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 new1{
	
	


    public static void main(String[] args)  throws IOException{
    	FastReader s = new FastReader();
    	BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
    	int t = s.nextInt();
    	for(int z = 0; z < t; z++) {
    		int n = s.nextInt();
    		HashMap<Integer, Integer> starts = new HashMap<Integer, Integer>();
    		HashMap<Integer, Integer> ends = new HashMap<Integer, Integer>();
    		int[][] arr = new int[n][2];
    		for(int i = 0; i <= n; i++) {
    			starts.put(i, 0); ends.put(i, 0);
    		}
    		for(int i = 0; i < n; i++) {
    			int a = s.nextInt(); int b = s.nextInt();
    			arr[i][0] = a; arr[i][1] = b;
    			starts.put(a, starts.get(a) + 1);
    			ends.put(b, ends.get(b) + 1);
    		}
//    		System.out.println(starts.toString());
//    		System.out.println(ends.toString());
//    		
    		long ways = 0;
    		for(int i = 0; i < n; i++) {
    			int a = arr[i][0]; int b = arr[i][1];
    			int aa = starts.get(a); int bb = ends.get(b);
    			ways = ways + (aa - 1)* (long ) (bb - 1);
//    			System.out.println((aa - 1) * (bb - 1) + " " + a + " " + b);
    		}
    		long total = ((long) n * (n - 1) * (n - 2)) / 6;
    		System.out.println((total - ways));
    		
    	}
    }
}
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();
    }
 
    public 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;
}}