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.lang.*;
import java.util.*;

public class Program{
    

    static Map<Integer, Integer> cache = new HashMap<>();

    public static void main(String[] args){
        cache.put(0, 0);
        cache.put(1, 1);
        cache.put(2, 1);
        cache.put(3, 2);
        cache.put(5, 2);
        Map<Integer, Integer> pairs = new HashMap<>();
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.nextLine());
        for(int i=0;i<n;i++){
            int x = sc.nextInt();
            int val = calc(x);
            Integer pairVal = pairs.get(val);
            pairs.put(val, pairVal==null?1:pairVal+1);
        }

        int res = 0;
        for(int x : pairs.values()){
            if(x>1)res += (x-1)*x/2;
        }

        System.out.println(res);
    }

    private static int calc(int x) {
        if(cache.containsKey(x)) return cache.get(x);
        if(x%2==0) return calc(x/2);
        return calc((x-1)/2)+1;
    }
}