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 Rust (1.15.1) (judge verdict: Accepted)

use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    let _: usize = read();
    let mut a = read_vec::<usize>();
    a.sort();

    let mut num_dict = HashMap::new();
    for num in a.iter() {
        *num_dict.entry(*num).or_insert(0) += 1;
    }
    let mut ans = 0;
    for num in a.iter().rev() {
        // already consumed
        if num_dict[num] == 0 {
            continue;
        }
        *num_dict.get_mut(num).unwrap() -= 1;
        let power = (*num as f64).log2() as usize + 1;
        let key = (1 << power) - *num;
        // println!("{:?}", (*num, 1 << power, key));
        if num_dict.contains_key(&key) && num_dict[&key] > 0 {
            *num_dict.get_mut(&key).unwrap() -= 1;
            ans += 1;
        }
    }
    println!("{:?}", ans);
}