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<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<math.h>
#include<map>
using namespace std;

const int N=3e5+5;
int n,a[N],calc[N],tl,ans;
map<int,int> M;

int ask(int x)
{
	int i;
	for(i=30;~i;--i)
		if(x&(1<<i))
			break;
	return (1<<i+1)-x;
}

void cc()
{
	int i,l=1;
	M.clear();
	for(i=1;i<=tl;++i) ++M[calc[i]];
	sort(calc+1,calc+tl+1);
	for(i=tl;i;--i)
	{
		if(!M[calc[i]]) continue;
		int mx=ask(calc[i]);
		if(mx!=calc[i])
		{
			if(M[mx])
				--M[calc[i]],--M[mx],++ans;
		}
		else
		{
			if(M[mx]>1)
				M[mx]-=2,++ans;
		}
	}
}

bool cmp(int x,int y)
{
	return (x&1)<(y&1);
}
void init()
{
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;++i) scanf("%d",&a[i]);
	while(n)
	{
		tl=0;
		sort(a+1,a+n+1,cmp);
		for(i=n;i;--i)
		{
			if(!(a[i]&1)) break;
			calc[++tl]=a[i];
		}
		cc();n=i;
		for(i=1;i<=n;++i) a[i]>>=1;
	}
	printf("%d\n",ans);
}

int main()
{
	init();
	return 0;
}