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 input = new Scanner(System.in);
    
    int n = input.nextInt();
    Map<Integer, Integer> map = new HashMap<>();
    int[] a = new int[n];
    
    for (int i = 0; i < n; i++) {
      a[i] = input.nextInt();
      map.merge(a[i], 1, Integer::sum);
    }
    
    long total = 0;
    
    for (int val : map.values()) {
      total += (long)(val) * (val - 1) / 2;
    }
    
    StringBuilder ans = new StringBuilder();
    for (int i = 0; i < n; i++) {
      int size = map.get(a[i]);
      long tmp = total - (long)(size) * (size - 1) / 2;
      tmp += (long)(size - 1) * (size - 2) / 2;
      ans.append(tmp).append("\n");
    }
    
    System.out.print(ans);
  }
}