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();
    long a[] = new long[n];
    HashMap<Long, Long> num1 = new HashMap<Long, Long>();
    HashMap<Long, Long> num2 = new HashMap<Long, Long>();
    for(int i = 0 ; i < n ; ++i){
      a[i] = sc.nextInt();
      if(!num1.containsKey(a[i])){
        num1.put(a[i],(long)1);
      }else{
        num1.put(a[i],num1.get(a[i])+1);
      }
    }
    long sum = 0;
    long ans = 0;
    
    for(long i : num1.keySet()){
      num2.put(i, num1.get(i) * (num1.get(i)-1) / 2);
      sum += num1.get(i)*(num1.get(i)-1)/ 2;
    }
    for (int i = 0 ; i < n ; ++i) {
      ans = sum-num2.get(a[i])+(num1.get(a[i])-1)*(num1.get(a[i])-2)/2;
      System.out.println(ans);
    }
  }
}