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: Time Limit Exceeded)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <list>
#include <random>
#include <iomanip>
#include <map>

using namespace std;

typedef long long ll;

bool twobeki(ll s) {
    for (int i = 1; i < 32; i++) {
        if (s == pow(2, i)) {
            return 1;
        }
    }
    return 0;
}

int main() {
    int N;
    vector<ll> A;
    cin >> N;
    ll a;
    for (int i = 0; i < N; i++) {
        cin >> a;
        A.push_back(a);
    }
    
    sort(A.begin(), A.end(), greater<ll>());
    ll s;
    bool flag = 0;
    int ans = 0;
    for (int i = 0; i < A.size()-1; i++) {
        for (int j = i+1; j < A.size(); j++) {
            s = A.at(i) + A.at(j);
            flag = twobeki(s);
            if (flag) {
                ans++;
                A.erase(A.begin() + j);
                break;
            }
        }
    }
    
    cout << ans << endl;
}