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.io.*;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
   
    int n = Integer.parseInt(br.readLine());
    
    int[] a = new int[n];
    int[] b = new int[n];
    String[] data = br.readLine().split(" ");
    int temp;
    for (int i=0; i<n; i++){
      temp = Integer.parseInt(data[i])-1;
      a[temp]++;
      b[i] = temp;
    }
    long sum = 0;
    for (int i=0; i<n; i++){
      sum += ((long) a[i]*((long) a[i]-1))/2;
    }
    long result;
    for (int i=0; i<n; i++){
      result = sum - ((long) a[b[i]]*((long) a[b[i]]-1))/2 + ((long) (a[b[i]]-1)*((long) a[b[i]]-2))/2;
      System.out.println(result);
    }
  }
}
