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.Arrays;
import java.util.Scanner;


public class Program {

    static int f(int k){
        if(k==0) return 0;
        if(k%2==1){
            return f((k-1)/2)+1;
        }
        else{
            return f(k/2);
        }
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] nums = new int[n];
        
        int readNum;
        for(int i=0; i<n; ++i){
            readNum = sc.nextInt();   // save numbers in line here
            nums[i] = readNum;
            
        }
        
        
        int[] resArr = new int[n];
        

        // save the results f[a_i] in resArr
        for(int i=0; i<n; ++i){
            resArr[i] = f(nums[i]);
        }
        
        Arrays.sort(resArr);
        
                
//      // TEST - print result array
//      System.out.println("sorted resArr2:");
//      for(int i=0; i<n; ++i){
//          System.out.print(resArr2[i] + " ");
//      }
//      System.out.println();
//      //
        
        
        long pairs=0;
        long occ=1;   
        for(int i=0; i<n-1; ++i){
            if(resArr[i]==resArr[i+1]){
                occ++;
            }
            else{
                pairs += ((occ-1)*occ)/2;
                occ = 1;
            }
        }
        pairs += ((occ-1)*occ)/2;
        
        
        System.out.println(pairs);
        
        
    }
        
}