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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <set>
#include <map>

std::map<int, int> mp;

int nxt(int number) {
  int p = 1;
  while(p <= number) 
    p *= 2;
  return p;
}

int main() {
  int n;
  std::cin >> n;
  for(int i = 1; i <= n; i++) {
    int val;
    std::cin >> val;
    mp[val]++;
  }
  int result = 0;
  while(0 < mp.size()) {
    std::map<int,int>::iterator  it = mp.end();
    it--;
    if(it->second == 0)
      mp.erase(it);
    else {
      int oth = nxt(it->first) - it->first;
      if(oth == it->first) {
        if(1 < it->second) {
          it->second -= 2;
          result++;
        } else
          mp.erase(it);
      } else {
        if(0 < mp[oth]) {
          it->second--;
          mp[oth]--;
          result++;
        } else
          mp.erase(it);
      }
    }
  }
  std::cout << result;
  return 0;
}