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 D {
		
	public static void main(String[] args) {
		
		FastReader f = new FastReader();
		StringBuffer sb=new StringBuffer();
		
		int test=f.nextInt();
		out:
		while(test-->0)
		{
			int n=f.nextInt();
			int a[][]=new int[n][2];
			for(int i=0;i<n;i++)
			{
				a[i][0]=f.nextInt();
				a[i][1]=f.nextInt();
			}
			long ans = (n*(n-1)*(n-2))/6L;
			long minus = RightAngled(a);
			
			sb.append((ans-minus) +"\n");
		}
		System.out.println(sb);
		
	}
	
	
	static long RightAngled(int a[][])
	{
	 
		int n=a.length;
	    // To store the number of points
	    // has same x or y coordinates
	    HashMap<Integer,
	              Integer> xpoints  = new HashMap<Integer,
	                                              Integer>();
	    HashMap<Integer,
	            Integer> ypoints  = new HashMap<Integer,
	                                              Integer>();
	 
	    for (int i = 0; i < n; i++)
	    {
	        if(xpoints.containsKey(a[i][0]))
	        {
	            xpoints.put(a[i][0], xpoints.get(a[i][0]) + 1);
	        }
	        else
	        {
	            xpoints.put(a[i][0], 1);
	        }
	        if(ypoints.containsKey(a[i][1]))
	        {
	            ypoints.put(a[i][1], ypoints.get(a[i][1]) + 1);
	        }
	        else
	        {
	            ypoints.put(a[i][1], 1);
	        }
	    }
	 
	    // Store the total count of triangle
	    long count = 0;
	 
	    // Iterate to check for total number
	    // of possible triangle
	    for (int i = 0; i < n; i++)
	    {
	        if (xpoints.get(a[i][0]) >= 1 &&
	            ypoints.get(a[i][1]) >= 1)
	        {
	 
	            // Add the count of triangles
	            // formed
	            count += (long)(xpoints.get(a[i][0]) - 1) *
	                     (long)(ypoints.get(a[i][1]) - 1);
	        }
	    }
	 
	    // Total possible triangle
	    return count;
	}
	
	static class FastReader 
	{ 
	    BufferedReader br; 
	    StringTokenizer st; 
 
	    public FastReader() {
	    	br = new BufferedReader(new
	                 InputStreamReader(System.in)); 
	    }
	    String next() { 
	        while (st == null || !st.hasMoreElements()) { 
	            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()); 
	    } 
	    double nextDouble() { 
	        return Double.parseDouble(next()); 
	    } 
	    String nextLine() { 
	        String str = ""; 
	        try{ 
	            str = br.readLine(); 
	        } 
	        catch (IOException e) { 
	            e.printStackTrace(); 
	        } 
	        return str; 
	    } 
	} 
}