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::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let mut a: Vec<usize> = (0..n).map(|_| it.next().unwrap().parse().unwrap()).collect();
    a.sort();
    let mut d: std::collections::VecDeque<_> = a.into_iter().collect();
    let mut ans = 0;
    for k in (1..31).rev() {
        let mut s = std::collections::VecDeque::new();
        let mut t = std::collections::VecDeque::new();
        while d.len() >= 2 {
            let a = d.pop_front().unwrap();
            let b = d.pop_back().unwrap();
            if a + b == (1 << k) {
                ans += 1;
            } else if a + b > (1 << k) {
                t.push_front(b);
                d.push_front(a);
            } else {
                s.push_back(a);
                d.push_back(b);
            }
        }
        while let Some(a) = d.pop_front() {
            s.push_back(a);
        }
        d.append(&mut s);
        d.append(&mut t);
    }
    println!("{}", ans);
}

fn main() {
    run();
}