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 <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vb = vector<bool>;
using vs = vector<string>;
using msi = map<string, int>;
using mii = map<int, int>;
using psi = pair<string, int>;
using pii = pair<int, int>;
using tii = tuple<int, int>;
using vlai = valarray<int>;
#define rep(i,n) for(int i=0;i<n;i++)
#define range(i,s,n) for(int i=s;i<n;i++)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define fs first
#define sc second
#define INF 1E9
#define LINF 1E18*5
#define EPS 1E-9
#define MOD 1000000007
#define PI 3.1415926535897932384

template<class S, class T>ostream& operator<<(ostream&os, pair<S, T>p) { os << "[" << p.first << ", " << p.second << "]"; return os; };
template<class S>auto&operator<<(ostream&os, vector<S>t) { bool a = 1; for (auto s : t) { os << (a ? "" : " ") << s; a = 0; } return os; }

//int dx[]={1,1,1,0,-1,-1,-1,0},dy[8]={1,0,-1,-1,-1,0,1,1,1};
//
constexpr ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }

class compare {
public:
	bool operator()(tuple<int, int> a, tuple<int, int> b) {
		return (get<1>(a) < get<1>(b));
	}
};

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	ll n;
	ll ans = 0;
	cin >> n;
	multiset<ll> s;
	vl v(n), pw;
	rep(i, n) {
		cin >> v[i];
		s.insert(v[i]);
	}
	ll tmp = 1;
	rep(i, 31) {
		tmp *= 2;
		pw.push_back(tmp);
	}
	while (!s.empty()) {
		auto ritr = s.end();
		ritr--;
		ll tmp = *ritr;
		s.erase(ritr);
		ll rtmp = *upper_bound(all(pw), tmp) - tmp;
		//cout << tmp << " " << rtmp << endl;
		auto itr = s.find(rtmp);
		if (itr != s.end()) {
			s.erase(itr);
			ans++;
		}
	}
	cout << ans << endl;
}