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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		
		int n = scan.nextInt();
		
		int[] in = new int[n];
		int[] arr = new int[n + 1];
		for (int i = 0; i < n; i++) {
			int a = scan.nextInt();
			in[i] = a;
			arr[a]++;
		}
		long[] res = new long[n + 1];
		long sum = 0;
		for (int i = 0; i <= n; i++) {
			res[i] = 0;
			for (int k = 1; k <= arr[i] - 1; k++) {
				res[i] += k;
			}
			sum += res[i];
		}
		for (int i = 0; i < n; i++) {
			long tmp = sum - res[in[i]];
			tmp += (res[in[i]] - 1) <= 0 ? 0 : (res[in[i]] - (arr[in[i]] - 1));
			System.out.println(tmp);
		}
	}

}
