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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int N;

int pair_of(int n) {
    int pow = 1;
    while(pow <= n) {
        pow *= 2;
    }
    return pow - n;
}

int main() {
    cin >> N;
    
    vector<int> A(N);
    
    for (int i = 0; i < N; i++) {
        cin >> A[i];
    }
    sort(A.begin(), A.end());
    
    int ans = 0;
    for (auto itr = A.end() - 1; itr != A.begin(); --itr) {
        if (*itr < 0)   continue;
        
        int i = pair_of(*itr);
        auto pair_itr = lower_bound(A.begin(), itr, i);
        if (pair_itr != itr && *pair_itr == i) {
            *pair_itr = -1;
            ans++;
        }
    }

    cout << ans << endl;
}