Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <algorithm>
#include <cmath>
#include <iostream>
#include <set>
#include <vector>
using namespace std;

int main() {
  int N;
  cin >> N;
  multiset<int> A;
  int atmp;
  while (cin >> atmp) {
    A.insert(atmp);
  }

  int nr_of_pairs = 0;

  while (!A.empty()) {
    auto itr_max = --A.end();
    auto max = *itr_max;
    A.erase(itr_max);
    int i;
    for (i = 1; i <= max; i *= 2)
      ;
    if (A.find(i - max) != A.end()) {
      A.erase(A.find(i - max));
      ++nr_of_pairs;
    }
  }

  cout << nr_of_pairs << endl;
  return 0;
}