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.HashMap;
import java.util.Iterator;
import java.util.Map;
import java.util.Scanner;


public class DimaandSequence {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
		for (int i = 0; i < n; i++) {
			int a = sc.nextInt();
			int sir = ylii(a,0);
			if(!map.containsKey(sir)){
				map.put(sir,1);
			}else map.put(sir, map.get(sir)+1);
		}
		int res = 0;
		Iterator it = map.entrySet().iterator();
	    while (it.hasNext()) {
	        Map.Entry pairs = (Map.Entry)it.next();
	        int qwe = (Integer)pairs.getValue();
	        res+= qwe*(qwe-1)/2;
	        it.remove(); // avoids a ConcurrentModificationException
	    }
	    System.out.println(res);
	}

	private static int ylii(int a, int sum) {
		if(a==1)return sum+1;
		if(a%2==0)return ylii(a/2,sum);
		return ylii(a/2,sum+1);
	}
}
