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.lang.reflect.Array;
import java.util.*;

public class AaoTumhareSaathBhiThodaKhele {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t>0)
        {
            t--;

            int n = sc.nextInt();
            int cnt[] = new int[n+1];
            ArrayList<Integer> adj[] = new ArrayList [n+1];
            for(int i=0;i<=n;i++)adj[i] = new ArrayList<Integer>();

            for(int i=0;i<n;i++)
            {
                int a = sc.nextInt();
                int b = sc.nextInt();
                adj[a].add(b);
                cnt[b]++;
            }

            long total =  (1L*n*(n-1)*(n-2))/6;
            long minus = 0;

            for(int i=1;i<=n;i++)
            {
                int sz =  adj[i].size();
                if(sz<=1)continue;
                for(int j=0;j<sz;j++)
                {
                    minus += (sz-1L)*(cnt[adj[i].get(j)]-1L);
                }
            }
            System.out.println(total-minus);

        }
    }
}