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 Sequence {
    public static int f(int n) {
        if (n == 0)
            return 0;
        if (n % 2 == 0)
            return f(n/2);
        else
            return f(n/2) + 1;
    }

    public static long choose(long n, long k) {
        if (k > n)
            return 0;

        if (k > n - k)
            k = n - k;

        long res = 1;
        for (int i = 0; i < k; i++) {
            res *= (n - i);
        }

        for (int i = 1; i <= k; i++) {
            res /= i;
        }

        return res;
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
        int n = scan.nextInt();

        for (int i = 0; i < n; i++) {
            int f = f(scan.nextInt());
            Integer v = map.get(f);
            if (v == null)
                map.put(f, 1);
            else
                map.put(f, v + 1);
        }

        long sum = 0;
        for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
            int value = entry.getValue();
            sum += choose(value, 2);
        }
        System.out.println(sum);
    }
}
