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.io.*;
import java.util.*;
import java.lang.Math.*;
public class seq
{
     public static void main(String args[])throws Exception
     {
         BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
         PrintWriter pw = new PrintWriter(System.out);
         StringTokenizer st;
         int n=Integer.parseInt(br.readLine());
         st=new StringTokenizer(br.readLine());
         int i,j,k,l;
         int a[]=new int[101];
         for(i=0;i<n;i++)
         {
             k=Integer.parseInt(st.nextToken());
             int sum=0;
             while(k>0)
             {
                 if(k%2==1)
                 {
                     sum+=1;
                    }
                 k/=2;   
             }
             a[sum]++;
             sum=0;
           
            }
         long val=0;   
         for(i=0;i<=100;i++)
         {
             val+=(long)((long)a[i]*(long)(a[i]-1))/(long)2;
            }
         System.out.println(val);   
     }
}