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.*;
import java.math.*;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;

public class Solution {

    public static long find(int n, long[] a, long[] b) {
        HashMap<Long, Long> m1 = new HashMap<>();
        HashMap<Long, Long> m2 = new HashMap<>();
        for (long l: a) {
            m1.put(l, m1.getOrDefault(l, 0L) + 1L);
        }
        for (long l: b) {
            m2.put(l, m2.getOrDefault(l, 0L) + 1L);
        }
//        System.out.println(m1);
//        System.out.println(m2);
        long res = ((long) n * (n - 1) * (n - 2)) / 6;
        for (int i = 0; i < a.length; i++) {
            if (m1.get(a[i]) > 1L && m2.get(b[i]) > 1L) {
//                System.out.println("i:" + i);
//                System.out.println(m1.get(a[i]));
//                System.out.println(m2.get(b[i]));
                res -= (m1.get(a[i]) - 1L) * (m2.get(b[i]) - 1L);
            }
        }
        return res;
    }


    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int t = Integer.parseInt(br.readLine());
        for (int j = 0; j < t; j++) {
            int k = Integer.parseInt(br.readLine());
            long[] a = new long[k];
            long[] b = new long[k];
            for (int i = 0; i < k; i++) {
                String[] s = br.readLine().split("\\s");
                a[i] = Long.parseLong(s[0]);
                b[i] = Long.parseLong(s[1]);
            }
            pw.println(find(k, a, b));
        }
        pw.flush();
    }
}