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::fs;
use std::io::{stdin, Read};
struct UnionFind {
    parents: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        let par = (0..n).collect();
        UnionFind { parents: par }
    }
    pub fn root(&mut self, x: usize) -> usize {
        if self.parents[x] == x {
            return x;
        }
        let par = self.parents[x];
        self.parents[x] = self.root(par);
        self.parents[x]
    }
    pub fn union(&mut self, x: usize, y: usize) {
        let rx = self.root(x);
        let ry = self.root(y);
        if rx == ry {
            return;
        }
        self.parents[rx] = ry;
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        let rx = self.root(x);
        let ry = self.root(y);
        rx == ry
    }
}

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}
fn binary_search_left<T: Ord>(v: &Vec<T>, x: T) -> usize {
    let mut l: isize = -1;
    let mut r: isize = v.len() as isize;
    while r - l > 1 {
        let m = (r + l) / 2;
        if v[m as usize] < x {
            l = m;
        } else {
            r = m;
        }
    }
    r as usize
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let n = parse!(it);
    let mut a: Vec<usize> = parse!(it, n);
    a.sort();
    let mut counts = std::collections::HashMap::<usize, usize>::new();
    for &a in a.iter() {
        *counts.entry(a).or_insert(0) += 1;
    }
    let mut ret = 0;
    for &a in a.iter().rev() {
        if counts[&a] == 0 {
            continue;
        }
        *counts.entry(a).or_insert(0) -= 1;
        let mut k = 1;
        while a > k {
            k <<= 1;
        }
        let b = if k == a { a } else { k - a };
        let mut e = counts.entry(b).or_insert(0);
        if *e > 0 {
            *e -= 1;
            ret += 1;
        }
    }
    println!("{}", ret);
}

fn test() {
    let mut f = fs::File::open("foo.txt").unwrap();
    let mut s = String::new();
    f.read_to_string(&mut s).unwrap();
    solve(&s);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_main() {
        test();
    }
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}