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();
        long L [] = new long[N+1];
        long DP[] = new long[N+1];
        long DP2[] = new long[N+1];
        int list[] = new int[N+1];
        Arrays.fill(L,0);
        Arrays.fill(DP,0);
        Arrays.fill(DP2,0);
        long sum = 0;
        for(int i=1;i<=N;i++){
            int num = sc.nextInt();
            L[num]++;
            list[i]=num;
        }
        for(int i=1;i<=N;i++) {
            if(L[i]!=0){
                DP[i] = (L[i]*(L[i]-1))/2;
                DP2[i] = ((L[i]-1)*(L[i]-2))/2;
                sum+=DP[i];
            }
        }
        for(int i=1;i<=N;i++){
           long opt = sum-DP[list[i]]+DP2[list[i]];
            System.out.println(opt);
        }
    }
}