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.*;
public class worms {
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int t =  sc.nextInt();
		Map<Long,Long> map = new HashMap<Long,Long>();
		Map<Long,Long> ans = new HashMap<Long, Long>();
		for(int i=0;i<t;i++)
		{
			long a  = sc.nextLong();
			long b = calculate(a);
			if(map.containsKey(b))
			{
				if(!ans.containsKey(b))
					ans.put(b, (long)0);
				long count=1;
				count = count*map.get(b);
				ans.put(b, count+ans.get(b));
				map.put(b, map.get(b)+1);
			}
			else{
				map.put(b, (long)1);
			}
			//System.out.println(b);
		}
		
		long sum =0;
		for(Map.Entry<Long, Long> entry:ans.entrySet())
		{
			sum = sum+entry.getValue();
		}
		System.out.println(sum);
	}
	
	public static long calculate(long a)
	{
		if(a==1 || a==2)
			return 1;
		
		if(a%2==0)
			return calculate(a/2);
		else
			return 1 + calculate((a-1)/2);
		
	}
}