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.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class B {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = scanner.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        for (int i = 0; i < n; i++) {
            int t = 0;
            while (a[i] != 0) {
                t += a[i] % 2;
                a[i] = a[i] / 2;
            }
            a[i] = t;
        }

        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            if (!map.containsKey(a[i])) map.put(a[i], 0);
            map.put(a[i], map.get(a[i]) + 1);
        }

        long ans = 0;
        for (int i : map.values()) {
            if (i != 1) ans += (long)i * (i - 1) / 2;
        }

        out.println(ans);
        out.close();
    }
}
