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.ArrayList;
import java.util.Hashtable;
import java.util.Iterator;
import java.util.Scanner;
import java.util.Vector;


public class codeforces {
public static void main(String[] args)
{
    Scanner s=new Scanner(System.in);
    int n=s.nextInt();
    Hashtable<Integer,Integer> v=new Hashtable<Integer,Integer>();
    long count=0;
    for(int i=0;i<n;i++)
    {
        int k=s.nextInt();
        int z=1;
        int t=number(k);
        if(!v.containsKey(t))
        {
            v.put(t,z);
        }
        else
        {
            int p=v.get(t);
             v.put(t, p+1);
        }
    }
    Iterator<Integer> it=v.keySet().iterator();
    while(it.hasNext())
    {   
        long w=v.get(it.next());
        if(w!=1)
        {
        long ncr=w*(w-1)/2;
        count=count+ncr;
        }
    }
    
    System.out.println(count);
    
}



public static int number(int n)
{
    if(n==0||n==-1)
        return 0;
    if(n%2!=0)
    return number(n/2-1/2)+1;
    if(n%2==0)
        return number(n/2);
    
    return 1000;
}
}
