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.HashMap;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] a = new int[n];
		HashMap<Integer, Long> map = new HashMap<Integer, Long>();

		for (int i = 0; i < n; i++) {
			a[i] = scanner.nextInt();
			if (map.containsKey(a[i])) {
				map.put(a[i], map.get(a[i]) + 1);
			} else {
				map.put(a[i], 1l);
			}
		}
		long sum = 0;
		for (long i : map.values()) {
			sum += i * (i - 1) / 2;
		}

		long[] ans = new long[n];

		long b = 0;
		for (int i = 0; i < n; i++) {
			b = map.get(a[i]) - 1;
			if (b > 0)
				ans[i] = sum - b;
			else
				ans[i] = sum;
		}

		for (long i : ans) {
			System.out.println(i);
		}
	}

}
