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.*;

public class B167{
	public static void main(String args[]){
		new B167().run();
	}

	public void run(){
		Scanner scanner = new Scanner(System.in);
		String line = scanner.nextLine();
		int n = Integer.parseInt(line);
		line = scanner.nextLine();
		String[] tmp = line.split(" ");
		int[] a = new int[tmp.length];
		for(int i = 0; i < a.length; i++) {
			a[i] = Integer.parseInt(tmp[i]);
			//System.out.println(a[i]);
		}

		int res = 0;
		int[] c = new int[a.length];
		for(int i = 0; i < a.length; i++){
			System.out.print(a[i] + " ");
			if(a[i] > 0) c[i] = 1;
			while(a[i] >= 2){
				if(a[i] % 2 == 0){
					a[i] /= 2;
				}
				else{
					a[i] /= 2;
					c[i]++;
				}
			}
			System.out.println(c[i]);
		}
		
		for(int i = 0; i < a.length - 1; i++){
			for(int j = i + 1; j < a.length; j++){
				if(c[i] == c[j]) res++;
			}
		}
		
		System.out.println(res);
	}

	public void Reading(){
		//File Reading
		try{
			FileReader f = new FileReader("input.txt");
			BufferedReader b = new BufferedReader(f);
			String s;
			s = b.readLine();
		} catch(Exception e){
		}

	}

	public void Writing(String s){
		try{
			FileWriter fw = new FileWriter("output.txt");
			fw.write(s);
			fw.close();
		} catch(Exception e){
		}
	}

}

