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;
const int INF = 0x3f3f3f3f;
long long check[100000 + 5], prim[100000 + 5];
long long a[100000 + 5];
map<long long, int> mp;
set<long long> scond;
int main() {
  long long i = 0, j = 0, k = 1, l = 0;
  long long n, m;
  long long y, x, s = 0;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    k = a[i];
    s = 0;
    while (k) {
      if (k % 2)
        s++, k = (k - 1) / 2;
      else
        k /= 2;
    }
    a[i] = s;
    scond.insert(s);
    mp[s]++;
  }
  s = 0;
  set<long long>::iterator it = scond.begin();
  for (; it != scond.end(); it++) {
    k = *it;
    x = mp[k];
    x = x * (x - 1) / 2;
    s += x;
  }
  cout << s << endl;
  return 0;
}
