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.Hashtable;
import java.util.Scanner;


public class DimaSequence {

	public static int f (int a) {
		if (a == 0)
			return 0;
		else
			return f((a - a % 2) / 2) + a % 2;
	}
	
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();

		int r[] = new int[32];
		int a[] = new int[n];
		
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			r[f(a[i])]++;
		}
				
		long t = 0;
		
		for (int i = 0; i < r.length; i++) {
			t += (long)r[i] * (r[i] - 1) / 2;
		}
		
		System.out.println(t);
			
		sc.close();
	}

}
