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.Scanner;


public class B {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Func func = new Func();
		func.solve();
		func.print();
	}

}


class Func {
	Func() {
		Scanner scr = new Scanner(System.in);
		n = scr.nextInt();
		a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scr.nextInt();
		}			
	}
	
	int red(int z){
		int b = 0; 
		while (z != 0) {
			b = b + z%2;
			z = z/2;
		}
		return b;
	}
	
	void solve() {
		int [] r = new int[MAGICCONST];

		for (int i = 0; i < n; i++){
			r[red(a[i])]++;
		}
		
		answer = 0;
		for (int j = 0; j < MAGICCONST; j++){
			answer = answer + (r[j]*(r[j]-1))/2;
		}
	}
	
	void print(){
		System.out.println(answer);
	}
	
	long answer;
	
	int n;
	int [] a;
	static final int MAGICCONST = 128;
}