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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
     private static int Find(int num){
        if (num==0) return 0;
        if (num==1) return 1;
        if (num%2==0) return Find(num/2);
        else return Find(num/2) + 1;
    }
    public static void main (String[] args)
    {       
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int arr[] = new int[n];
        for (int i=0;i<n;++i){
            arr[i] = sc.nextInt();
            arr[i] = Find(arr[i]);
        }
        Map<Integer, Integer> m= new HashMap<Integer, Integer>();
       // for (int i=0;i<n;++i) System.out.print(arr[i] + " ");
       // System.out.println();
        for (int i=0;i<n;++i){
            //System.out.print(arr[i] + " ");
            if (m.containsKey(arr[i])) m.put(arr[i],(Integer) m.get(arr[i])+1);
            else m.put(arr[i], 1);
        }
        long res = 0;
        for (Integer entry : m.keySet()){
            long k = (long) m.get(entry);
            res += k*(k-1)/2;
        }
        System.out.println(res);
        sc.close();
    }
}