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)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: i32 = read();
    let mut vec: Vec<i32> = vec![];
    for _ in 0..n {
        vec.push(read());
    }
    // for (i, v) in vec.iter().enumerate().map(|(x, y)| (x + 1, y)).rev() {
    let mut rev_ans = vec![];
    let mut m = 0;
    let mut ans = vec![];
    for (i_1, v) in vec.iter().enumerate().rev() {
        let i = i_1 + 1;
        // if i * 2 > vec.len() {
        //     rev_ans.push(vec[i_1]);
        //     if vec[i_1] == 1 {
        //         ans.push(i_1);
        //         m += 1;
        //     }
        // } else {
        let mut sum = 0;
        for j in 1..(vec.len() / i) {
            // eprintln!(
            //     "i:{}, v:{}, rev_ans:{:?}, vec.len:{}, j:{}",
            //     i,
            //     v,
            //     rev_ans,
            //     vec.len(),
            //     j
            // );
            sum += rev_ans[vec.len() - (i * j) - 1];
        }
        if sum % 2 == vec[i_1] {
            rev_ans.push(0);
        } else {
            rev_ans.push(1);
            ans.push(i);
            m += 1;
        }
        // }
    }
    println!("{}", m);
    for v in ans {
        print!("{}", v);
    }
    println!();
}