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;

#define rep(i, N) for (int i = 0; i < N; i++)

using ll = long long int;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

int main()
{
    int N;
    cin >> N;
    vector<int> A(N);
    rep(i, N) cin >> A[i];

    unordered_map<int, set<int>> a_to_indice;
    rep(i, N) a_to_indice[A[i]].insert(i);

    // make pair
    int npair = 0;
    sort(A.rbegin(), A.rend());
    rep(i, N)
    {
        int a = A[i];
        if (a == 0)
            continue;
        a_to_indice[a].erase(i);

        int power_of_two = pow(2, (int)floor(log2(a)) + 1);
        int b = power_of_two - a;
        if (!a_to_indice[b].empty())
        {
            int index_b = *a_to_indice[b].begin();
            a_to_indice[b].erase(index_b);
            A[index_b] = 0;
            npair++;
        }
    }

    cout << npair << endl;
}