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.IOException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextInt();

		long[] a = new long[(int) N];
		long[] values = new long[(int) (N+1)];

		for (int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
			values[(int) a[i]]++;
		}
		sc.close();

		long sum = 0;
		for (long c : values) {
			if(c > 1) {
			sum += (c-1)*c/2;
			}
		}

		for (long c :a) {
			System.out.println(sum - (values[(int) c]-1));
		}

	}

}
