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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long count[] = new long[N + 1];
		long sum[] = new long[N + 1];
		Arrays.fill(count, 0);
		Arrays.fill(sum, 0);
		int A[] = new int[N];

		for (int i = 0; i < N; i++) {
			int tmp = sc.nextInt();
			A[i] = tmp;
			count[tmp]++;
		}

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

		for (int i = 0; i < N; i++) {
			int tmp = A[i];
			long tmp2 = ((count[tmp] - 1) * ((count[tmp] - 1) - 1)) / 2;
			System.out.println(allSum - sum[tmp] + tmp2);
		}
	}
}