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 CF5 {
    public static void main(String[] args) {
        FastScanner sc=new FastScanner();
        int T=sc.nextInt();
        for (int xx=0; xx<T; xx++){
            int n = sc.nextInt();
            long ans = ((n)*(n-1)*(n-2))/6L;
            long wrong =0L;
            Pair pp[]=new Pair[n];
            Map<Integer, Integer> map1= new HashMap<>();
            Map<Integer, Integer> map2= new HashMap<>();
            for (int i=0; i<n; i++){
                int x= sc.nextInt();
                int y = sc.nextInt();
                if (map1.containsKey(x)) map1.put(x, map1.get(x)+1);
                else map1.put(x,1);
                if (map2.containsKey(y)) map2.put(y, map2.get(y)+1);
                else map2.put(y,1);
                pp[i]= new Pair(x,y);
            }
            for (int i=0; i<n; i++){
                int x=pp[i].x;
                int y= pp[i].y;
                wrong= map1.get(x)-1;
                wrong *= map2.get(y)-1;
                ans-=wrong;
            }
            System.out.println(ans);
        }
    }
    static long fact(int n){
        if (n<2) return 0;
        else {
            long sum=(n*(n-1))/2;
            return sum;
        }
    }
    static long mod = 1000000007L;
    static long power (long a, long b){
        long res=1;
        while (b>0){
            if ((b&1)== 1){
                res= (res * a % mod)%mod;
            }
            a=(a%mod * a%mod)%mod;
            b=b>>1;
        }
        return res;
    }
    static int gcd (int n, int m){
        if (m==0) return n;
        else return gcd(m, n%m);
    }
    static class Pair{
        Integer x,y;
        public Pair(int x, int y){
            this.x = x;
            this.y = y;
        }


        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair key = (Pair) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {


            int result = x.hashCode() + y;
            return result;
        }
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        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());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}