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;
const int inf = ~0U >> 1;
int lowbit(int n) { return n & -n; }
int main() {
  int n, a[200000], b[200000], c[35] = {};
  long long ans = 0;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    while (a[i]) {
      if (a[i] & 1) b[i]++;
      a[i] /= 2;
    }
    c[b[i]]++;
  }
  for (int i = 1; i < 35; i++) {
    long long tmp = (long long)(c[i]);
    if (c[i] & 1)
      ans += tmp * ((tmp - 1) / 2);
    else
      ans += (tmp / 2) * (tmp - 1);
  }
  cout << ans;
}
