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];
      HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
      for(int i=0;i<N;i++){
        A[i] = sc.nextInt();
        if(map.containsKey(A[i])){
          map.put(A[i],map.get(A[i])+1);
        }else{
          map.put(A[i],1);
        }
      }
      long sum = 0;
      for(Integer v : map.values()){
		 for(int i=1;i<v;i++){
           sum+=i;
         }
      }
      for(int i=0;i<N;i++){
        System.out.println(sum-(map.get(A[i])-1));
      }
    }
}
