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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		long[] sum = new long[n + 1];
		for(int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			sum[a[i]]++;
		}
		long ans = 0;
		for(int i = 1; i < n + 1; i++) {
			if(sum[i] >= 2) {
				ans += sum[i] * (sum[i] - 1) / 2;
			}
		}
		for(int i = 0; i < n; i++) {
			long tmp = ans;
			if(sum[a[i]] >= 2) {
				tmp -= sum[a[i]] * (sum[a[i]] - 1) / 2;
			}
			if(sum[a[i]] - 1 >= 2) {
				tmp += (sum[a[i]] - 1) * (sum[a[i]] - 2) / 2;
			}
			System.out.println(tmp);
		}
	}

}
