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

int main()
{
    int N;
    cin >> N;

    long long A;
    map<long long, int> m;
    for (int i = 0; i < N; i++)
    {
        cin >> A;
        m[A]++;
    }

    long long ans = 0;
    for (auto itr = m.rbegin(); itr != m.rend(); itr++)
    {
        long long x = itr->first;
        long long target = 1;
        long long exp = 0;
        while (x > 0)
        {
            if (~x & 1)
            {
                target += (1 << exp);
            }
            exp++;
            x >>= 1;
        }
        while (itr->second > 0)
        {
            itr->second--;
            if (m[target] > 0)
            {
                m[target]--;
                ans++;
            }
            else
            {
                itr->second++;
                break;
            }
        }
    }
    cout << ans << endl;
}