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;

public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] a = new int[n];
		long[] sum = new long[n + 1];
		long[] com = new long[n + 1];
		long[] subcom = new long[n + 1];

		int i;
		for(i = 0; i < n; i++) {
			a[i] = scan.nextInt();
			sum[a[i]]++;
		}
		for(i = 0; i < n + 1; i++) {
			if(sum[i] == 0 || sum[i] == 1)
				continue;
			subcom[i] = ((sum[i] - 2) * (sum[i] - 1)) / 2;
		}

		long total = 0;
		for(i = 0; i < n + 1; i++) {
			if(sum[i] == 0 || sum[i] == 1)
				continue;
			com[i] = ((sum[i] - 1) * sum[i]) / 2;
			total += com[i];
		}

		for(i = 0; i < n; i++) {
			System.out.println(total - com[a[i]] + subcom[a[i]]);
		}
	}
}