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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();

		int[] a = new int[n];
		int[] k = new int[n];
		for ( int i=0; i<n; i++ ) {
			a[i] = sc.nextInt() - 1;
			k[a[i]]++;
		}

		long c = 0;
		for ( int i=0; i<n; i++ ) {
			c = c + (long)k[i]*((long)k[i]-1l)/2l;
		}
		for ( int i=0; i<n; i++ ) {
			long c0 = (long)k[a[i]]*((long)k[a[i]]-1l)/2l;
			long c1 = 0;
			if ( k[a[i]]!=0) {
				c1 = ((long)k[a[i]]-1l)*((long)k[a[i]]-2l)/2l;
			}

			System.out.println(c-c0+c1);
		}

	}
}