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();
    long ans = 0;
    HashMap<Integer, Long> map = new HashMap<Integer, Long>();
    int[] a = new int[n];
    for(int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
      if(map.containsKey(a[i])) {
        ans += map.get(a[i]);
        map.put(a[i], map.get(a[i]) + 1);
      } else {
        map.put(a[i], (long)1);
      }
    }
    for(int i = 0; i < n; i++) {
      System.out.println(ans - (map.get(a[i]) - 1));
    }
  }
}