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.*;
public class Main {
	public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
    	long add = 0;
    	long ans = 0;
    	
		int N = sc.nextInt();
		long arry[]=new long[N+1];
		HashMap<Long, Long> map = new HashMap<Long, Long>();
		for(int i=1;i<=N;i++){
			long key1=sc.nextInt();
			arry[i]=key1;
			if (map.containsKey(key1)){
				map.put(key1,map.get(key1)+1);
			}
			else{
				map.put(key1,(long) 1);
			}
		}
//		for (Integer val : map.values()) {
//			add=add+val;
//		}
		for (Long key : map.keySet()) {
			add=add+(map.get(key)*(map.get(key)-1)/2);
		}
		for(int i=1;i<=N;i++){
			ans=add-(map.get(arry[i])-1);
			System.out.println(ans);
		}
    }
}