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.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int[] a = new int[n];
			Map<Integer, Integer> map = new HashMap<>();
			IntStream.range(0, n).forEach(i -> {
				a[i] = scanner.nextInt();
				map.put(a[i], map.getOrDefault(a[i], 0) + 1);
			});
			long sum = map.entrySet().stream().mapToLong(entry -> c(entry.getValue(), 2)).sum();
			Arrays.stream(a).forEach(i -> System.out.println(sum - c(map.get(i), 2) + c(map.get(i) - 1, 2)));
		}
	}

	private static long c(int n, int m) {
		if (m <= n) {
			long answer = 1L;
			for (int i = 1; i <= m; i++) {
				answer *= n + 1 - i;
				answer /= i;
			}
			return answer;
		}
		return 0L;
	}
}
