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;
public class B274 {
    long f[];
    public static void main (String[] args ) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        String s[] = br.readLine().split(" ");
        int a[] = new int[n];
        for(int i=0;i<n;i++){
            a[i] = f(Integer.parseInt(s[i]));
            //System.out.println(a[i]);
        }
        long ans=0;
        int arr[] = new int[31];
        for(int i=0;i<n;i++){
            arr[a[i]]++;
        }
        for(int i=0;i<31;i++){
            ans=ans+(arr[i]*(arr[i]-1))/2;
        }
        System.out.println(ans);
    }    
    public static int f(int j){
        if(j==0)return 0;
        else if(j==1) return 1;
        else if(j%2==0) return f(j/2);
        else return (1+f(j/2));
    }
}