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 scan = new Scanner(System.in);
		long N = scan.nextLong();
		int arr[] = new int[(int)N];
		long count[] = new long[(int)N+1];
		long sum = 0;

		for (int i = 0; i < N ; i ++){
			arr[i] = scan.nextInt();
			count[arr[i]] += 1;
		}

		for(int i = 0; i <= N; i++){
			if(count[i] != 0 ){
				sum += count[i] * (count[i] -1) / 2;
			}
		}

		for(int k =0; k < N; k++){
			long ans = sum;
			if(count[arr[k]] > 1){
				ans -= count[arr[k]] * (count[arr[k]] - 1) / 2;
				ans += (count[arr[k]] - 1) * (count[arr[k]] - 2) / 2;
			}
			System.out.println(ans);
		}

	}
}