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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.StringTokenizer;

public class TC
{
    static HashMap<Integer, Integer> memo=new HashMap();
    static HashMap<Integer, Integer> cnt=new HashMap();
    static int[] a;
    
    static int f( int n )
    {
        if( n==0 )
            return 0;
        
        if( memo.containsKey( n ))
            return memo.get( n );
        
        int res=-1;
        
        if( n%2 == 0 )
            res=f( n/2 );
        
        else
            res= f( n/2 )+1;
        
       memo.put( n,res );
       return res;
        
    }
    
    static void solve()
    {
        long res=0;
        
        for( int i=0; i<a.length; i++ )
        {
            int val=f( a[i]);
            
            if( cnt.containsKey(val))
                cnt.put( val, cnt.get(val)+1 );
            else
                cnt.put( val, 1 );
        }
        
        for( int key : cnt.keySet() )
        {
            int val=cnt.get( key );
            res += (long)val*( val-1 )/2;
        }
        
        System.out.println( res );
    }
    
    public static void main( String[] args ) throws IOException
    {
        BufferedReader br=new BufferedReader( new InputStreamReader( System.in ) );
        int n=Integer.parseInt( br.readLine() );
        a=new int[n];
        String s=br.readLine();
        StringTokenizer tok=new StringTokenizer( s );
        for( int i=0; i<n; i++ )
            a[i]=Integer.parseInt(tok.nextToken());
        solve();
    }
}   