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;
vector<int> vec;
map<int, int> mp, mp1;
queue<int> q;
int a[100002], d[1000002];
string s;
int main() {
  int i, j, k, l, m, n, x, y, sum = 0;
  scanf("%d", &n);
  mp[1] = 1;
  for (i = 1; i <= 100000; i++) {
    if (!mp[i] || i == 1) {
      for (j = 2 * i; j <= 100000; j *= 2) {
        mp[j] = mp[j / 2];
        mp[j + 1] = mp[j / 2] + 1;
      }
    }
  }
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i] = mp[a[i]];
    mp1[a[i]]++;
  }
  for (i = 1; i <= n; i++) {
    sum += max(0, mp1[a[i]] - 1);
    mp1[a[i]]--;
  }
  cout << sum;
  return 0;
}
