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 scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int[] a = new int[N];
        HashMap<Integer,Integer> count = new HashMap<>();
        for(int i=0; i<N; i++){
            a[i] = scanner.nextInt();
            int c = count.getOrDefault(a[i], 0);
            count.put(a[i], ++c);
        }
        long allpair = 0;
        for(int i:count.keySet()){
            int val = count.get(i);
            if(val>0){
                allpair += (long)val*((long)val-1)/2;
            }
        }
        for(int i=0; i<N; i++){
            int num = a[i];
            if(count.get(num)>1){
                System.out.println(allpair - (count.get(num)-1));
            }else{
                System.out.println(allpair);
            }
        }
    }
}