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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int[] a = new int[n];
        Map<Integer, Integer> map = new HashMap<>();
        for(int i = 0; i < n; i++){
            a[i] = Integer.parseInt(sc.next());
            map.put(a[i], map.getOrDefault(a[i], 0) +1);
        }
        
        long c = 0;
        for (Integer i : map.keySet()) {
            long j = map.get(i);
            if(j >= 2){
                c += (j * (j-1)) /2;
            }
        }
        
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < n; i++){
            sb.append(c - (map.get(a[i]) -1)).append(System.lineSeparator());
        }
        System.out.print(sb);
    }
}