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 f(int x) {
  if (x == 0)
    return 0;
  else if (!(x % 2))
    return f(x / 2);
  else if (x % 2)
    return f((x - 1) / 2) + 1;
}
int main() {
  long long int sayac = 0, i, n, t, mm = 9999999, ma = -1, max = 1, x,
                arr[1000000] = {0};
  scanf("%lld", &n);
  for (i = 0; i < n; i++) {
    scanf("%lld", &x);
    t = f(x);
    arr[t]++;
    if (t > ma) ma = t;
    if (t < mm) mm = t;
  }
  for (i = mm; i <= ma; i++)
    if (arr[i]) sayac += (arr[i] * (arr[i] - 1)) / 2;
  printf("%lld", sayac);
  return 0;
}
