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.HashMap;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        HashMap<Integer, Integer> hm = new HashMap();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            if (hm.get(a[i]) == null) {
                hm.put(a[i], 1);
            }
            else {
                hm.put(a[i], hm.get(a[i]) + 1);
            }
        }
        long sum = 0;
        for( int key : hm.keySet()) {
            long tmp = hm.get(key);
            if (tmp < 2) continue;
            sum += (tmp * (tmp - 1)) / 2;
        }

        for (int ansIndex = 0; ansIndex < n; ansIndex++) {
            long ans = sum;
            long tmp = hm.get(a[ansIndex]);
            ans = ans - (tmp * (tmp - 1) / 2) + ((tmp - 1) * (tmp - 2) / 2);
            System.out.println(ans);
        }
    }
}