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;
long long memo[10000000];
map<long long, long long> freq;
long long solve(long long n) {
  if (n < 10000000 && memo[n] != -1) return memo[n];
  return solve(n / 2) + n % 2;
}
int main() {
  ios::sync_with_stdio(false);
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  memset(memo, -1, sizeof memo);
  memo[0] = 0;
  long long n;
  long long temp;
  cin >> n;
  while (n--) cin >> temp, freq[solve(temp)]++;
  long long sum = 0;
  for (auto it = freq.begin(); it != freq.end(); it++)
    sum += it->second * (it->second - 1) / 2;
  cout << sum << endl;
  return 0;
}
