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.Map;
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> m = new HashMap<Integer,Long>(); 
			
			
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
				m.merge(a[i], 1L, Long::sum);
			}
			
			long ret = 0L;
			
			for(Map.Entry<Integer, Long> e :m.entrySet()) {
	  			int key = e.getKey();
	  			long val = e.getValue();
	  			ret+=val*(val-1)/2;
	  		}
			
			for(int k=0;k<n;k++) {
		  		System.out.println(ret-(m.get(a[k])-1));
			}
			
	    }
				
	}
	
