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.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

public class D {
    public static long count(ArrayList<ArrayList<Integer>> a) {
        HashMap<ArrayList<Integer>, Long> counts=new HashMap<>();
        for (ArrayList<Integer> x : a) {
            counts.put(x, counts.getOrDefault(x,0L)+1);
        }
        long sum = 0;
        long pairwise = 0;  // sum_i sum_j (i=/=j) s[i]*s[j]
        for (ArrayList<Integer> x : counts.keySet()) {
            sum += counts.get(x);
        }
        for (ArrayList<Integer> x : counts.keySet()) {
            pairwise += counts.get(x) * (sum-counts.get(x));
        }
        pairwise /= 2;
        long ans=0;
        for (ArrayList<Integer> x : counts.keySet()) {
            ans += (pairwise - (counts.get(x) * (sum-counts.get(x))))*counts.get(x);
            //System.out.println(x+" "+counts.get(x)+" "+(pairwise - (counts.get(x) * (sum-counts.get(x)))));
        }
        //System.out.println(counts);
        //System.out.println(sum+" "+pairwise+" "+(ans/3));
        return ans/3;
    }
    public static long count1d(ArrayList<Integer> a) {
        HashMap<Integer, Long> counts=new HashMap<>();
        for (int x : a) {
            counts.put(x, counts.getOrDefault(x,0L)+1);
        }
        long sum = a.size();
        long pairwise = 0;  // sum_i sum_j (i=/=j) s[i]*s[j]
        for (int x : counts.keySet()) {
            pairwise += counts.get(x) * (sum-counts.get(x));
        }
        pairwise /= 2;
        long ans=0;
        for (int x : counts.keySet()) {
            ans += (pairwise - (counts.get(x) * (sum-counts.get(x))))*counts.get(x);
            //System.out.println(x+" "+counts.get(x)+" "+(pairwise - (counts.get(x) * (sum-counts.get(x)))));
        }
        //System.out.println(counts);
        //System.out.println(sum+" "+pairwise+" "+(ans/3));
        return ans/3;
    }
    public static long count2d(ArrayList<ArrayList<Integer>> a) {
        HashMap<ArrayList<Integer>, Long> counts=new HashMap<>();
        for (ArrayList<Integer> x : a) {
            counts.put(x, counts.getOrDefault(x,0L)+1);
        }
        HashMap<Integer, Long> d1hash=new HashMap<>();
        HashMap<Integer, Long> d2hash=new HashMap<>();
        for (ArrayList<Integer> x : a) {
            d1hash.put(x.get(0), d1hash.getOrDefault(x.get(0),0L)+1);
            d2hash.put(x.get(1), d2hash.getOrDefault(x.get(1),0L)+1);
        }
        long sum = a.size();

        // for any x, # of elements with different d1 and d2
        // = sum-d1hash[x]-d2hash[x]+counts[x]

        HashMap<ArrayList<Integer>, Long> hashPairs=new HashMap<>();
        HashMap<Integer, Long> d1hashPairs=new HashMap<>();
        HashMap<Integer, Long> d2hashPairs=new HashMap<>();
        long pairwise = 0;  // sum_i sum_j (i=/=j) s[i]*s[j]
        for (ArrayList<Integer> x : counts.keySet()) {
            long pairs =counts.get(x) * (sum-d1hash.get(x.get(0))-d2hash.get(x.get(1))+counts.get(x));
            pairwise += pairs;
            hashPairs.put(x, hashPairs.getOrDefault(x, 0L)+pairs);
            d1hashPairs.put(x.get(0), d1hashPairs.getOrDefault(x.get(0), 0L)+pairs);
            d2hashPairs.put(x.get(1), d2hashPairs.getOrDefault(x.get(1), 0L)+pairs);
        }
        pairwise /= 2;
        long ans=0;
        for (ArrayList<Integer> x : counts.keySet()) {
            // Subtract pairs that involve some y whose d1 and/or d2 are the same as x
            ans += (
                    pairwise
                    - d1hashPairs.get(x.get(0))
                    - d2hashPairs.get(x.get(1))
                    + hashPairs.get(x)
                    + (d1hash.get(x.get(0))-1)*(d2hash.get(x.get(1))-1)   // # pairs (y,z) where y[0]==x[0] and z[1]==x[1]
                    ) * counts.get(x);

            //ans += (pairwise - (counts.get(x) * (sum-counts.get(x))))*counts.get(x);
            //System.out.println(x+" "+counts.get(x)+" "
            //        + pairwise + " " + d1hashPairs.get(x.get(0)) + " "
            //        + d2hashPairs.get(x.get(1)) + " " + hashPairs.get(x)
            //);
        }
        //System.out.println(counts);
        //System.out.println(sum+" "+pairwise+" "+(ans/3));
        //System.out.println(hashPairs+" "+d1hashPairs+" "+d2hashPairs);
        return ans/3;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for (int ti = 0; ti < t; ti++) {
            int n=Integer.parseInt(in.readLine());
            ArrayList<Integer> top=new ArrayList<>(), dif=new ArrayList<>();
            ArrayList<ArrayList<Integer>> td=new ArrayList<>();
            for (int i=0;i<n;i++) {
                String[] l=in.readLine().split(" ");
                int a=Integer.parseInt(l[0]),b=Integer.parseInt(l[1]);
                top.add(a);
                dif.add(b);
                ArrayList<Integer> l3=new ArrayList<>();
                l3.add(a);
                l3.add(b);
                td.add(l3);
            }
            //System.out.println(count(top));
            System.out.println(count1d(top)-count2d(td)+count1d(dif));
        }
    }
}
