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 A1 {
    static final Reader s = new Reader();
    static final PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        int t  = s.nextInt();
//        int t=1;
        for(int i=1; i<=t; ++i) {
//            out.print("Case #"+i+": ");
            new Solver();
        }
        out.close();
    }
    static class Solver {
        Solver() {
        	int n = s.nextInt();
        	int[] a = new int[n];
        	int[] b = new int[n];
        	int[] f1 = new int[n+1];
        	int[] f2 = new int[n+1];
        	for(int i=0;i<n;i++) {
        		a[i] = s.nextInt();
        		b[i] = s.nextInt();
        		f1[a[i]]++;
        		f2[b[i]]++;
        	}
        	long c = (n*(long)(n-1)*(long)(n-2))/6;
        	for(int i=0;i<n;i++)c-=((f1[a[i]]-1)*(f2[b[i]]-1));
        	System.out.println(c);
        }
    }
    static class Reader {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        String next() {
            while(st==null||!st.hasMoreTokens()) {
                try {
                    st=new StringTokenizer(in.readLine());
                } catch(Exception e) {}
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

}