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.*;

public class Coder {

  static StringBuffer str=new StringBuffer();
  static int n;
  static List<long []> l;

  static void solve(){
    Map<Long, Long> lm=new HashMap<>();
    Map<Long, Long> rm=new HashMap<>();

    for(int i=0;i<n;i++){
      long x=l.get(i)[0];
      long y=l.get(i)[1];
      lm.put(x, lm.getOrDefault(x, 0l)+1l);
      rm.put(y, rm.getOrDefault(y, 0l)+1l);
    }

    long ans=((long)(n * (n-1))/2 * (long)(n-2))/3l;
    for(int i=0;i<n;i++){
      long x=l.get(i)[0];
      long y=l.get(i)[1];
      lm.put(x, lm.get(x)-1);
      rm.put(y, rm.get(y)-1);
      ans-=(lm.get(x) * rm.get(y));
    }
    str.append(ans).append("\n");
  }

  public static void main(String[] args) throws java.lang.Exception {
    BufferedReader bf;
    PrintWriter pw;
    boolean lenv=false;
    if(lenv){
      bf = new BufferedReader(
                          new FileReader("input.txt"));
      pw=new PrintWriter(new
            BufferedWriter(new FileWriter("output.txt")));
    }else{
      bf = new BufferedReader(new InputStreamReader(System.in));
      pw = new PrintWriter(new OutputStreamWriter(System.out));
    }
    int q = Integer.parseInt(bf.readLine().trim());
    while (q-- > 0) {
      n=Integer.parseInt(bf.readLine().trim());
      l=new ArrayList<>();
      for(int i=0;i<n;i++){
        String s[]=bf.readLine().trim().split("\\s+");
        l.add(new long[]{Long.parseLong(s[0]), Long.parseLong(s[1])});
      }
      solve();
    }
    pw.print(str);
    pw.flush();
    // System.out.print(str);
  }
}