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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define eps DBL_EPSILON
#define moder 10007
#define int long long
#define ll long long
#define INF LLONG_MAX/3
#define P std::pair<int,int>
#define prique priority_queue<int,vector<int>,greater<int>>
using namespace std;
int n,a[200010],b[100];
bool used[200010];
bool check(int s){
	while(s%2==0)s/=2;
	return s==1;
}
int cnt=1;
void func(){
	int s=2;
	while(s<=INT_MAX*(ll)3){
		b[cnt]=s;
		cnt++;
		s*=2;
	}
}
signed main(){
	cin>>n;
	rep(i,n)cin>>a[i];
	func();
	sort(a,a+n);
	int ans=0;
	for(int i=n-1;i>=0;i--){
		for(int j=cnt-1;j>=0;j--){
			if(a[i]>b[j]||used[i])continue;
			if(upper_bound(a,a+n,b[j]-a[i])-lower_bound(a,a+n,b[j]-a[i])){
				if(used[lower_bound(a,a+n,b[j]-a[i])-a]||lower_bound(a,a+n,b[j]-a[i])==&a[i])continue;
				ans++;
				used[i]=true;
				used[lower_bound(a,a+n,b[j]-a[i])-a]=true;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}