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();

      Map<Integer, Long> freqMap = new HashMap<>();
      int[] balls = new int[n];
      for(int i = 0; i < n; i++) {
        balls[i] = sc.nextInt();
        freqMap.put(balls[i], freqMap.getOrDefault(balls[i], 0L) + 1);
      }

      long cnt = 0;
      for(Map.Entry<Integer, Long> entry : freqMap.entrySet()) {
        if(entry.getValue() < 2) continue;
        cnt += comb(entry.getValue());
      }

      for(int k = 0; k < n; k++) {
        int num = balls[k];
        long freq = freqMap.get(num);
        if(freq < 2) System.out.println(cnt);
        else {
          long removeCnt = comb(freq);
          long newCnt = comb(freq-1);
          System.out.println(cnt - removeCnt + newCnt);
        }
      }
  }

  private static long comb(long a) {
    if(a < 2) return 0;
    return a * (a - 1) / 2;
  }
}