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: Time Limit Exceeded)

use std::io::Read;
use std::str::SplitWhitespace;
use std::str::FromStr;

pub fn read_stdin() -> String {
    let mut s = String::new();
    ::std::io::stdin().read_to_string(&mut s).unwrap();
    s
}

pub trait Parse<T> {
    fn parse(&mut self) -> T;
}

impl<'a, T> Parse<T> for SplitWhitespace<'a>
where
    T: FromStr,
{
    fn parse(&mut self) -> T {
        let word = self.next().unwrap();
        word.parse().ok().unwrap()
    }
}


fn main() {
    let source = read_stdin();
    let mut iter = source.split_whitespace();
    let n: usize = iter.parse();
    let v: Vec<u32> = (0..n).map(|_| iter.parse()).collect();

    let mut ans = Vec::new();
    for i in (0..n).rev() {
        let c = ans.iter().filter(|&x| x % (i + 1) == 0).count() as u32;
        if v[i] != c % 2 {
            ans.push(i + 1);
        }
    }

    println!("{}", ans.len());
    if !ans.is_empty() {
        println!(
            "{}",
            ans.into_iter()
                .map(|x| x.to_string())
                .collect::<Vec<_>>()
                .join(" ")
        );
    }
}