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.HashMap;
import java.util.HashSet;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		HashSet<Long> first = new HashSet<>();
		HashMap<Long, Long> map = new HashMap<>();

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] array = new long[n];
		for (int i = 0; i < n; i++) {
			long a = sc.nextInt();
			array[i] = a;
			if (first.contains(a)) {
				if (map.containsKey(a)) {
					long num = map.get(a);
					map.put(a, num + 1);
				} else {
					map.put(a, 2L);
				}
			} else {
				first.add(a);
			}
		}
		sc.close();

		long answer = 0;
		for (long value : map.values()) {
			long product = (value * (value - 1)) / 2;
			answer = answer + product;
		}

		for (int i = 0; i < n; i++) {
			long a = array[i];
			if (!map.containsKey(a)) {
				print(answer);
			} else {
				long dup = map.get(a);
				long subtractAns = answer - dup + 1;
				print(subtractAns);
			}
		}

	}

	public static void print(Object obj) {
		System.out.println(obj);
	}

}