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 cnt = 0;
int main() {
  int n;
  int a[30] = {1,        2,        4,        8,         16,        32,
               64,       128,      256,      512,       1024,      2048,
               4096,     8192,     16384,    32768,     65536,     131072,
               262144,   524288,   1048576,  2097152,   4194304,   8388608,
               16777216, 33554432, 67108864, 134217728, 268435456, 536870912};
  cin >> n;
  vector<int> v(n + 1);
  for (int i = 1; i <= n; i++) {
    bool ind = 0;
    int x;
    cin >> x;
    if (x % 2 == 1 && x != 1) {
      ind = 1;
      x--;
    }
    for (int j = 30; j >= 0; j--)
      if (x % a[j] == 0) {
        v[i] = x / a[j];
        if (ind) v[i] *= (-1);
        break;
      };
    for (int j = 1; j < i; j++)
      if (v[j] == v[i]) cnt++;
  }
  cout << cnt;
  return 0;
}
