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 Main1 {
public static void main(String[] args) throws IOException {
	File file = new File("in");
	BufferedReader in;
	StringBuilder out = new StringBuilder("");
	if (file.exists()) {
		in = new BufferedReader(new FileReader(file));
	} else {
		in = new BufferedReader(new InputStreamReader(System.in));
	}
	String line, lines[];
	int n = Integer.parseInt(in.readLine());
	int arr[] = readInts(in.readLine());
	for( int i = 0; i<  n; i++ )
	{
		arr[i] = f(arr[i]);
	}
	//System.out.println(arr);
	Arrays.sort(arr);

	int b = arr[0];
	long count = 1l;
	long result = 0l;
	for( int i = 1; i < n; i++ )
	{
		if ( arr[i] != b )
		{
			result += (count*(count-1))/2l;
			b = arr[i];
			count = 1;
		}
		else
		{
			count++;
		}
	}
	result += (count*(count-1))/2l;
	System.out.println(result);
	
}
public static int f(int v)
{
	if ( v == 0l) return 0;
	if ( v%2 == 1 ) return 1 + f(v/2);
	return f(v/2);
}
public static int[] readInts(String line) {
	String lines[] = line.split("\\s+");
	int[] result = new int[lines.length];
	for (int i = 0; i < lines.length; i++)
		result[i] = Integer.parseInt(lines[i]);
	return result;
}
}
