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<set>
#include<map>
#include<stack>
#include<queue>
#include<deque>
#include<cmath>
#include<tr1/unordered_map>
#include<ctime>
#include<cstdio>
#include<vector>
#include<climits>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define LL long long
int read(){
    int f=1,x=0;char c=getchar();
    while(c<'0'||'9'<c){if(c=='-')f=-1;c=getchar();}
    while('0'<=c&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
    return f*x;
}
#define INF 0x3f3f3f3f
#define MAXN 200000
int a[MAXN+5];
bool use[MAXN+5];
map<int,bool> Map;
int main(){
	int n=read();
	for(int i=1;i<=n;i++)
		a[i]=read();
	sort(a+1,a+n+1);
	for(int i=0;i<=30;i++)
		Map[(1<<i)]=1;
	int cnt=0;
	for(int i=1;i<=n;i++)
		if(!use[i])
			for(int j=n;j>i;j--)
				if(!use[j]&&Map[a[i]+a[j]])
					use[j]=1,cnt++;
	printf("%d\n",cnt);
    return 0;
}