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 <cstdlib>
#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
/* 
 * ===  FUNCTION  ======================================================================
 *         Name:  main
 *  Description:  
 * =====================================================================================
 */
int _f(int a) {

	int ans=0;
	while(a) {
		ans += (a&0x1)? 1:0;
		a/=2;
	}
	return ans;
}
int arr[100005];
int main ( int argc, char *argv[] )
{
	int n,i=0,t;
	for(cin >> n;i<n;++i){
		cin >> t;
		arr[i] = _f(t);
	}

	sort(arr,arr+n);
	int tmp = 1;
	__int64 ans = 0;
	for(int i=1;i<n;++i) {
		if(arr[i] == arr[i-1]) {
			++tmp;
		} else {
			ans += (tmp-1)*tmp/2;
			tmp = 1;
		}
	}
	
	if(tmp>0) ans += (tmp-1)*tmp/2;
	cout << ans << endl;
}/* ----------  end of function main  ---------- */
