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