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

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int inp_num = sc.nextInt();
        int[] history = new int[inp_num];
        HashMap<Integer,Long> counter = new HashMap<>();
        for(int i = 0;i < inp_num; i++){
            int num = sc.nextInt();
            history[i] = num;
            if(counter.containsKey(num)){
                counter.put(num,counter.get(num)+1);
            }else{
                counter.put(num, 1L);
            }
        }

        long total = 0;
        for(Entry<Integer,Long> key_value :counter.entrySet()){
            total += (key_value.getValue()*(key_value.getValue()-1))/2;
        }
        for(int num: history){
            System.out.println(total-(counter.get(num)-1));
        }
    }
}