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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class B_Dima_And_Sequence {
    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        String str = rd.readLine();
        int n = Integer.parseInt(str);
        str = rd.readLine();
        StringTokenizer tk = new StringTokenizer(str);
    //  ArrayList<Integer> arr = new ArrayList <Integer> ();
        int b = 0;
        int a = 0;
        int count = 0;
        int [] mas = new int [100000];
        for(int i=0; i<n; i++){
            b = Integer.parseInt(tk.nextToken());
            a = rec(b);
        //  System.out.println(a);
        //  count += mas[a];
            mas[a]++;
        }
        int k = 0;
        for(int i=0; i<n; i++){
            if(mas[i] > 1){
                k = mas[i];
                for(int j=1; j<k; j++){
                    count += j;
                }
            }
        }
        out.print(count);
        out.flush();    
    }
    
    private static int rec (int n){
        if(n == 0)return 0;
        if(n == 1)return 1;
        if(n%2 == 0)return rec(n/2);
        return rec((n-1)/2)+1;
    }
}
