter((System.out))));
        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 null;
            }
        }

        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[] readArrayLong(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

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

        @Override
        public void close() throws Exception {
            out.flush();
            out.close();
            br.close();
        }
    }
}