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<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#include<algorithm>

using namespace::std;

int n;
int a[100005];
int b[40];
__int64 la;

void input()
{
	int i,a1;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		a1=0;
		while(a[i]!=0)
		{
			if(a[i]%2==1)
				a1++;
			a[i]/=2;
		}
		b[a1]++;
	}
	for(i=1;i<=35;i++)
		la+=(__int64)(b[i]*(b[i]-1))/2;
}
void process()
{
}
void output()
{
	printf("%I64d",la);
}

int main()
{
	input();
	process();
	output();
	return 0;
}