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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main
{
    public static void main(String[] arg)
    {
        Scanner scan = new Scanner(System.in);

        long n = scan.nextLong();

        long[] w = new  long[33];
        for(long i = 0; i < n; i++)
             w[calc(scan.nextLong())]++;    // w[Integer.bitCount(scan.nextInt())]++;

        long res = 0;
        for(int i = 0; i < 33; i++)
            res += w[i] * (w[i]-1) / 2;

        System.out.println(res);

    }

    private static int calc(long x)
    {
        if(x == 0)
            return 0;
        return x % 2 == 0 ? calc(x/2) : calc(x/2)+1;
    }
}
