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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());

		Map<Integer, Long> map = new HashMap<>();
		int a[] = new int[n];

		String str[] = br.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			int aa = Integer.parseInt(str[i]);
			a[i] = aa;

			if (map.containsKey(aa))
				map.put(aa, map.get(aa) + 1);
			else
				map.put(aa, 1L);
		}

		long res = 0;
		for (int key : map.keySet()) {
			res += map.get(key) * (map.get(key) - 1) / 2;
		}

		for (int i = 0; i < n; i++) {
			long val = map.get(a[i]);
			long before = val * (val - 1) / 2;
			long after = (val - 1) * (val - 2) / 2;
			System.out.println(res - before + after);
		}
	}
}