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.StringTokenizer;


public class Main {
	static AReader scan = new AReader();
	static int N = 10010;

	static void slove() {
		int n = scan.nextInt();
		int[] a = new int[n];
		int[] b = new int[n];
		int[] c1 = new int[n+10];
		int[] c2 = new int[n+10];
		for(int i = 0;i<n;i++){
			a[i] = scan.nextInt();
			b[i] = scan.nextInt();
			c1[a[i]]++;
			c2[b[i]]++;
		}
		long res = (long)n * (n - 1) * (n - 2) / 6;
		for(int i = 0;i<n;i++){
			res -= (long)(c1[a[i]] - 1) * (c2[b[i] - 1]);
		}
		System.out.println(res);


	}



	public static void main(String[] args) {
		int T = scan.nextInt();
		while (T-- > 0) {
			slove();
		}

	}
}


class AReader {
	private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	private StringTokenizer tokenizer = new StringTokenizer("");

	private String innerNextLine() {
		try {
			return reader.readLine();
		} catch (IOException ex) {
			return null;
		}
	}

	public boolean hasNext() {
		while (!tokenizer.hasMoreTokens()) {
			String nextLine = innerNextLine();
			if (nextLine == null) {
				return false;
			}
			tokenizer = new StringTokenizer(nextLine);
		}
		return true;
	}

	public String nextLine() {
		tokenizer = new StringTokenizer("");
		return innerNextLine();
	}

	public String next() {
		hasNext();
		return tokenizer.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}





























