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 <cmath>
# include <windows.h>
# include <algorithm>
# include <fstream>

using namespace std;
int a[100001];
int f(__int64 x)
{
	if (x == 0) return 0;
	if (x % 2) return 1 + f((x - 1) / 2);
	return f(x / 2);
}

int main()
{
	//ifstream cin ("input.txt");
	//ofstream cout ("output.txt");
	
	int x, z = 0;
	__int64 y, mx = 0;
	cin >> x;
	for (int i = 1; i <= x; ++i)
	{
		cin >> y;
		y = f(y);
		++a[y];
		mx = max(mx, y);
	}
	for (int i = 1; i <= mx; ++i)
	    if (a[i] > 1)
	       z += a[i] - ((a[i] % 2) ? 0 : 1);
	cout << z;
	return 0;
}

