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.*;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = 200000;
        int[] b = new int[n];
        int[] a = new int[m+1];

        for(int i=0; i<n; i++) {
            b[i] = sc.nextInt();
            a[b[i]]++;
        }
        long sum = 0;
        for(int i=1; i<m; i++) {
            sum += ((long)a[i] * (a[i]-1) / 2);
        }

        for(int i=0; i<n; i++) {
            int num = b[i];
            long res = sum - (long)a[num] * (a[num]-1) / 2 + (long)(a[num]-1) * (a[num]-2) / 2;
            System.out.println(res);
        }
    }


}