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 <bits/stdc++.h>
int main() {
  std::cin.tie(0); std::cin.sync_with_stdio(false);
  size_t n; std::cin >> n;
  std::multiset<int, std::greater<int>> set;
  for (size_t i = 0; i < n; i++) {
    int x; std::cin >> x;
    set.insert(x);
  }
  int ret = 0;
  while (!set.empty()) {
    int x = *set.begin(); set.erase(set.begin());
    int y = std::pow(2, (int)std::log2(x) + 1) - x;
    auto it = set.find(y);
    if (it != set.end()) {
      ret++;
      set.erase(it);
    }
  }
  std::cout << ret << std::endl;
  return 0;
}