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.Scanner;

public class DimaandSequence
{
	public static int numOf1(int n)
	{
		int res = 0;
		while (n != 0)
		{
			if (n % 2 == 1)
			{
				++res;
			}
			n /= 2;
		}
		return res;
	}

	public static void main(String[] args)
	{
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		long[] num = new long[31];
		for (int i = 0; i <= 30; ++i)
		{
			num[i] = 0;
		}
		int temp;
		for (int i = 0; i < n; ++i)
		{
			temp = input.nextInt();
			++num[numOf1(temp)];
		}
		long res = 0;
		for (int i = 0; i <= 30; ++i)
		{
			if (num[i] > 1)
			{
				res += num[i] * (num[i] - 1) / 2;
			}
		}
		System.out.println(res);
	}
}