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.Scanner;

public class Main {

    static int c(int a, int n) {
        int res = 1;
        for (int i = 0; i < a; i++) {
            res *= n;
            n--;
        }
        for (int i = 1; i <= a; i++) {
            res /= i;
        }
        return res;
    }

    public static void main(String[] args) {

        Scanner cin = new Scanner(System.in);

        final int max = 100000;

        int n = cin.nextInt();
        int[] a = new int[35];
        Long sum = 0L;
        for (int i = 0; i < n; i++) {
            int p = cin.nextInt();
            int s = 0;
            while (p != 0) {
                s += p & 1;
                p >>= 1;
            }

            a[s]++;
        }

        for(int i=1;i<a.length;++i){
            if(a[i]<2){
                continue;
            }
            sum+=c(2,a[i]);
        }
        System.out.println(sum);

    }

}
