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)

/***********************
*  Author: xuziyuan    * 
***********************/

#include <bits/stdc++.h>

#define rt0 return 0
#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
#define replet(c) for(char c='a';c<='z';c++)
#define LL long long
#define pii pair <LL,LL>
#define pb push_back
#define fi first
#define se second
#define mpr make_pair
#define sqr(a) ((a)*(a))

using namespace std;

const LL MOD=1e9+7;

LL n,ans=0;
pii a[200010];

int main()
{
	cin>>n;
	rep(i,n) cin>>a[i].fi;
	sort(a,a+n);
	for(int i=n-1;i>=0;i--)
	{
		if(a[i].se==1) continue;
		LL pw=1;
		while(pw<=a[i].fi) pw*=2;
		int pos=upper_bound(a,a+i,mpr(pw-a[i].fi,0LL))-a;
		//cout<<i<<' '<<a[i].fi<<' '<<pw<<' '<<pos<<endl;
		//cout<<i<<' '<<pos<<" "<<a[i].fi<<' '<<a[pos-1].fi<<endl;
		if(pos<=i&&a[i].fi+a[pos-1].fi==pw)
		{
			ans++;
			a[pos-1].se=1;
		}
	}
	cout<<ans<<endl;
	rt0;
}