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.util.ArrayList;
import java.util.List;
import java.util.Scanner;


public class Solution {
	
	static int alfabetSize = 26;
	static char[] codes;
	static int k;
	static int count;

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] results = new int[100];
		for(int i=0;i<n;i++){
			long curr = sc.nextLong();
			int res = calcFunction(curr);
			results[res]++;
		}
		long result = 0;
		for(int i=0;i<results.length;i++){
			long temp = results[i]*(results[i]-1)/2l;
			result += temp;
		}
		
		System.out.println(result);
		
		
	}
	
	
	
	static int calcFunction(long number){
		if(number==0){
			return 0;
		}else{
			if(number%2==0){
				return calcFunction(number/2);
			}else{
				return calcFunction((number-1l)/2)+1;
			}
		}
	}
	
	
	


	
}


