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 Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int t=Integer.parseInt(bu.readLine());
        while(t-->0)
        {
            int n=Integer.parseInt(bu.readLine());
            int a[][]=new int[n][2],i,r[]=new int[n],c[]=new int[n];
            for(i=0;i<n;i++)
            {
                String s[]=bu.readLine().split(" ");
                a[i][0]=Integer.parseInt(s[0])-1;
                a[i][1]=Integer.parseInt(s[1])-1;
                r[a[i][0]]++;
                c[a[i][1]]++;
            }

            long ans=nc3(n),del=0;
            for(i=0;i<n;i++)
            {
                r[a[i][0]]--;
                c[a[i][1]]--;
                del+=1l*r[a[i][0]]*c[a[i][1]];
                r[a[i][0]]++;
                c[a[i][1]]++;
            }
            ans-=del;
            sb.append(ans+"\n");
        }
        System.out.print(sb);
    }

    static long nc3(long n)
    {
        return n*(n-1)*(n-2)/6;
    }
}