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.InputStreamReader;
import java.util.StringTokenizer;



public class Main {
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        int n=Integer.parseInt(br.readLine());
        st=new StringTokenizer(br.readLine());
        int arr[]=new int[33];
        for(int i=0;i<n;i++)
        {
            int count=0;
            int temp=Integer.parseInt(st.nextToken());
            for(int j=0;j<32 && temp!=0;j++)
            {
                if(temp%2==1)
                {
                    count++;
                }
                temp=temp>>1;
            }
            arr[count]++;
        }
        
        long sum=0;
        for(int i=1;i<33;i++)
        {
            if(arr[i]>1)
            sum+=(long)((long)arr[i]*((long)arr[i]-1))/2;
        }
        System.out.print(sum);
    }
}
