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	Main{
	static	int	Bcnt1(int	n){
		n=(0x55555555&n)+(0x55555555&n>>1);
		n=(0x33333333&n)+(0x33333333&n>>2);
		n=(0xF0F0F0F&n)+(0xF0F0F0F&n>>4);
		n=(0xFF00FF&n)+(0xFF00FF&n>>8);
		return	(0xFFFF&n)+(0xFFFF&n>>16);
	}
	public	static	void	main(String[]args){
		Scanner	cin=new	Scanner(System.in);
		int	S[]=new	int[29];
		for(long	s;cin.hasNextInt();System.out.println(1+s>>1)){
			for(s=cin.nextInt(),Arrays.fill(S,0);0<s--;++S[Bcnt1(cin.nextInt())-1]);
			for(long	e:S)	s+=(e-1)*e;
		}
	}
}
