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];
        long[] num = new long[n + 1];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
            num[a[i]]++;
        }

        long[] ncr = new long[n + 1];
        long[] ncr1 = new long[n + 1];
        long sum = 0;

        for(int i = 1; i <= n; i++){
            ncr[i] = num[i] * (num[i] - 1) / 2;
            ncr1[i] = (num[i] - 1) * (num[i] - 2) / 2;
            sum += ncr[i];
        }

        for(int i = 0; i < n; i++){
            System.out.println(sum - ncr[a[i]] + ncr1[a[i]]);
        }

    }
}
