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){
        int n=s.nextInt();
        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>();
        for(int i=0;i<n;i++){
            int a=s.nextInt();
            int b=s.nextInt();
           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);
         }

        }
        int size1=list1.size();
        int size2=list2.size();
        long ans=0;
        if(size1>size2){
             ans=  solve(list1,map1,n,map2);
        }
        else{
            ans=solve(list2,map2,n,map1);
        }
        res.append(ans+"\n");
        p++;
    }
    System.out.println(res);
        

    }
    private static long solve(ArrayList<Integer> list1, HashMap<Integer, ArrayList<Integer>> map1, int n,
            HashMap<Integer, ArrayList<Integer>> map2) {
                int size=list1.size();
                long dp[][]= new long[4][size];
                for(int i=size-1;i>=0;i--){
                    long num=map1.get(list1.get(i)).size();
                    for(int j=1;j<4;j++){
                        if(j==1){
                            if(i+1<size){   
                                dp[j][i]=num+dp[1][i+1];
                            }
                            else{
                                dp[j][i]=num;
                            }
                        }
                        else if(j==2){
                           
                                if(i+1<size){
                                    long yo=num*dp[1][i+1];
                                    dp[j][i]=yo+dp[j][i+1];
                                }
                                else{
                                    dp[j][i]=0;
                                }
                        }
                        else{
                           
                            if(i+1<size){
                                long yo=num*dp[2][i+1];
                                dp[j][i]=yo+dp[j][i+1];
                            }
                            else{
                                dp[j][i]=0;
                            }
                        }
                    }
                }
                long ans=dp[3][0];
                for(int i=0;i<list1.size();i++){
                    int num=list1.get(i);// type
                    ArrayList<Integer> nice = map1.get(num);
                    for(int j=0;j<nice.size();j++){
                        int a=nice.get(j);
                        for(int k=j+1;k<nice.size();k++){
                            int b=nice.get(k);
                            long yo2=n-map2.get(a).size()-map2.get(b).size();
                            ans+=yo2;
                        }
                    }
                }
                return ans;
    }
    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;
       }
   }


}