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 {
	public static void main(String[] args) throws Exception{
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int[] a = new int[n];
		for(int i=0; i<n; i++){
			a[i] = scn.nextInt();
		}
      	int[] b = new int[n+1];
      	for(int i=0; i<n; i++){
          b[a[i]] ++;
        }
      	long all = 0;
      	for (int i=1; i<n+1; i++) {
			if(b[i]>0){
				all += (long)b[i]*(b[i]-1)/2;
			}
		}
		for (int i=0; i<a.length; i++) {
			int x = a[i];
			System.out.println(all-(b[x]-1));
        }
	}
}
