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.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        List<Integer> A = new ArrayList<Integer>();
        for (int i=0; i<N; i++) {
            A.add(sc.nextInt());
        }
        Map<Object, Long> countDict = A.stream().collect(
                        Collectors.groupingBy(x -> x, Collectors.counting()));
        long total = 0;
        for (Object key: countDict.keySet()) {
            long count = countDict.get(key);;
            total += count * (count - 1) / 2;
        }
        for (int k=0; k<N; k++) {
            System.out.println(total - countDict.get(A.get(k)) + 1);
        }
    }
}