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>
#pragma optimize("Ofast")
using namespace std;
using ll = long long;
const int N = 1e5 + 5;
int solve(int x) {
  if (x == 0) return 0;
  if (x & 1)
    return solve(x / 2) + 1;
  else
    return solve(x / 2);
}
int main() {
  ios_base::sync_with_stdio(0);
  int n;
  cin >> n;
  map<ll, ll> cnt;
  for (int i = 0; i < n; ++i) {
    ll x;
    cin >> x;
    cnt[solve(x)]++;
  }
  ll ans = 0;
  for (auto itr : cnt) ans = ans + (itr.second * (itr.second - 1)) / 2;
  cout << ans;
  return 0;
}
