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.*;
public final class little_lcm
{
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	
	static long fx(long x)
	{
		if(x==1)
			return 1;
		else
			return (x%2==0)?fx(x/2):fx(x/2)+1;
	}
	
	static long fact(long num)
	{
		num--;
		long sum=0;
		while(num>=1)
		{
			sum+=num;
			num--;
		}
		return sum;
	}
	
	public static void main(String args[]) throws Exception
	{
		int n=sc.nextInt();
		int[] a=new int[n];
		int[] cnt=new int[(int)Math.pow(10,6)+1];
		int max=-1;
		for(int i=0;i<n;i++)
		{
			long val=sc.nextLong();
			if(val==0)
			{
				a[i]=0;
			}
			else
			{
				a[i]=(int)fx(val);
			}
			cnt[a[i]]++;
			if(a[i]>max)
			{
				max=a[i];
			}
		}
		//out.println(Arrays.toString(a));
		long c=0;
		for(int i=0;i<=max;i++)
		{
			if(cnt[i]>1)
			{
				c+=fact(cnt[i]);
			}
		}
		out.println(c);
		out.close();
	}
}