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 main() {
    let n: usize = read();
    let a: Vec<usize> = (0..n).map(|_| read()).collect();

    let mut prime: Vec<usize> = vec![];
    for i in 2..n+1 {
        let mut num = 2;
        let mut check = true;
        while num*num <= i {
            if i % num == 0 {
                check = false;
                break;
            }
            num += 1;
        }
        if check {
            prime.push(i);
        }
    }

    let mut b: Vec<usize> = vec![0; n];
    let mut sum: Vec<usize> = vec![0; n];
    let mut ok = true;
    for i in (0..n).rev() {
        if a[i] < sum[i] {
            ok = false;
            break;
        }
        b[i] = a[i] - sum[i];
        for p in &prime {
            if *p >= i {
                break;
            }
            if (i+1) % *p == 0 {
                sum[*p-1] += b[i];
            }
        }
        sum[0] += b[i];
    }
    if ok {
        let mut cnt = 0;
        for i in 0..n {
            if b[i] > 0 {
                cnt += 1;
            }
        }
        println!("{}", cnt);
        for i in 0..n {
            if b[i] > 0 {
                println!("{}", b[i]);
            }
        }
    } else {
        println!("-1");
    }
}

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