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.Arrays;
import java.util.Scanner;

public class Prob272B {
	public static void main(String[] Args) {
		Scanner scan = new Scanner(System.in);
		int x = scan.nextInt();

		int[] arr = new int[x];
		for (int i = 0; i < x; i++)
			arr[i] = scan.nextInt();
		Arrays.sort(arr);

		int[] f = new int[arr[x - 1]];
		int max = 0;
		for (int i = 1; i < f.length; i++) {
			if (i % 2 == 0)
				f[i] = f[i / 2];
			else
				f[i] = f[i - 1] + 1;
			max = Math.max(max, f[i]);
		}
		
		int[] occ = new int[max + 1];
		for (int i = 0; i < x; i++)
			occ[f[arr[i] - 1]]++;

		long answer = 0;
		for (int i = 0; i < max + 1; i++)
			answer += (long)(occ[i]*(occ[i]-1))/2;
		
		System.out.println(answer);
	}
}
