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.io.*;

public class Main{
  public static void main(String[] args)throws Exception{
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.nextLine());
    String[] S = sc.nextLine().split(" ");
    Map<Long, Long> map = new HashMap<>();
    long[] val = new long[N];
    for(int i = 0; i < N; i++){
      val[i] = Long.parseLong(S[i]);
    }
    for(int i = 0; i < N; i++){
      if(map.containsKey(val[i])){
        map.put(val[i], map.get(val[i])+1);
      }else{
        map.put(val[i],1l);
      }
    }
    
    long ans = 0;
    for(Map.Entry<Long, Long> en : map.entrySet()){
      long b = en.getValue();
      ans += (b*(b-1))/2;
    }
    
    for(int i = 0; i < N; i++){
      long a = map.get(val[i]);
      long b = ((a*(a-1))-((a-1)*(a-2)))/2;
      System.out.println(ans-b);
    }
  }
}