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 static java.lang.System.*;
import java.util.*;
public class Main {
	public static void main(String[] args) {
        Scanner sc = new Scanner(in);
        int N = sc.nextInt();
        int[] a = new int [N];
        int[] count = new int[200001];
        Set<Integer> set = new HashSet<>();
        for (int i=0; i<N; i++) {
            int num = sc.nextInt();
            a[i] = num;
            count[num] += 1;
            set.add(num);
        }
        long ans = 0;
        ArrayList<Integer> list = new ArrayList<>(set);
        for (int j=0; j<list.size(); j++) {
            int cnum = count[list.get(j)];
            ans += ((long)cnum*(long)(cnum-1)/2);
        }
        for (int k=0; k<N; k++)
            out.println(ans-(count[a[k]]-1));
    }
}