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 TaskB {

    
    public static void main(String[] args) {
        Scanner read = new Scanner(System.in);
        
        int n = read.nextInt();
        int [] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i]=read.nextInt();
        }
        int k=0;
        
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                if (f(a[i],a[j])) k++;
            }
        }
        System.out.println(k+1);

    }

    private static boolean f(int x, int y) {
       if (x==0 && y==0) return true;
       if (2*x==y) return true;
       if (2*x+1==y+1) return true;
       return false;
    }
}
