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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    
    int n = sc.nextInt();
    long[] val = new long[n+1];
    for(int i=0;i<n+1;i++){
      val[i] = 0;
    }
    int[] a = new int[n];
    
    int tmp;
      
    for(int i=0;i<n;i++){
      tmp = sc.nextInt();
      a[i] = tmp;
      val[tmp] += 1;
    }
    
    long ans =0;
    for(int k=1;k<n+1;k++){
      ans += val[k]*(val[k]-1)/2;
    }
    
    long g =0;
    for(int j=0;j<n;j++){
      g = val[a[j]] -1 ;
      System.out.println(ans - g);
    }
      
      
   
  }
}