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: Accepted)

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
using namespace std;
LL A[505050];
int n,ans;
bool Tag[2020202];
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
		scanf("%lld",&A[i]);
	sort(A+1,A+n+1);
	for (LL x=(1ll<<31);x>0;x>>=1ll){
		int r=n;
		for (int l=1;l<=n;l++){
			if (l>=r) break;
			if (Tag[l]) continue;
			while (r>l&&(Tag[r]||A[l]+A[r]>x)) r--;
			if (l>=r) break;
			if (A[l]+A[r]==x){
				Tag[l]=1; Tag[r]=1; ans++;
			}
		}
	}
	cout<<ans;
}