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();
        Map<Integer, Integer> numMap = new HashMap<>();
        int[] numList = new int[N];
        for (int i = 0; i < N; i++) {
            int num = sc.nextInt();
            Integer count = numMap.get(num);
            if (Objects.isNull(count)) {
                numMap.put(num, 1);
            } else {
                numMap.put(num, count + 1);
            }
            numList[i] = num;
        }

        long allPatterns = 0;
        for (Integer count : numMap.keySet()) {
            long counts = numMap.get(count);
            if (counts <= 1) {
                allPatterns += 0;
            } else {
                allPatterns += counts * (counts - 1L) / 2L;
            }
        }
        for (int var : numList) {
            System.out.println(allPatterns - (long) (numMap.get(var) - 1));
        }
        sc.close();
    }

}
