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;

class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		long[] a = new long[200001];
		long[] b = new long[200001];
		int[] actual = new int[n];
		for(int i=0; i<n; i++) {
			int x = scanner.nextInt();
			a[x] += 1;
			actual[i] = x;
		}
		long total = 0;

		for(int i=0; i<200001; i++) {
			b[i] = (a[i]*(a[i]-1))/2;
			total += b[i];
		}

		for(int x : actual) {
			System.out.println(total - b[x] + ((a[x]-1) * (a[x]-2))/2);
		}
	}
}