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.math.*;

public class Main {
static Scanner sc;
static PrintWriter pw;

static int maxi(int a,int b)
{
	if (a>b) return a;else return b;
}

public static void main(String[] argv)
{ sc = new Scanner(System.in);
  pw = new PrintWriter(System.out);
   int n = sc.nextInt();
   int a[] = new int [n];
   for (int i=0;i<n;i++)
    { a[i] = sc.nextInt();
    }
   int m[] = new int [100];
   for (int i=0;i<n;i++)
   {  int count=0;
	  while (a[i]>0)
	  {
		 if (a[i]%2!=0) count++;
		 a[i]/=2;
	  }
	  m[count]++;
   }
   int res=0;
   for (int i=0;i<100;i++)
   {
	   if (m[i]>1) 
	   {
		   res = res + (m[i]*(m[i]-1))/2;
	   }
   }
  pw.print(res);
   pw.close();
}
}