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.util.*;
 import java.lang.*;
 import java.io.*;

public class D_Training_Session
 {
     static int M = 1_000_000_007;
     static final PrintWriter out =new PrintWriter(System.out);
     static final FastReader fs = new FastReader();
     static boolean prime[];
     public static void main (String[] args) throws java.lang.Exception
     {
           
           int t= fs.nextInt();
           for(int i=0;i<t;i++)
           {
               int n= fs.nextInt();
               int a[]=new int[n];
               int b[]=new int[n];
               HashMap<Integer, ArrayList<Integer>> hm1=new HashMap<Integer,ArrayList<Integer>>();
               HashMap<Integer, ArrayList<Integer>> hm3=new HashMap<Integer,ArrayList<Integer>>();
              //HashMap<Integer, Integer> hm2=new HashMap<Integer,Integer>();
               for(int j=0;j<n;j++){
                    a[j]=fs.nextInt();
                    b[j]=fs.nextInt();
                    if(hm1.get(a[j])==null){
                    hm1.put(a[j],new ArrayList<Integer>());
                }
                    if(hm3.get(b[j])==null){
                    hm3.put(b[j],new ArrayList<Integer>());
                }
                    hm1.get(a[j]).add(b[j]);
                    hm3.get(b[j]).add(a[j]);
                   
               }
               long ans=nCk(n, 3);
               for(Map.Entry<Integer,ArrayList<Integer>> entry:hm1.entrySet()){
                  // int ai=entry.getKey();
                   for(int jj=0;jj<entry.getValue().size();jj++){
                    ans=ans-(entry.getValue().size()-1)*(hm3.get(entry.getValue().get(jj)).size()-1);
                   }                 
               }
               out.println(ans);
           }
           out.flush();
  }
  public static long power(long x, long y)
  {
      long temp;
      if (y == 0)
          return 1;
      temp = power(x, y / 2);

      if (y % 2 == 0)
          return modMult(temp,temp);
      else {
          if (y > 0)
              return modMult(x,modMult(temp,temp));
          else
              return (modMult(temp,temp)) / x;
      }
  }
  static void sieveOfEratosthenes(int n)
    {
         prime = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
            prime[i] = true;
            prime[0]=false;
            if(1<=n)
            prime[1]=false;
        for (int p = 2; p * p <= n; p++)
        {
            
            if (prime[p] == true)
            {
               
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
         static 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;
         }
 int [] arrayIn(int n) throws IOException
     {
         int  arr[] = new int[n];
         for(int i=0; i<n; i++)
         {
             arr[i] = nextInt();
         }
         return arr;
     }
     }
     
     public static class Pairs implements Comparable<Pairs>
     {
         int value,index;
         Pairs(int value, int index)
         {
             this.value = value;
             this.index = index;
         }
         public int compareTo(Pairs p)
         {
             return Integer.compare(this.value, p.value);
         }
     }
     static final Random random = new Random();
  
     static void ruffleSort(int arr[])
     {
         int n = arr.length;
         for(int i=0; i<n; i++)
         {
             int j = random.nextInt(n),temp = arr[j];
             arr[j] = arr[i];
             arr[i] = temp;
         }
         Arrays.sort(arr);
     }
     static long nCk(int n, int k) {
         return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
     }
  
     static long fact (long n) {
  
         long fact =1;
         for(int i=1; i<=n; i++) {
             fact = modMult(fact,i);
         }
         return fact%M;
     }
  
     static long modMult(long a,long b) {
         return a*b%M;
     }
  
     static long fastexp(long x, int y){
         if(y==1) return x;
  
         long ans = fastexp(x,y/2);
         if(y%2 == 0) return modMult(ans,ans);
         else return modMult(ans,modMult(ans,x));
     }
 }