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;
using ll = long long;
const int mod = 1e9 + 7;
const int inf = (1 << 30) - 1;
const ll infll = (1LL << 61) - 1;
int f(int a) {
  if (a == 0)
    return 0;
  else if (a % 2 == 0)
    return f(a / 2);
  else
    return f(a / 2) + 1;
}
int N;
ll ans = 0;
int main() {
  cin >> N;
  vector<int> a(N);
  map<int, ll> mp;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
    mp[f(a[i])]++;
  }
  for (auto &p : mp) {
    ans += p.second * (p.second - 1) / 2;
  }
  cout << ans << endl;
}
