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;
vector<long long int> v;
map<long long int, long long int> m;
long long int f(long long int x) {
  long long int c = 0;
  while (x != 0) {
    if (x % 2 != 0) c++;
    x /= 2;
  }
  return c;
}
int main() {
  long long int x, n, z, s = 0, i;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> x;
    z = f(x);
    if (m[z] == 0) {
      m[z] = 1;
      v.push_back(z);
    } else
      m[z]++;
  }
  for (i = 0; i < v.size(); i++) {
    x = m[v[i]];
    s += (x * (x - 1) / 2);
  }
  cout << s << endl;
  return 0;
}
