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.Scanner;

final class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Scanner sc) {
		int N = sc.nextInt();
		int[] A = new int[N];
		int[] count = new int[2 * 100000];
		for (int i = 0; i < N; i++) {
			count[(A[i] = sc.nextInt()) - 1] += 1;
		}
		long pattern = 0;
		for (int i : count) {
			pattern += i * (i - 1L) / 2;
		}
		for (int a : A) {
			int c = count[a - 1];
			long orig = (c * (c - 1L)) / 2;
			long to = Math.max(((c - 1L) * (c - 2)) / 2, 0);
			System.out.println(pattern - orig + to);
		}
	}
}

class Main {
	public static void main(String... args) {
		Scanner in = new Scanner(System.in);

		Solver.INSTANCE.solve(in);

		in.close();
	}
}