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.Scanner;
class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] in = new int[n];
    int[] cal = new int[n];
    for(int i = 0; i < n; i++){
      in[i] = Integer.parseInt(sc.next());
      cal[in[i] - 1]++;
    }
    long sum = 0L;
    for(int i = 0; i < n; i++){
      if(cal[i] == 0){
        continue;
      }else{
       sum += ((long)cal[i] * (cal[i] - 1)) /  2;
      }
    }
    long[] out = new long[n];
    for(int i = 0; i < n; i++){
      if(cal[i] == 0){
        continue;
      }else{
        out[i] = sum - (cal[i] - 1);
      }
    }
    for(int i = 0; i < n; i++){
      System.out.println(out[in[i] - 1]);
    }
  }
}