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.*;
/*

1
4
2 4
3 4
2 1
1 3

*/

 
 public class D2{
	static FastReader sc=null;
	
	public static void main(String[] args) {
		sc=new FastReader();
		int t=sc.nextInt();
		for(int tt=0;tt<t;tt++) {
			int n=sc.nextInt();
			Pair p[]=new Pair[n];
			for(int i=0;i<n;i++)
				p[i]=new Pair(sc.nextInt()-1,sc.nextInt()-1);
			
			int as[]=new int[n],bs[]=new int[n];
			
			for(int i=0;i<n;i++) {
				as[p[i].a]++;
				bs[p[i].b]++;
			}
			
			long bad=0;
			
//			for(int e:as)bad+=nc3(e)+ nc2(e)*(n-e);
//			for(int e:bs)bad+=nc3(e)+ nc2(e)*(n-e);
//			
//			System.out.println(bad);
			
			for(int i=0;i<n;i++) {
				long sub=(as[p[i].a]-1)*1L*(bs[p[i].b]-1);
				bad+=sub;
			}
			
			long ans=nc3(n)-bad;
			System.out.println(ans);
			
		}
		
	}
	static long nc2(long n) {
		return n*(n-1)/2;
	}
	static long nc3(long n) {
		return (n*(n-1)*(n-2))/6;
	}
	
	static class Pair implements Comparable<Pair>{
		int a,b;
		Pair(int a,int b){
			this.a=a;
			this.b=b;
		}
		
		public int compareTo(Pair o) {
			return this.a-o.a;
		}
	}
	
	static int[] ruffleSort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i:a)al.add(i);
		Collections.sort(al);
		for(int i=0;i<a.length;i++)a[i]=al.get(i);
		return a;
	}
	
	static void print(int a[]) {
		for(int e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	
	static class FastReader{
		
		StringTokenizer st=new StringTokenizer("");
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String next() {
			while(!st.hasMoreTokens()) 
				try {
					st=new StringTokenizer(br.readLine());
				}
			   catch(IOException e){
				   e.printStackTrace();
			   }
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int[] readArray(int n) {
			int a[]=new int[n];
			for(int i=0;i<n;i++)a[i]=sc.nextInt();
			return a;
		}
	}
	
	
}
