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.*;

public class B {

	private static HashMap<Integer, Integer> map;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		map = new HashMap<Integer, Integer>();
		int n = sc.nextInt();
		int[] a = new int[n];
		int i = 0;
		while (i < n) {
			int k = sc.nextInt();
			a[i] = k;
			++i;
		}
		sc.close();

		long c = 0;
		for (i = 0; i < a.length; ++i) {
			for (int j = i + 1; j < a.length; ++j) {
				if (f(a[i]) == f(a[j])) {
					++c;
				}
			}
		}

		System.out.println(c);
	}

	public static int f(int x) {
		int c = 0;
		int n = x;

		while (true) {
			if (map.containsKey(n)) {
				if (map.size() < 200000) {
					map.put(x, c);
				}
				return map.get(n) + c;
			} else {
				if (n == 1) {
					++c;
					break;
				}
				if (n == 0) {
					break;
				}
				if (n % 2 == 1) {
					++c;
					--n;
				} else {
					while (n % 2 == 0) {
						n /= 2;
						if (map.containsKey(n)) {
							if (map.size() < 200000) {
								map.put(x, c);
							}
							return map.get(n) + c;
						}
					}
				}
			}
		}
		if (map.size() < 200000) {
			map.put(x, c);
		}
		return c;
	}
}