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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn main() {
    input! {
        n: usize,
        a: [usize; n],
    }
    let mut count = HashMap::new();
    for i in 0..n {
        *count.entry(a[i]).or_insert(0) += 1;
    }
    let mut keys = count.keys().map(|&k| k).collect::<Vec<usize>>();
    keys.sort();
    keys.reverse();

    let mut b = vec![];
    for i in 1..40 {
        b.push(2usize.pow(i));
    }
    b.reverse();

    let mut result = 0;
    for &bi in &b {
        for &k1 in &keys {
            if k1 >= bi {
                continue;
            }
            let c1 = count[&k1];
            let k2 = bi - k1;
            if let Some(&c2) = count.get(&k2) {
                if k1 == k2 {
                    let c = c1 / 2;
                    // eprintln!("{} {} {}", k1, k2, c);
                    result += c;
                    *count.get_mut(&k1).unwrap() -= c;
                } else {
                    let c = min(c1, c2);
                    // eprintln!("{} {} {}", k1, k2, c);
                    result += c;
                    *count.get_mut(&k1).unwrap() -= c;
                    *count.get_mut(&k2).unwrap() -= c;
                }
            }
        }
    }
    println!("{}", result);
}
*/

fn main() {
    let exe = "/tmp/binF16D9176";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";