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 sz(int a) {
  if (a == 0) return 1;
  if (a % 2)
    return (sz((a - 1) / 2) + 1);
  else
    return sz(a / 2);
}
bool pd(long long a, long long b) {
  bool o = false;
  long long t;
  if (a > b) {
    t = a;
    a = b;
    b = t;
  }
  if (b % a == 0 && b / a)
    if (a == sz(b))
      o = true;
    else
      o = false;
  return o;
}
int main() {
  int n;
  long long a[100001] = {0}, i, j, sum = 0, t, b[100] = {0};
  scanf("%d", &n);
  for (i = 1; i <= n; i++) cin >> a[i];
  for (i = 1; i <= n; i++) b[sz(a[i])]++;
  for (i = 0; i <= 50; i++) sum += b[i] * (b[i] - 1) / 2;
  cout << sum << endl;
  return 0;
}
