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: Wrong Answer)

#include <cstdio>
#include <set>
#include <algorithm>

int as[200005];

int invert(int X){
  int k=0;
  while((1<<k)<=X) k++;
  //printf("invert(%d)=%d\n",X,(1<<k)-X);
  return (1<<k)-X;
}

int main(){
  int N;
  scanf("%d",&N);
  for(int i=0;i<N;i++){
    scanf("%d",&as[i]);
  }
  std::sort(as,as+N);
  std::multiset<int> look;
  int match;
  for(int i=N-1;i>=0;i--){
    if(look.count(as[i])){
      look.erase(look.find(as[i]));
      match++;
    }else{
      look.insert(invert(as[i]));
    }
  }
  printf("%d\n",match);
  return 0;
}