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.Arrays;
import java.util.Scanner;

public class Main {
	
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int[] a = new int[n];
		int[] b = new int[10000];
		Arrays.fill(b, 0);
		
		for(int i=0; i<n; i++){
			a[i] = in.nextInt();
			b[f(a[i])]++;
		}
		

	
		long sum=0;
		
		for(int i=0; i<b.length; i++){
			long x;
			if(b[i]<=1) x=0; else
				x=(long)(((long)b[i]*(long)(b[i]-1))/(long)2);
			sum+=x;
		}
		
		System.out.print(sum);
		
	}
	
	public static int f(int x){
		int s=1;
		while(x!=1){
			if((x%2)==1)
				s++;
			x/=2;
		}
		return s;
	}

}