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.Map;
import java.util.Scanner;

public class Main {

    private static Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {

        solve();
    }

    private static void solve() {

        int n = scanner.nextInt();

        Map<Integer, Long> count = new HashMap<>();
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            int a = scanner.nextInt();
            arr[i] = a;
            long c = count.getOrDefault(a, 0l);
            count.put(a, c + 1);
        }

        long total = 0;

        for (Map.Entry<Integer, Long> e : count.entrySet()) {
            total += e.getValue() * (e.getValue() - 1) / 2;
        }

        for (int a : arr) {
            long c = count.get(a);
            long res = total - c + 1;
            System.out.println(res);
        }
    }
}