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.*;

/**
 * -----------------|___________|---------------------
 * CCCCCCCCC   OOOOOOOOOO   DDDDDDDD      EEEEEEEEE
 * CCCC        OOO    OOO   DD    DDD     EEEE
 * CCCC        OOO    OOO   DD     DDD    EEEEEEEEEE
 * CCCC        OOO    OOO   DD     DDDD   EEEE
 * CCCCCCCCC   OOOOOOOOOO   DDDDDDDDDDDD  EEEEEEEEEE
 * -----------------|___________|---------------------
 */

public class Main {
    private static final int MOD = 1000000007;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter sout = new PrintWriter(outputStream);

        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            int[] a = new int[n];
            int[]b = new int[n];
            int[] dp1 = new int[n+1];
            int[] dp2 = new int[n+1];
            for(int i = 0; i<n; i++){
                a[i] = in.nextInt();
                b[i]  =in.nextInt();
                dp1[a[i]]++;
                dp2[b[i]]++;
            }
            long answer = (long) n*(n-1)*(n-2)/6;
            for(int i = 0; i<n; i++){
                if(dp1[a[i]]==0 || dp2[b[i]]==0){
                    continue;
                }
                answer-= (long) (dp1[a[i]] - 1) * (dp2[b[i]] - 1);
            }
            sout.println(answer);
        }
        sout.close();
    }

    public static int binarySearch(long[] array, long value) {
        int left = 0, right = array.length - 1;
        while (left <= right) {
            int m = (left + right) / 2;
            if (array[m] == value)
                return m;
            else if (array[m] < value)
                left = m + 1;
            else
                right = m - 1;
        }
        return -1;
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

    private static int upperBound(int[] a, int low, int high, int element) {
        while (low < high) {
            int middle = low + (high - low) / 2;
            if (a[middle] > element)
                high = middle;
            else
                low = middle + 1;
        }
        return low;
    }

    public static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
