Dima got into number sequences. Now he's got sequence a1, a2, ..., an, consisting of n positive integers. Also, Dima has got a function f(x), which can be defined with the following recurrence:

  * f(0) = 0; 
  * f(2·x) = f(x); 
  * f(2·x + 1) = f(x) + 1. 



Dima wonders, how many pairs of indexes (i, j) (1 ≤ i < j ≤ n) are there, such that f(ai) = f(aj). Help him, count the number of such pairs. 

Input

The first line contains integer n (1 ≤ n ≤ 105). The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

The numbers in the lines are separated by single spaces.

Output

In a single line print the answer to the problem.

Please, don't use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3
1 2 4


Output

3


Input

3
5 3 1


Output

1

Note

In the first sample any pair (i, j) will do, so the answer is 3.

In the second sample only pair (1, 2) will do.
import java.util.Scanner;
import java.util.Arrays;
import java.io.*;

public class Main
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] ar = new int[33];
        for (int i = 1; i <= n; ++i)
        {
            int a = in.nextInt();
            int tmp = 0;
            while (a > 0)
            {
                if (a % 2 == 1) 
                {
                    ++tmp;
                }
                a = a >> 1;
            }
            ar[tmp]++;
        }

        long sum = 0;
        for (int i = 0; i<=32; ++i)
        {
            sum += ar[i] *1L* (ar[i]-1)/2;
        }

        System.out.print(sum);
    }
}
    

