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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static FastScanners fs = new FastScanners();

    public static void main(String[] args) {
        int testCase = 1;
        testCase = fs.nextInt();
        for (int i = 0; i < testCase; i++) {
            solve();
        }
    }

    public static void solve() {
        int n = fs.nextInt();
        long ans = 0;
        pair[] pairs = new pair[n];
        Map<Integer, Integer> task = new HashMap<>();
        Map<Integer, Integer> difficulty = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int tsk = fs.nextInt();
            int diff = fs.nextInt();
            task.put(tsk, task.getOrDefault(tsk, 0) + 1);
            difficulty.put(diff, difficulty.getOrDefault(diff, 0) + 1);
            pair p = new pair(tsk, diff);
            pairs[i] = p;
        }
        ans += ((long) n * (n - 1) * (n - 2));
        ans /= 6;
        for (int i = 0; i < n; i++) {
            int currentTask = pairs[i].a;
            int currentDiff = pairs[i].b;
            int similarTaskCount = task.get(currentTask) - 1;
            int similarDiffCount = difficulty.get(currentDiff) - 1;
            ans -= ((long) similarDiffCount * similarTaskCount);
        }
        System.out.println(ans);
    }

}

class pair implements Comparable<pair> {

    int a;
    int b;

    @Override
    public int compareTo(pair o) {
        return (int) (a - o.a);
    }

    public pair(int a, int b) {

        this.a = a;
        this.b = b;

    }

}


class FastScanners {
    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();
    }

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

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

}

