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)

/*---- enazuma11-------  */
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define mp make_pair
#define all(v) v.begin(),v.end()
#define inc(a,n) sort(a,a+n)
#define dec(a,n) sort(a,a+n,greater<int>() )
#define F first
#define S second
#define M 1000000007
vector<ll> p;
void f(){
	ll t=1;
	while(t<=2e9){
		p.pb(t);
		t=t<<1;
	}
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	f();
	
	int n;
	cin>>n;
	map<ll,ll> m;
	ll a[n];
	for(int i=0;i<n;i++){
		cin>>a[i];
		m[a[i]]++;
	}
	int c=0;
	sort(a,a+n);
	for(int i=0;i<n;i++){
		if(m[a[i]]<=0)
		continue;
		int j=lower_bound(all(p),a[i])-p.begin();
		ll r=p[j]-a[i];
		if(m.find(r)!=m.end() && m[r]>0){
			//cout<<a[i]<<" "<<r;
			c++;
			m[r]--;
			m[a[i]]--;
		}
	}
	cout<<c;
	return 0;
}