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 p272B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		ArrayList<Integer> arr = new ArrayList<Integer>();

		int n = in.nextInt();
		for(int i=0; i<n; ++i) {
			arr.add(f(in.nextInt()));
		}

		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		for(Integer i : arr) {
			if(map.containsKey(i))
				map.put(i, map.get(i)+1);
			else
				map.put(i, 1);
		}

		long total = 0;
		for(Integer i : map.keySet()) {
			long tmp = map.get(i);

			if(tmp > 1) {
				total += (tmp*(tmp-1))/2;
			}
		}

		System.out.println(total);
	}

	public static int f(int x) {
		if(x == 0)
			return 0;

		if(x % 2 == 0) {
			return f(x/2);
		}
		else {
			return f(x/2) + 1;
		}
	}
}