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[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] a = new int[n];

    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
    }

    int[] cnt = new int[n];
    for (int m : a) {
      cnt[m - 1]++;
    }

    long sum = 0;
    for (int i = 0; i < n; i++) {
      if (cnt[i] < 2) {
        continue;
      }

      long tmp = cnt[i];
      sum += tmp * (tmp - 1) / 2;
    }

    for (int i = 0; i < n; i++) {
      int tmp = a[i] - 1;
      if (cnt[tmp] < 2) {
        System.out.println(sum);
      } else {
        System.out.println(sum - (cnt[tmp] - 1));
      }
    }
  }
}
