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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int n = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();
		int[] c = new int[n + 1];
		for (int i = 0; i < n; i++)
			c[a[i]]++;
		long r = 0;
		for (int i = 0; i <= n; i++)
			if (c[i] > 1)
				r += (long) c[i] * ((long) c[i] - 1) / 2;
		for (int i = 0; i < n; i++) {
			long ans = solve(n, a[i], c, r);
			System.out.println(ans);
		}
	}

	private static long solve(int n, int a, int[] c, long r) {
		if (c[a] > 1)
			return r - c[a] + 1;
		else
			return r;
	}
}