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){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a=new int[n];
		Map<Integer,Long> group=new HashMap<>();
		for(int i=0;i<n;i++){
			a[i]= sc.nextInt();
			Long x=group.get(a[i]);
			if(x==null){
				group.put(a[i],(long)1);
			}else{
				group.put(a[i],x+1);
			}
		}
      	long all=0;
      	for(Integer key:group.keySet()){
          long v=group.get(key);
          all+=v*(v-1)/2;
        }  
		for(int i=0;i<n;i++){
			System.out.println(all-group.get(a[i])+1);
		}
		
	}
}
