Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <set>

int main() {
  size_t N;

  std::cin >> N;

  std::multiset<size_t> A;

  for (size_t i=0; i<N; i++) {
    size_t a;
    std::cin >> a;
    A.insert(a);
  }

  size_t ans=0;

  while (A.size() > 1) {
    auto const max = *std::prev(A.end());
    A.erase(std::prev(A.end()));

    for (size_t sum=0x80000000; sum>1; sum>>=1) {
      if (max >= sum) break;

      auto it_tgt = A.lower_bound(sum - max);

      if (it_tgt == A.end()) continue;

      std::cerr << sum << ' '
                << max << ' '
                << *it_tgt << std::endl;

      if (*it_tgt + max == sum) {
        ans++;
        A.erase(it_tgt);
      }
    }
  }

  std::cout << ans << std::endl;

  return 0;
}