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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;


public class B {
	
	public static int func(int x){
		int ret = 0;
		if(x == 0){
			return 0;
		}else if(x % 2 == 0){
			return func(x / 2);
		}else{
			return func(x / 2) + 1;
		}
	}
	
	public static long comb(long n, long r){
		if(n == r){
			return 1L;
		}else if(r == 0){
			return 1L;
		}else if(r == 1){
			return n;
		}else{
			return comb(n-1, r-1) + comb(n-1, r);
		}
	}
	
	public static void main(String[] args) throws IOException{
		Scanner sc = new Scanner(System.in);
		
		final int n = sc.nextInt();
		
		int[] count = new int[40];
		
		for(int i = 0; i < n; i++){
			count[func(sc.nextInt())]++;
		}
		
		long sum = 0;
		for(int i = 0; i < 40; i++){
			if(count[i] >= 2){
				sum += comb(count[i], 2);
			}
		}
		
		System.out.println(sum);
		
		sc.close();
	}
}
