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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Task272B {
	
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(in.readLine());
		int[] c = new int[30];
		StringTokenizer st = new StringTokenizer(in.readLine());
		for (int i = 0; i < n; i++) {
			c[fCalculate(Integer.parseInt(st.nextToken()))]++;
		}
		
		long pq = 0;
		for (int i = 1; i < 30; i++) {
			long ci = c[i];
			pq += (ci * (ci - 1) / 2);
		}
		
		System.out.println(pq);
	}
	
	private static int fCalculate(int a) {
		if (a % 2 == 1) {
			return fCalculate(a >> 1) + 1;
		} else if (a == 0) {
			return 0;
		} else {
			return fCalculate(a >> 1);
		}
	}
}