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>
int main(void) {
  long a[300];
  long b, c, d, max;
  long long e, sum;
  scanf("%ld", &b);
  max = 0;
  sum = 0;
  for (c = 0; c <= 299; c++) a[c] = 0;
  for (c = 1; c <= b; c++) {
    d = 0;
    scanf("%lld", &e);
    while (e > 0) {
      if (e % 2 == 0)
        e = e / 2;
      else {
        e = (e - 1) / 2;
        d++;
      }
    }
    if (d > max) max = d;
    a[d]++;
  }
  for (c = 0; c <= max; c++)
    if (a[c] > 1) sum = sum + (a[c] * (a[c] - 1)) / 2;
  printf("%lld\n", sum);
  return 0;
}
