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 func(long long int a);
int c[12] = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3};
int main() {
  int n, i, j;
  scanf("%d", &n);
  long long int a[n], b[n], count = 0;
  for (i = 0; i < n; i++) scanf("%I64d", &a[i]);
  sort(a, a + n);
  for (i = 0; i < n; i++) {
    b[i] = func(a[i]);
  }
  for (i = 0; i < n; i++) {
    for (j = i + 1; j < n; j++) {
      if (b[i] == b[j]) {
        count++;
      }
    }
  }
  printf("%I64d", count);
  return 0;
}
long long int func(long long int a) {
  if (a <= 11) return c[a];
  if (a % 2 == 0) return (a / 2);
  if (a % 2 == 1) return (a / 2) + 1;
}
