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 A[100000];
int F(int x) {
  int res;
  if (x == 1) {
    return 1;
  }
  res = 0;
  while (x != 1) {
    if (x & 1) {
      ++res;
    }
    x /= 2;
  }
  return res + 1;
}
int main() {
  int N, i, j;
  long long Sum, Cnt;
  scanf("%d", &N);
  for (i = 0; i < N; ++i) {
    scanf("%d", &A[i]);
    A[i] = F(A[i]);
  }
  for (Sum = 0, i = 1; i < 33; ++i) {
    for (Cnt = j = 0; j < N; ++j) {
      if (A[j] == i) {
        ++Cnt;
      }
    }
    Sum += Cnt * (Cnt - 1) / 2;
  }
  printf("%I64d\n", Sum);
  return 0;
}
