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 P272B_DimaAndSequence {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		long count[] = new long[32];
		int number = -1, result = -1;

		for (int i = 0; i < n; i++) {
			number = scanner.nextInt();
			result = 0;

			while (number > 0) {
				if (number % 2 == 1) {
					result++;
				}

				number /= 2;
			}

			count[result]++;
		}

		scanner.close();
		long countResult = 0;

		for (int i = 0; i < count.length; i++) {
			long temp = count[i];
			countResult += temp * (temp - 1) / 2;
		}

		System.out.println(countResult);
	}
}
