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;

public class Main{
    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] a = new int[n];
    long[] numSumList = new long[n + 1];
    long all = 0;

    for(int i = 0 ; i < n ; i++){
      a[i] = sc.nextInt();
      numSumList[a[i]]++;
    }
      for(int i = 1 ; i <= n ; i++){
        long j = numSumList[i];
        all += j * (j - 1L) / 2L;
	}
      String s = "";
      StringBuilder sb = new StringBuilder(s);
      for(int i = 0 ; i < a.length ; i++){
        long k = numSumList[a[i]];
        sb.append(all - (k - 1) + "\n");
      }
      System.out.println(sb.toString());
    }
}
