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.*;

public class D_Training_Session{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
      //  PrintWriter out=new PrintWriter(System.out);
        //end of program 
        //out.println(answer);
        //out.close();
        StringBuilder res = new StringBuilder();
        int t=s.nextInt();
        int p=0;
        while(p<t){
        long n=s.nextLong();
        ArrayList<Integer> list1 = new  ArrayList<Integer>();// for type
        HashMap<Integer,ArrayList<Integer>> map1 = new HashMap<Integer,ArrayList<Integer>>();// for type

        ArrayList<Integer> list2 = new  ArrayList<Integer>();// for difficulty
        HashMap<Integer,ArrayList<Integer>> map2 = new HashMap<Integer,ArrayList<Integer>>();// for difficulty
      // HashMap<Integer,Integer> map = new  HashMap<Integer,Integer>();
      ArrayList<pair> nice= new  ArrayList<pair>();
        for(int i=0;i<n;i++){
            int a=s.nextInt();
            int b=s.nextInt();
        pair obj5 = new pair(a,b);
        nice.add(obj5);
           if(map1.containsKey(a)){
              map1.get(a).add(b);
           }
           else{
               ArrayList<Integer> obj = new  ArrayList<Integer>();
               obj.add(b);
               map1.put(a,obj);
               list1.add(a);

           }
           if(map2.containsKey(b)){
            map2.get(b).add(a);
         }
         else{
             ArrayList<Integer> obj = new  ArrayList<Integer>();
             obj.add(a);
             map2.put(b,obj);
             list2.add(b);
         }

        }
        long sub=0;
        for(int i=0;i<n;i++){
            pair obj = nice.get(i);
            long a=map1.get(obj.a).size()-1;
            long b=map2.get(obj.b).size()-1;
            long c=(a*b);
            sub+=c;
        }

        long ans=(n*(n-1)*(n-2))/6;
        ans-=sub;
        res.append(ans+"\n");
        p++;

       
    }
    System.out.println(res);
        

    }
   
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

   static class pair{
       int a;
       int b;
       pair(int c, int d){
           a=c;
           b=d;
       }
   }


}