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<string>
#include<algorithm>
#include<map>
#include<set>
#include<cmath>
#include<utility>
#include<queue>
#include<vector>
#include<cstdio>
using namespace std;
map <int,int>m;
map <int,int>sum;
int n;
int a[100005];
int tmp[100005];  
bool hash[10000004];
int mx=0;
int ans=0;
int work(int x)
{
	if(x==0)return sum[x]=0;
	if(sum[x]!=0)return sum[x];
	if(x%2==1)return sum[x]=work((x-1)/2)+1;
	else return sum[x]=work(x/2);
}
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{cin>>a[i];
	if(a[i]>mx)mx=a[i];
	tmp[i]=work(a[i]);
	tmp[i]=sum[a[i]];}
	for(int i=0;i<n;i++)
	{
		if(hash[tmp[i]]==false)hash[tmp[i]]=true;
		else
		{
			m[tmp[i]]++;
		}
    }
    for( map<int,int> ::iterator ii=m.begin();ii!=m.end();ii++)
    {
		int x=(*ii).second;
		if(x>0)
		{
			int p=1;
			for(int j=1;j<=x+1;j++)
			p*=j;
			ans+=p/2;
		}
	}
	cout<<ans;
	//system("pause");
	return 0;
}
