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.Scanner;

public class Main {
    public static void main(String[] argv) {
        Scanner scanner = new Scanner(System.in);

        String line = scanner.nextLine();
        int n = Integer.parseInt(line);

        String ballStr = scanner.nextLine();
        String[] ballStrs = ballStr.split(" ");
        int[] balls = new int[n];
        int i = 0;
        for (String ballS : ballStrs) {
            balls[i++] = Integer.parseInt(ballS);
        }

        long[] map = new long[n + 1];
        for (int ball : balls) {
            map[ball]++;
        }

        long total = 0;

        for (long key : map) {
            if (key > 1) {
                total += key * (key - 1) / 2;
            }
        }

        for (int ball : balls) {
            long count = map[ball];
            System.out.println(total - (count - 1));
        }
    }
}