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.*;
import java.util.TreeMap;
import java.util.Map;
 
class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
 
        int N = sc.nextInt();
        int[] A = new int[N];
        TreeMap<Integer, Integer> map = new TreeMap<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(int i : map.keySet()){
            sum += (long)map.get(i) * (map.get(i) - 1) / 2;
        }

        for(int i=0; i<N; i++){
            long a = sum;
            a -= (long)map.get(A[i]) * (map.get(A[i]) - 1) / 2;
            a += (long)(map.get(A[i]) - 1) * (map.get(A[i]) - 2) / 2;
            System.out.println(a);
        }
    }
}