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.util.Collection;
import java.util.HashMap;
import java.util.StringTokenizer;

/**
 * Created with IntelliJ IDEA.
 * User: dima
 * Date: 13.02.13
 * Time: 19:28
 * To change this template use File | Settings | File Templates.
 */
public class TaskB {
    static BufferedReader in = new BufferedReader(new InputStreamReader(
            System.in));
    static StringTokenizer str;
    static String SK;

    static String next() throws IOException {
        while ((str == null) || (!str.hasMoreTokens())) {
            SK = in.readLine();
            if (SK == null)
                return null;
            str = new StringTokenizer(SK);
        }
        return str.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public static void main(String[] args) throws IOException {
        int n = nextInt();
        int[] mas = new int[n];
        for (int i = 0; i < n; i++) {
            mas[i] = nextInt();
        }
        HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            int cur = mas[i];
            int cnt = 0;
            while (cur != 0) {
                if (cur % 2 == 1) {
                    cnt++;
                }
                cur = cur/2;
            }
            Integer gg = map.get(cnt);
            if(gg==null){
                map.put(cnt,1);
            } else {
                gg++;
                map.put(cnt,gg);
            }
        }
        Collection<Integer> vals = map.values();
        long ans = 0;
        for (Integer in: vals){
            ans+=(((long)in*((long)in-1)/2));
        }
        System.out.println(ans);
    }
}