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<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<set>
using namespace std;
const int N=200005;
int n,ans,a[N],b[N],tot[N];
set<int> st;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	for(int i=1,j=0;j<=30;i*=2,j++){
		st.insert(i);
	}
	sort(a+1,a+n+1);
	memcpy(b,a,4*(n+1));
	b[0]=unique(b+1,b+n+1)-b-1;
	for(int i=1;i<=b[0];i++){
		tot[i]=upper_bound(a+1,a+n+1,b[i])-lower_bound(a+1,a+n+1,b[i]);
	}
	for(int i=b[0];i>=1;i--){
		if(st.count(b[i])){
			ans+=tot[i]/2;
		}else{
			int res=*st.upper_bound(b[i])-b[i];
			if(upper_bound(a+1,a+n+1,res)-lower_bound(a+1,a+n+1,res)){
				res=lower_bound(b+1,b+n+1,res)-b;
				int tmp=min(tot[res],tot[i]);
				ans+=tmp;
				tot[i]-=tmp;
				tot[res]-=tmp;
			}
		}
	}
	printf("%d\n",ans);
	return 0;
}