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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;

int w[35];

int main()
{
	int n,val;
	__int64 sum = 0;
	scanf("%d",&n);
	for(int i=1; i<=n; i++)
	{
		scanf("%d",&val);
		int ans = 0;
		while(val)
		{
			if(val&1) ans++;
			val>>=1;
		}
		w[ans]++;
	}
	for(int i=1; i<=30; i++)
	sum += w[i]*(w[i]-1)/2;
	printf("%I64d\n",sum);
	return 0;
}
	  	 	 				 	  		   				 	