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<iomanip>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#include<vector>
#include<queue>
#include<stack>
#include<map>
#include<set>
using namespace std;
const int inf=2147483647,dx[]={-1,0,1,0},dy[]={0,-1,0,1},N=100005,M=1000005,mod=1000000007;
const long long llinf=9223372036854775807ll;
int n,a[M],l,r,ans;
bool u[M];
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i];
	sort(a+1,a+1+n);
	l=1,r=n;
	while(l<r)
	{
		for(int p=2;p<=(1<<30);p<<=1)
			if(p>a[r])
			{
				int i;
				for(i=l;i<r&&a[i]+a[r]<=p;i++)
					if(a[i]+a[r]==p&&!u[i]&&!u[r])
					{
						ans++,u[i]=u[r]=true,l=i+1,r--;
						break;
					}
				if(i==r||a[i]+a[r]>p)
					r--;
				break;
			}
	}
	cout<<ans;
	return 0;
}