We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.

* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.

Constraints

* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

For each k=1,2,...,N, print a line containing the answer.

Examples

Input

5
1 1 2 1 2


Output

2
2
3
2
3


Input

4
1 2 3 4


Output

0
0
0
0


Input

5
3 3 3 3 3


Output

6
6
6
6
6


Input

8
1 2 1 4 2 1 4 1


Output

5
7
5
7
7
5
7
5
import java.util.*;
import static java.lang.System.*;

import java.io.IOException;
import java.io.InputStream;

public class Main{
  public static void main(String[] args){
	  Scanner sc = new Scanner(System.in);
	  int N = sc.nextInt();
	  long[]score = new long[N+1];
	  int[] k = new int[N+1];
	  long sum = 0;
	  
	  for(int i=0; i<N; i++) {
		  int n = sc.nextInt();
		  score[n]++;
		  k[i+1] = n;
	  }
	  for(int i=1; i<=N; i++) {
		  sum += score[i] * (score[i]-1) / 2;
	  }
	  //out.println(sum);
	  for(int i=1; i<=N; i++) {
		  long ans = sum - score[k[i]] + 1;
		  if (ans < 0 ) ans = 0;
		  out.println(ans);
	  }

  }
}

