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)

#include<bits/stdc++.h>
using namespace std;

int main(){
    size_t N;
    scanf("%ld", &N);

    deque<pair<int_fast64_t, int_fast64_t>> a(N, pair<int_fast64_t, int_fast64_t>(0, 1));

    for(size_t i = 0; i < N; ++i)scanf("%ld", &(a[i].first));
    sort(a.begin(), a.end());

    uint_fast64_t A(0);
    for(; a.empty();){
        auto v = a.back();
        a.pop_back();
        if(v.second){
            auto k = pair<int_fast64_t, int_fast64_t>((1LL << (64 - __builtin_clzll(v.first))) - v.first, 1LL);
            auto t = lower_bound(a.begin(), a.end(), k);
            if(t != a.end() && t -> first == k.first){
                ++A;
                t -> second = 0;
            }
        }
    }

    cout << A << endl;
    return 0;
}