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 (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;
use std::collections::HashMap;

fn prime_factorization(mut input: usize) -> Vec<usize> {
  let mut result: HashMap<usize, bool> = HashMap::new();
  let mut val = 2;
  let base_input = input;
  while val * val < base_input {
    if input % val == 0 {
      input /= val;
      result.insert(val, true);
    }
    val += 1;
  }
  result.insert(input, true);
  
  if input != 1 {
    result.insert(1, true);
  }
  
  result.keys().into_iter().map(|v| *v).collect::<Vec<usize>>()
}

fn main() {
  input! {
    n: usize,
    ais: [usize;n]
  }
  let mut result: Vec<usize> = vec![];
  let mut dp: Vec<usize> = vec![0;n+1];
  let mut index = n - 1;
  loop {
    let dp_index = index + 1;
    let primes = prime_factorization(dp_index);
    let val = if dp[dp_index] % 2 != ais[index] {
      result.push(dp_index);
      dp[dp_index] + 1
    } else {
      dp[dp_index]
    };
    
    for v in primes {
      dp[v] += val;
    }
    
    if index == 0 {
      break
    }
    index -= 1;
  }
  
  result.sort();
  println!("{}", result.len());
  if !result.is_empty() {
    println!("{}", result
                    .into_iter()
                    .map(|i| i.to_string())
                    .collect::<Vec<String>>()
                    .join(" ")
    );
  }
}