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

int main(void){
  multiset<long,greater<long>>ball;
  size_t n;cin>>n;
  for(int i=0;i<n;i++){
    int x;cin>>x;
    ball.insert(x);
  }
  int ans=0;
  while(!ball.empty()){
    int x=*ball.begin();ball.erase(x);
    int y=pow(2,(int)log2(x)+1)-x;
    auto it=ball.find(y);
    if(it!=ball.end()){
      ball.erase(it);
      ans+=1;
    }
  }
  cout<<ans<<endl;
}