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 <set>
#include <map>
#include <cstdio>
#include <cctype>
#include <vector>
#include <algorithm>
//#define mp std::make_pair
#define pr std::pair<int,int>
#define pc putchar
#define gc() getchar()
typedef long long LL;
const int N=2e5+5;

int A[N],vis[N];
std::map<LL,int> mp;

inline int read()
{
	int now=0,f=1;register char c=gc();
	for(;!isdigit(c);c=='-'&&(f=-1),c=gc());
	for(;isdigit(c);now=now*10+c-'0',c=gc());
	return now*f;
}

int main()
{
	int n=read(),ans=0;
	for(int i=1; i<=n; ++i) ++mp[A[i]=read()];
	std::sort(A+1,A+1+n);
	for(int i=n; i; --i)
		if(mp[A[i]])
			for(int j=31; ~j; --j)
			{
				LL pw=1ll<<j;
				if(pw==A[i]+A[i] && mp[A[i]]>=2) {mp[A[i]]-=2, ++ans; break;}
				else if(pw!=A[i]+A[i] && pw>A[i] && mp[pw-A[i]]) {--mp[pw-A[i]], --mp[A[i]], ++ans; break;}
			}
	printf("%d\n",ans);

	return 0;
}