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();
        HashMap<Integer,List<Integer>>map=new HashMap<>();
        int[] a=new int[n+1];
        for(int i=1;i<=n;i++)
        {
            int ball=sc.nextInt();
            a[i]=ball;
            if(map.get(ball)==null)map.put(ball,new ArrayList<>());
            map.get(ball).add(i);
        }

        long sum=0;
        for(int ball:map.keySet()){
            long s=map.get(ball).size();
            sum+=s*(s-1)/2;
        }
        for(int k=1;k<=n;k++){
            long res=sum;
            int ball=a[k];
            long s=map.get(ball).size();
            res-=s-1;
            System.out.println(res);
        }
    }
}