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.*;
import java.lang.Math;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);  
   	int n = sc.nextInt();
    int as[] = new int[n+1];
    int as2[] = new int[n+1];
    Map nMap = new HashMap<Integer,Integer>();
    List nList = new ArrayList<Integer>();
    int count = 0;
    long ap = 0;
    int istack;
    int cnt;
    
    for(int i = 0;i < n;i++) {
      as[i] = sc.nextInt();
      as2[i] = as[i];
    }
    as2[n] = n + 1;
    Arrays.sort(as2);
    istack = as2[0];
    cnt = 1;
    for(int i = 1;i <= n;i++){
      if(istack == as2[i]) cnt++;
      else{
        ap += (long)cnt*(cnt-1);
        nMap.put(istack,cnt-1);
        istack = as2[i];
        cnt = 1;
      }
    }
    ap /= (long)2;
    
    for(int i = 0;i < n;i++){
      System.out.println(ap - (int)nMap.get(as[i]));
    }
    
    

  }
}
