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)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let n: usize = read_as_vec()[0];
    let a: Vec<i32> = read_as_vec();
    
    //if status[i] == true, we put a ball into ith box
    let mut status: Vec<bool> = vec![false;n];

    for i in (0..n).rev(){
        //println!("i = {}, a[i] = {}", i, a[i]);
        //let mut sum = status.iter().enumerate().skip(i)
        //    .step_by(i+1).filter(|x| (x.0+1)%(i+1) == 0 && *x.1).count();
        let mut sum = 0;

        let step = i+1;
        let mut j = i;
        while j < n{
            if status[j]{
                sum += 1;
            }
            j += step;
        }
        
        if (sum%2 == 0 && a[i] == 1) || (sum%2 == 1 && a[i] == 0){
            status[i] = true;
        }
        //println!("{:?}", status);
    }
    let num_balls = status.iter().filter(|x| **x == true).count();
    println!("{}", num_balls);
    
    if num_balls == 0{
        return;
    }
    
    for (i, is_ball) in status.iter().enumerate(){
        if *is_ball{
            print!("{} ", i+1);
        }
    }
    println!("");
}