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.*;
import java.util.*;


public class B {

    static int ret(int n){
        int cont=0;
        while(n!=1){
            if(n%2!=0) cont++;
            n/=2;           
        }
        return cont;
    }
    
    static long calc(int n){
        return n*(n-1)/2;
    }
    
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();       
        int may[]=new int[30];
        for(int i=0;i<n;i++){
            may[ret(in.nextInt())]++;
        }
        long ans=0;
        for(int i=0;i<30;i++){
            ans+=calc(may[i]);      
        }
        System.out.println(ans);
        
    }

}