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 sc = new Scanner(System.in);

		int N = sc.nextInt();
		int[] arr = new int[N];
		long[] con_arr = new long[N + 1];
		long all = 0;

		for (int i = 0; i < N; i++) {
			int let = sc.nextInt();
			arr[i] = let;
			con_arr[let]++;
		}

		for (int i = 1; i < N + 1; i++) {
			if (con_arr[i] > 0) {
				all += con_arr[i] * (con_arr[i] - 1) / 2;
			}
		}

		for (int i = 0; i < arr.length; i++) {
			int bannd = arr[i];
			System.out.println(all - (con_arr[bannd] - 1));
		}
	}
}