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.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];
    HashMap<Integer, Long> map = new HashMap<>();
    for (int i = 0; i < N; i++) {
      A[i] = sc.nextInt();
      map.put(A[i], map.getOrDefault(A[i], 0L) + 1);
    }
    long sum = 0;
    for (Long val : map.values()) {
      sum += val * (val - 1) / 2;
    }
    for (int i = 0; i < N; i++) {
      long sum1 = sum;
      long val = map.get(A[i]);
      sum1 -= val * (val - 1) / 2;
      if (val > 2) {
        sum1 += (val - 1) * (val - 2) / 2;
      }
      System.out.println(sum1);
    }
  }
}
