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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define ln '\n';
int lim=1e6;
int inf=1e9+7;
int main()
{	
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int n;cin>>n;
	int a[n];
	for(int i=0;i<n;i++){
		cin>>a[i];	
	}	
	int ans=0;
	vector<bool> done(n,0);
	sort(a,a+n);
	for(int i=n-1;i>=0;i--){
		if(done[i]){
			continue;
		}
		int tmp=log2(a[i]);
		tmp=(int)(pow(2,tmp+1));
		tmp-=a[i];
		done[i]=1;
		int* pt=lower_bound(a,a+i,tmp);
		while(pt<a+n and *pt==tmp){
			if(!done[pt-a]){
				ans++;done[pt-a]=1;break;
			}
			pt++;
		}
	}
	cout<<ans<<ln;
}