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.*;
import java.math.*;

public class Main{

    static PrintWriter out = new PrintWriter(System.out);
    static FastScanner in = new FastScanner(System.in);
    static final int inf = (int)1e9;

    static int f(int x){
        if (x == 0) return 0;
        if (x%2 == 1) return f(x/2) + 1;
        return f(x/2);
    }

    public static void main(String[] args) throws IOException{
        long a[] = new long[100];

        int n = in.nextInt();

        for (int i=0;i<n;i++){
            int x = in.nextInt();
            a[f(x)]++;
        }

        long ans = 0;
        for (int i=0;i<100;i++){
            ans += a[i]*(a[i]-1)/2;
        }

        out.println(ans);

        out.close();
    }


}

class FastScanner {
    
    BufferedReader reader;
    StringTokenizer strTok;

    public FastScanner(String str) throws IOException{
        reader = new BufferedReader(new FileReader(str));
    }
    
    public FastScanner(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
    }
    
    public String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            strTok = new StringTokenizer(reader.readLine());
        }
        return strTok.nextToken();
    }
    public String next()throws IOException{
        return nextToken();
    }
    
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    
}