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 B {
	static int f(int x){
		if (x == 0){
			return 0;
		}
		if ((x&1) == 0){
			return f(x>>1);
		}
		return f(x>>1) + 1;
	}
	static final int MAX = 31;
	public static void main(String [] args){
		try (Scanner s = new Scanner(System.in)){
			final long [] count = new long[MAX];
			for (int i = s.nextInt(); i > 0; --i){
				count[f(s.nextInt())]++;
			}
			long res = 0;
			for (int i = 0; i < MAX; ++i){
				if (count[i] > 1){
					res += (count[i]*(count[i] - 1)) >> 1;
				}
			}			
			System.out.println(res);
		}
	}
}