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 i64 = long long;

int main() {
    int n;
    std::cin >> n;
    std::multiset<i64, std::greater<>> s;
    for (int i = 0; i < n; i++) {
        int a;
        std::cin >> a;
        s.insert(a);
    }

    int ret = 0;
    while (!s.empty()) {
        auto mm = *s.begin();
        s.erase(s.begin());
        for (i64 x = 1; x <= 2 * mm; x *= 2) {
            if (x <= mm) continue;
            auto it = s.find(x - mm);
            if (it == s.end()) continue;
            s.erase(it);
            ret++;
            break;
        }
    }

    std::cout << ret << std::endl;

    return 0;
}