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 Main {
    Scanner sc = new Scanner(System.in);

    private void doit(){
        while(sc.hasNext()){
            int n = sc.nextInt();
            int [] data = new int[n];
            for(int i = 0; i < n; i++){
                data[i] = sc.nextInt();
            }
            int [] freq = new int[100];
            for(int i = 0; i < n;i++){
                int num = Integer.bitCount(data[i]);
                freq[num]++;
            }
            long res = 0;
            for(int i = 0; i < 100; i++){
                res += (long)(freq[i]) * (freq[i] - 1) / 2;
            }
            System.out.println(res);
        }
    }

    private void debug(Object... o) {
        System.out.println("debug = " + Arrays.deepToString(o));
    }

    public static void main(String[] args) {
        new Main().doit();
    }
}