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();
  		int[] a=new int[n];

  		long[] b=new long[n+1];
  		b[0]=0;
		for(int c=0;c<n;c++){
    		a[c]=sc.nextInt();
          	b[a[c]]++;
    	}
  		long d=0;
  
  		for(int c=0;c<n+1;c++){
        	d+=b[c]*(b[c]-1)/2;
        }
  		long ans=0;
  		for(int c=1;c<n+1;c++){
          if(b[a[c-1]]!=0){
        	ans=d-b[a[c-1]]*(b[a[c-1]]-1)/2+(b[a[c-1]]-1)*(b[a[c-1]]-2)/2;
          }else{
          ans=d;
          }
          System.out.println(ans);
        }
    
 	

    	
    }
}