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 a[20] = {0}, b[20];
int main() {
  int n, i, j, k, ct;
  long long ans = 0;
  bool flag;
  scanf("%d", &n);
  b[0] = 1;
  for (i = 1; i < 20; ++i) b[i] = b[i - 1] * 2;
  for (i = 0; i < n; ++i) {
    flag = 0;
    ct = 0;
    scanf("%d", &j);
    while (1) {
      for (k = 0; k < 20; ++k)
        if (b[k] == j) {
          flag = 1;
          break;
        }
      if (flag) break;
      if (j & 1) {
        j /= 2;
        ct++;
      } else
        j /= 2;
    }
    a[ct]++;
  }
  for (i = 0; i < 20; ++i) {
    if (a[i]) ans += a[i] * (a[i] - 1) / 2;
  }
  printf("%I64d\n", ans);
  return 0;
}
