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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class TrainingSesion {

	public static void main(String[] args) {
		
//		Scanner sc = new Scanner(System.in);
		FastReader sc = new FastReader();
		int t = sc.nextInt();
		for(int o = 0 ; o<t;o++) {
			int n = sc.nextInt();
			int [] arr1 = new int[n];
			int [] arr2 = new int[n];
			for(int i = 0 ; i<n;i++) {
				int a = sc.nextInt();
				int b = sc.nextInt();
				arr1[i] = a;
				arr2[i] = b;
			}
		
			HashMap<Integer,Integer> map1 = new HashMap<Integer, Integer>();
			HashMap<Integer,Integer> map2 = new HashMap<Integer, Integer>();
			for(int i = 0 ; i<n;i++){
				if(!map1.containsKey(arr1[i])) {
					map1.put(arr1[i], 1);
				}else map1.put(arr1[i], map1.get(arr1[i]) +1);
			
				if(!map2.containsKey(arr2[i])) {
					map2.put(arr2[i], 1);
				}else map2.put(arr2[i], map2.get(arr2[i]) +1);
			
			}
		long val = n*(n-1)*(n-2)/6;
		long temp = 0;
		for(int i = 0 ; i<n;i++) {
			int a = arr1[i];
			int b = arr2[i];
			int x = map1.get(a)-1;
			int y = map2.get(b)-1;
			temp += (long)x*y;
		}
		val -= temp;
		System.out.println(val);
		
		}

	}

}
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;
    }
}
