Problem:
Score : 400 points

Problem Statement

There are N empty boxes arranged in a row from left to right.
The integer i is written on the i-th box from the left (1 \leq i \leq N).

For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.

We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:

For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.

Does there exist a good set of choices? If the answer is yes, find one good set of choices.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

a_i is 0 or 1.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If a good set of choices does not exist, print -1.

If a good set of choices exists, print one such set of choices in the following format:

M
b_1 b_2 ... b_M

where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.

Sample Input 1

3
1 0 0

Sample Output 1

1
1

Consider putting a ball only in the box with 1 written on it.

There are three boxes with multiples of 1 written on them: the boxes with 1, 2, and 3. The total number of balls contained in these boxes is 1.

There is only one box with a multiple of 2 written on it: the box with 2. The total number of balls contained in these boxes is 0.

There is only one box with a multiple of 3 written on it: the box with 3. The total number of balls contained in these boxes is 0.

Thus, the condition is satisfied, so this set of choices is good.

Sample Input 2

5
0 0 0 0 0

Sample Output 2

0

Putting nothing in the boxes can be a good set of choices.

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

mod stdin_reader {
  use std::io::stdin;
  use std::io::Read;

  pub struct StdinReader {
    pub buf: Vec<String>,
    pub cursor: usize,
  }

  pub fn new() -> StdinReader {
    StdinReader::new()
  }

  impl StdinReader {
    pub fn new() -> Self {
      let mut s = String::new();
      let stdin = stdin();
      stdin.lock().read_to_string(&mut s).unwrap();
      let buf = s.split_whitespace().map(|s| s.to_string()).collect();
      return StdinReader { buf: buf, cursor: 0 }
    }

    pub fn read_all(&self) -> Vec<String> {
      return self.buf.clone()
    }

    pub fn next(&mut self) -> Option<String> {
      let val = self.buf.get(self.cursor).cloned();
      self.cursor += 1;
      return val
    }

    pub fn as_i64(&mut self) -> Option<i64> {
      self.next().and_then(|s| s.parse::<i64>().ok())
    }

    pub fn as_f64(&mut self) -> Option<f64> {
      self.next().and_then(|s| s.parse::<f64>().ok())
    }

    pub fn as_usize(&mut self) -> Option<usize> {
      self.next().and_then(|s| s.parse::<usize>().ok())
    }
  }
}

mod utils {
  pub fn is_int(n: f64) -> bool {
    let trunc = (n.trunc() as i64) as f64;
    return (n - trunc) < 0.0001
  }
}

fn main() {
  // stdout
  use std::io::{stdout, Write, BufWriter};
  let stdout = stdout();
  let mut writer = BufWriter::new(stdout.lock());

  // stdin
  let mut reader = stdin_reader::new();

  let n = reader.as_usize().unwrap();
  let mut a_list = vec![0];
  a_list.extend((0..n).map(|_| reader.as_i64().unwrap()));
  let mut boxes = vec![0; n+1];
  let mut result_rev = vec![];
  for i in (1..(n+1)).rev() {
    let bigger_sum: i64 = ((i+1)..(n+1)).filter(|cursor| cursor % i == 0).map(|cursor| boxes[cursor]).fold(0, |sum, val| sum + val);
    if bigger_sum % 2 == a_list[i] {
      // do nothing
    } else {
      boxes[i] = 1;
      result_rev.push(i);
    }
  }

  println!("{}", result_rev.len());
  for b in result_rev.into_iter().rev() {
    write!(writer, "{}", b);
  }
}