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 accepted{
public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int b[]=new int[1000000];
    for (int i = 1; i <=n; i++) {
        int x=sc.nextInt();
        b[f(x)]++;
    }
    long sum=0;
    for (int i =0; i <=100000; i++) {
        if(b[i]>1){
            sum+=((1+b[i]-1)*(long)(b[i]-1))/2;
        }
    }
    System.out.println(sum);
}

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