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 f[200000];
long long kt(long long a, long long b) {
  long long x1 = a, x2 = a;
  long long y = b;
  x2 = x2 * 2 + 1;
  if (x2 == y)
    return 1;
  else {
    while (x1 < y) {
      x1 = x1 * 2;
      if (x1 == y) {
        return 1;
        break;
      }
    }
    return 0;
  }
}
int main() {
  long long m[200000], n, dem = 0, s = 0;
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> m[i];
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = i + 1; j <= n; j++) {
      if (m[i] > m[j]) {
        s = m[i];
        m[i] = m[j];
        m[j] = s;
      }
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = i + 1; j <= n; j++) {
      if (m[i] == 0)
        continue;
      else {
        if (kt(m[i], m[j]) == 1) {
          dem++;
        }
      }
    }
  }
  cout << dem;
}
