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();
			long[] a = new long[n];
			long[] num = new long[n+1];
			
			for(int i=0;i<n;i++) {
				a[i] = sc.nextInt();
				num[(int)a[i]-1]++;
			}
			
			long aret = 0;
			
			for(int i=0;i<n;i++) {
				if(num[i]<=1) {
					continue;
				}else {
					aret+=num[i]*(num[i]-1)/2;
				}
				
			}
			
			for(int i=0;i<n;i++) {
				System.out.println(aret-num[(int)a[i]-1]+1);
			}
			
			
	    }
				
	}
