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;
map<int, int> mp1;
int main() {
  int n;
  scanf("%d", &n);
  for (int(i) = (0); (i) < (n); ++(i)) {
    int temp;
    scanf("%d", &temp);
    int count1 = 0;
    int temp1 = temp;
    while (temp1 != 0) {
      if (temp1 % 2 == 1) {
        count1++;
        temp1 = temp1 / 2;
      } else {
        temp1 = temp1 / 2;
      }
    }
    mp1[count1]++;
  }
  long long answer1 = 0;
  for (auto &(t1) : (mp1)) {
    long long temp1 = t1.second;
    answer1 = answer1 + (temp1 * (temp1 - 1)) / 2;
  }
  printf("%lld\n", answer1);
  return 0;
}
