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.stream.*;
import java.io.*;

public class Main {

  public static void main(String[] args) throws IOException {

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

    String[] in;
    in = br.readLine().split(" ");
    int n = Integer.parseInt(in[0]);

    in = br.readLine().split(" ");
    long[] a = Stream.of(in).mapToLong(Long::parseLong).toArray();

    br.close();

    Map<Long, Long> m = new HashMap<>();

    for(int i = 0; i < n; i++){
      m.put(a[i], m.getOrDefault(a[i], 0L) + 1L);
    }

    long ans = 0;

    for(Map.Entry<Long, Long> e : m.entrySet()){
      ans += e.getValue() * (e.getValue() - 1) / 2;
    }

    for(int i = 0; i < n; i++){
      System.out.println(ans - m.get(a[i]) + 1);
    }
    
  }
}