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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Dima {
    public static void main(String[] args) {
        FastReader in = new FastReader();
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);

        int i,j,a,b = 0,c,n,k,l;
        long sum = 0;
        n = in.nextInt();
        int[] arr = new int[n];

        for (i=0; i<n; i++)
            arr[i] = in.nextInt();

        for (i=0; i<n; i++){
            a = arr[i];
            b = 0;
            while (a > 0){
                if (a % 2 != 0) b ++;
                a /= 2;
            }

            arr[i] = b;
        }


        Arrays.sort(arr);
        a = 0;

        for (i=0; i<n; i++){

            if (i + 1 < n  && arr[i] == arr[i+1]){

                for (j=i; j<n-1; j++){

                    if (arr[i] != arr[j+1]){
                        break;
                    }
                }

                a = j - i + 1;
               // System.out.println(j);
                sum += (a * (a-1)) / 2;
                i = j;
            }
        }

        System.out.println(sum);

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}
