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.*;
import java.util.*;
import java.math.*;


public class Main
{

    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int arr[] = new int[n+1];
        long num[] = new long[n+1];
        for(int i=1;i<=n;i++){
            arr[i] = sc.nextInt();
            num[arr[i]]++;
        }
        long ans = 0;
        for(int i=1;i<=n;i++){
            // System.out.println(num[i]);
            ans += num[i]*(num[i]-1)/2;
        }
        // System.out.println(ans);
        for(int i=1;i<=n;i++){
            long x = ans - (num[arr[i]] - 1);
            System.out.println(x);
        }
    }

}
