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 <bits/stdc++.h>
using namespace std;
int f(int n) {
  if (n == 0) return 0;
  if (n % 2 == 0) return f(n / 2);
  return f(n - 1) + 1;
}
int main() {
  long long num[32];
  int n;
  cin >> n;
  for (int i = 0; i < 32; i++) num[i] = 0;
  for (int i = 0; i < n; i++) {
    int tmp;
    cin >> tmp;
    num[f(tmp)]++;
  }
  long long ret = 0;
  for (int i = 0; i < 32; i++) ret += num[i] * (num[i] - 1) / 2;
  cout << ret << "\n";
}
