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;
long long int arr_res[1100];
int main() {
  int n;
  cin >> n;
  int* a = new int[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    int temp = a[i];
    int res = 0;
    while (temp != 0) {
      int j = 1;
      for (int k = 1; k < 32; k++) {
        if (j <= temp && j * 2 > temp) {
          res += 1;
          temp -= j;
          break;
        }
        j *= 2;
      }
    }
    arr_res[res]++;
  }
  long long int res = 0;
  for (int i = 0; i < 1100; i++)
    if (arr_res[i] > 1) res += (arr_res[i] * (arr_res[i] - 1)) / 2;
  cout << res;
  return 0;
}
