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.HashMap;
import java.util.Scanner;

public class Main {
	

	
	public static void main(String[] args) {

		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int a[] = new int[n];
		HashMap<Integer,Long> h = new HashMap<>();
		for(int i=0;i<n;i++)
		{
			a[i] = s.nextInt();
			if(h.containsKey(a[i])) {
				h.put(a[i], h.get(a[i])+1);
			}
			else {
				h.put(a[i],1l);
			}
		}
	
		long sum = 0;
		for(int i:h.keySet()) {
			sum+=(h.get(i)*(h.get(i)-1))/2;
		}
		
		for(int i=0;i<n;i++) {
			long a1 = h.get(a[i]);
			long ans = sum-((a1)*(a1-1))/2+((a1-1)*(a1-2))/2;
			System.out.println(ans);
		}
		
		
		
		
	}
}