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.Map;
import java.util.Scanner;
import java.util.Set;

public class Main {

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		int[] balls = new int[N];
		long[] sizes = new long[N + 1];
		Set<Integer> contain = new HashSet<>();
		long answerT = 0;
		Map<Integer, Long> temp1 = new HashMap<>();
		Map<Integer, Long> temp2 = new HashMap<>();

		for (int i = 0; i < N; i++) {
			int num = scanner.nextInt();
			balls[i] = num;
			contain.add(num);
			sizes[num]++;
		}

		for (int k : contain) {
			long size = sizes[k];
			temp1.put(k, size * (size - 1) / 2);
			temp2.put(k, (size - 1) * (size - 2) / 2);
			answerT += temp1.get(k);
		}

		for (int i = 0; i < N; i++) {
			int ball = balls[i];
			long answer = 0;

			answer = answerT - temp1.get(ball) + temp2.get(ball);
			System.out.println(answer);
		}
	}
}