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.Collections;
import java.util.Scanner;

/**
 * @author: Serhat YILMAZ
 * @date: Feb 13, 2013
 * @file: R165_2.java
 */

/**
 * @author Serhat YILMAZ
 *
 */
public class R165_2 {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		int[] result = new int[50];
		for (int i = 0; i < result.length; i++) {
			result[i] = 0;
		}
		for (int i = 0; i < N; i++) {
			long n = scan.nextInt();
			result[getValue(n)]++;
		}
		int total = 0;
		for (int i = 0; i < 50; i++) {
			int a = result[i] * (result[i] - 1);
			a = a/2;
			total = total + a;
		}
		System.out.println(total);
	}

	private static int getValue(long n) {
		if(n == 0) {
			return 0;
		}
		if(n%2 == 0) {
			return getValue(n/2);
		}
		return 1 + getValue(n/2);
	}

}
