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.InputStream;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.StringTokenizer;

public class Round_167_B {

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        int n = in.nextInt();
        HashMap<Integer, Integer> M = new HashMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            long val = in.nextLong();
            int c = popcount(val);
            Integer t = M.get(c);
            if (t == null) {
                M.put(c, 1);
            } else
                M.put(c, t + 1);
        }
        long val = 0, minival;
        for (Entry<Integer, Integer> S : M.entrySet()) {
            minival = S.getValue();
            if (minival >= 2) {
                if (minival % 2 == 0) {
                    minival = minival / 2 * (minival - 1);
                    val += minival;
                } else {
                    minival = (minival - 1) / 2 * minival;
                    val += minival;
                }
            }
        }
        System.out.println(val);
    }

    public static int popcount(long x) {
        int c = 0;
        for (; x > 0; x &= x - 1)
            c++;
        return c;
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
                return null;
            }
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

}
