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.Arrays;
import java.util.StringTokenizer;

public class CF22 {

	private static int fl;
	private static int[] sl;
	private static int[] f;
	private static int ans = 0;

	public static void main(String[] args) throws NumberFormatException,
			IOException {
		readData();

		f = new int[fl];
		for (int i = 0; i < fl; i++) {
			f[i] = countF(sl[i]);
		}

		Arrays.sort(f);
		int counter = 1;
		for (int i = 1; i < fl; i++) {
			if (f[i] == f[i - 1]) {
				counter++;
			} else {
				ans += counter * (counter - 1) / 2;
				counter = 1;
			}
		}
		ans += counter * (counter - 1) / 2;

		System.out.println(ans);

	}

	private static int countF(int i) {
		if (i == 0)
			return 0;

		if (i % 2 == 0)
			return countF(i / 2);

		return countF((i - 1) / 2) + 1;
	}

	private static void readData() throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		fl = Integer.parseInt(br.readLine());
		sl = new int[fl];
		String nums = (br.readLine());
		StringTokenizer st = new StringTokenizer(nums);
		int i = 0;
		while (st.hasMoreTokens()) {
			String key = st.nextToken();
			sl[i] = Integer.parseInt(key);
			i++;
		}
	}
}