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: Accepted)

pub struct Poper<'a> {
	iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Poper<'a> {
	pub fn new(iter: std::str::SplitWhitespace) -> Poper {
		Poper { iter: iter }
	}
	pub fn read<T: std::str::FromStr>(&mut self) -> T
	where
		<T as std::str::FromStr>::Err: std::fmt::Debug,
	{
		self.iter.next().unwrap().parse().unwrap()
	}
}

fn main() {
	let input = {
		use std::io::Read;
		let mut s = String::new();
		std::io::stdin().read_to_string(&mut s).unwrap();
		s
	};
	let mut iter = Poper::new(input.split_whitespace());

	let n: usize = iter.read();
	let a_list = {
		let mut a_list: Vec<(usize, u32)> = (0..n)
			.into_iter()
			.map(|_| iter.read())
			.enumerate()
			.collect();
		a_list.reverse();
		a_list
	};

	let mut x_list: Vec<u32> = vec![0; n];
	let mut i_list: Vec<usize> = vec![];

	for &(i, a) in a_list.iter() {
		let t = cnt(&x_list, i);
		x_list[i] = if t == a {
			0
		} else {
			i_list.push(i);
			1
		};
	}

	let l = i_list.len();
	println!("{}", l);
	if 0 < l {
		println!(
			"{}",
			i_list
				.into_iter()
				.map(|n| (n + 1).to_string())
				.collect::<Vec<String>>()
				.join(" ")
		);
	}
}

fn cnt(x_list: &Vec<u32>, i: usize) -> u32 {
	let mut j = i;
	let i = i + 1;
	let mut r = 0;
	let s = x_list.len();
	loop {
		j += i;
		if j >= s {
			return r % 2;
		}
		let x = x_list[j];
		if 0 < x {
			r += 1;
		}
	}
}