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>
using namespace std;
int n,s;
multiset<int> Set;
int main()
{
	int a;
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a;
		Set.insert(a);
	 } 
	 if(!Set.empty())
	 {
	 	auto it=Set.end();
	 	int x=*it;
	 	Set.erase(x);
	 	for(int i=2;i<=300000;i*=2)
	 	{
	 		if(Set.find(i-x)!=Set.end())
	 		{
	 			Set.erase(Set.find(i-x));
			 s++;
	 		}
	 	}
	 }
	 cout<<s<<endl;
	 return 0;
}