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.
#include <iostream>
#include <conio.h>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <iomanip>

#define pb push_back
#define mp make_pair
#define f first
#define s second 
#define ll long long 
#define ld long double 
#define PII pair <int , int> 
#define PIS pair <int , string>
#define PDD pair <double , double>
#define PLL pair <long long , long long>

using namespace std ;

const int maxn=10000*10+1 ;
	
int n , a[maxn] , k , d[maxn] , ans ;
int main (){
	cin >> n ;
	for (int i=0 ; i<n ; i++){
		cin >> a[i] ;
		while (!(a[i]%2))	a[i]/=2 ;
	}
	for (int i=0 ; i<n ; i++)	d[i]=1 ;
	sort (a , a+n) ;
	for (int i=0 ; i<n-1 ; i++){
		if (a[i]==a[i+1])	{d[k]++ ; ans=max (ans , d[k]) ;}
		else	k++;
	}	
	cout << max (ans , 1) << endl ;
	//getch ();
	return 0;
}
