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.math.BigInteger;
import java.util.Scanner;
public class A {
	static public int f(int x)
	{
		
		if(x==0) return 0;
		if(x%2==0) return f(x/2);
			return (f((x-1)/2)+1);
	}
	
	

	public static void main(String[] args) {
		Scanner sc = new Scanner (System.in);
		int n = sc.nextInt();
		int max = 0;
		int mass[] = new int [n];
		for(int i=0 ; i<n; i++)
			{
				mass[i]=sc.nextInt();
				if(max<mass[i]) max=mass[i];
			}
		for(int i=0; i<n; i++)
		{
			mass[i]=A.f(mass[i]);
		}
		BigInteger two = new BigInteger("2");
		int res=0;
		BigInteger r = new BigInteger("0");
		for(int i=0; i<=50; i++)
		{
			res=0;
			for(int j=0; j<n; j++)
				if(mass[j]==i) res++;
				BigInteger r1 = new BigInteger(Integer.toString(res-1));
				BigInteger r2 = new BigInteger(Integer.toString(res));
				r1=r1.multiply(r2).divide(two);
				r=r.add(r1);
		}
		System.out.println(r);
	}

}
