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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        long[] a = new long[n];
        Map<Long, Long> map = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            long temp = Long.parseLong(sc.next());
            a[i] = temp;
            if (map.containsKey(temp)) {
                map.put(temp, map.get(temp) + 1);
            } else {
                map.put(temp, 1L);
            }
        }
        long ans = 0;
        for (Map.Entry<Long, Long> e : map.entrySet()) {
            ans += e.getValue() * (e.getValue() - 1) / 2;
        }
        for (int i = 0; i < n; i++) {
            System.out.println(ans - (map.get(a[i]) - 1));
        }
    }
}