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 <set>
#include <vector>
#include <string>
#include <iterator>
#include <algorithm>

using namespace std;
using ll = long long;
using ld = long double;

multiset<int> AA;
int result = 0;

void findAndReduce() {
    while (!AA.empty()) {
        auto itr = AA.rbegin();
        auto a = *itr;
        //itrを削除
        AA.erase(AA.find(a));
        int tw = 1;
        for (int i = 1; i < 40; ++i) {
            tw *= 2;
            if(tw > a){
                break;
            }
        }
        auto b = tw - a;
        auto itr2 = AA.find(b);
        if (itr2 == AA.end()) {
            continue;
        }
        AA.erase(itr2);
        result++;
    }
}

int main() {

    int N;
    cin >> N;

    for (int i = 0; i < N; ++i) {
        int n;
        cin >> n;
        AA.insert(n);
    }


    findAndReduce();

    cout << result << endl;


    return 0;
}