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.HashMap;
import java.util.StringTokenizer;


public class Seq {
	static HashMap< Integer, Integer> map1 = new HashMap();
	static HashMap< Integer, Integer> map2 = new HashMap();
	static int[] arr;
	
	
	static int f(int n){
		if(n==0)
			return 0;
			
		if(map1.containsKey(n)){
			return map1.get(n);
		}
		
		int res = -1;
		
		if( n % 2 == 0 ){
			res = f(n/2);
		}
		else{
			res = f(n/2)+1;
		}
		map1.put(n,res);
		return res;
	}
	
	
	 static void solve(){
		 long ans=0;
		for(int j=0;j<arr.length;j++){
			int value = f(arr[j]);
			if(map2.containsKey(value)){
				map2.put(value,map2.get(value)+1);
			}
			else{
				map2.put(value, 1);
			}
		}
		for(int key: map2.keySet()){
			int val = map2.get(key);
			ans += (long)val*(val-1)/2;// n combination 2
		}
		System.out.println(ans);
	}
	
	
	public static void main(String args[]) throws IOException {
		/*Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		array = new int[n];
		for(int i=0;i<n;i++){
			array[i] = sc.nextInt();
		}
		solve();*/
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		arr = new int[n];
		String s = br.readLine();
		StringTokenizer tok = new StringTokenizer(s);
		for(int i=0;i<n;i++){
			arr[i] = Integer.parseInt(tok.nextToken());
		}
		
		solve();
	}
}
