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;
int conversion(string p) {
  int o;
  o = atoi(p.c_str());
  return o;
}
string toString(int h) {
  stringstream ss;
  ss << h;
  return ss.str();
}
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return (a * (b / gcd(a, b))); }
long long toi(string p) {
  long long x;
  istringstream in(p);
  in >> x;
  return x;
}
int go(int n) {
  int sum = 1;
  while (n / 2 > 0) {
    if (n % 2 != 0) sum++;
    n /= 2;
  }
  return sum;
}
int main() {
  int n, x;
  cin >> n;
  long long res = 0;
  map<int, long long> M;
  for (int i = 0; i < n; i++) {
    cin >> x;
    M[go(x)]++;
  }
  for (map<int, long long>::iterator it = M.begin(); it != M.end(); it++)
    res += ((it->second - 1) * (it->second)) / 2LL;
  cout << res << endl;
}
