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.Map.Entry;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int n = scanner.nextInt();
    int[] a = new int[n];
    Map<Integer, Long> counter = new HashMap<>();
    long sum = 0;

    for (int i = 0; i < n; i++) {
      a[i] = scanner.nextInt();
      if (counter.containsKey(a[i])) {
        counter.put(a[i], counter.get(a[i]) + 1);
      } else {
        counter.put(a[i], (long) 1);
      }
    }

    for (final Entry<Integer, Long> entry : counter.entrySet()) {
      if (entry.getValue() > 1) {
        sum += entry.getValue() * (entry.getValue() - 1) / 2;
      }
    }

    for (int i = 0; i < n; i++) {
      long count = counter.get(a[i]);
      if (count == 1) {
        System.out.println(sum);
      } else {
        System.out.println(sum - (count * (count - 1) / 2) + ((count - 1) * (count - 2) / 2));
      }
    }
  }
}
