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::io::*;

const SP: u8 = b' ';
const LF: u8 = b'\n';

struct CharacterInput<'a> {
    locked_stdin: StdinLock<'a>,
    bytes_buffer: Vec<u8>,
}

impl<'a> CharacterInput<'a> {
    fn read(&mut self, delimiter: u8) -> &[u8] {
        self.bytes_buffer.clear();

        let mut len = self
            .locked_stdin
            .read_until(delimiter, &mut self.bytes_buffer)
            .unwrap();

        if len > 0 {
            len -= 1;
        }

        &self.bytes_buffer[0..len]
    }

    fn scan_u(&mut self, delimiter: u8) -> u32 {
        self.read(delimiter)
            .into_iter()
            .fold(0, |accumulator, byte| {
                (byte - b'0') as u32 + accumulator * 10
            })
    }

    fn scan_u_vec(&mut self, n: usize, separator: u8, delimiter: u8) -> Vec<u32> {
        let mut vector = Vec::with_capacity(n as usize);
        for _i in 0..n - 1 {
            vector.push(self.scan_u(separator));
        }
        vector.push(self.scan_u(delimiter));
        vector
    }

    fn scan_u_pair(&mut self, separator: u8, delimiter: u8) -> (u32, u32) {
        (self.scan_u(separator), self.scan_u(delimiter))
    }

    fn scan_u_triple(&mut self, separator: u8, delimiter: u8) -> (u32, u32, u32) {
        (
            self.scan_u(separator),
            self.scan_u(separator),
            self.scan_u(delimiter),
        )
    }

    fn scan_s(&mut self, delimiter: u8) -> &str {
        unsafe { std::str::from_utf8_unchecked(self.read(delimiter)) }
    }

    fn scan_i(&mut self, delimiter: u8) -> i32 {
        self.scan_s(delimiter).parse().unwrap()
    }
}

fn create_cin<'a>(input: StdinLock<'a>, buffer_capacity: usize) -> CharacterInput {
    CharacterInput {
        locked_stdin: input,
        bytes_buffer: Vec::with_capacity(buffer_capacity),
    }
}

struct CharacterOutput {
    string_buffer: String,
}

impl CharacterOutput {
    fn push_s(&mut self, s: &str) {
        self.string_buffer += s;
    }

    fn add_s(&mut self, s: &str, separator: char) {
        self.push_s(s);
        self.string_buffer.push(separator);
    }

    fn push<T: ToString>(&mut self, n: T) {
        self.push_s(&n.to_string());
    }

    fn add<T: ToString>(&mut self, n: T, separator: char) {
        self.push(n);
        self.string_buffer.push(separator);
    }

    fn add_from_iterator<T: ToString, I>(
        &mut self,
        iterator: &mut I,
        length: usize,
        separator: char,
        delimiter: char,
    ) where
        I: Iterator<Item = T>,
    {
        for element in iterator.by_ref().take(length - 1) {
            self.add(element, separator);
        }
        self.add(iterator.next().unwrap(), delimiter);
    }

    fn flush(&mut self) {
        let out = stdout();
        let mut out = out.lock();
        out.write_all(self.string_buffer.as_bytes()).unwrap();
        self.string_buffer.clear();
    }
}

fn create_cout(capacity: usize) -> CharacterOutput {
    CharacterOutput {
        string_buffer: String::with_capacity(capacity),
    }
}

// easy
fn println<T: std::string::ToString>(s: T) {
    println!("{}", s.to_string());
}

fn print_from_iterator<T: ToString, I>(
    iterator: &mut I,
    length: usize,
    separator: &str,
    buffer_capacity: usize
) where
    I: Iterator<Item = T>,
{
    println!(
        "{}",
        iterator
            .map(|e| e.to_string())
            .collect::<Vec<String>>()
            .join(separator),
    );
}

// ------------------------------------------------------------------------

trait Parity {
    fn is_even(self) -> bool;
    fn is_odd(self) -> bool;
    fn has_same_parity<T: Parity>(self, other: T) -> bool;
}

macro_rules! impl_parity {
    ($($t:ty),+) => {
        $(impl Parity for $t {
            fn is_even(self) -> bool {
                self & 1 == 0
            }
            fn is_odd(self) -> bool {
                self & 1 == 1
            }
            fn has_same_parity<T: Parity>(self, other: T) -> bool {
                self.is_even() == other.is_even()
            }
        })+
    }
}

impl_parity!(u32);

// ------------------------------------------------------------------------

fn main() {
    let cin = stdin();
    let cin = &mut create_cin(cin.lock(), 16);

    let n = cin.scan_u(LF) as usize;
    let a = cin.scan_u_vec(n, SP, LF);

    let mut ball:Vec<u32> = vec!(0; n);
    let mut box_num_list = Vec::<usize>::new();

    for i in (0..n).rev() {
        let mut k = i;
        let mut acc = ball[k];
        k += i + 1;
        while k < n {
            acc += ball[k];
            k += i + 1;
        }

        if !acc.has_same_parity(a[i]) {
            ball[i] = 1;
            box_num_list.push(i + 1);
        }
    }

    let cout = &mut create_cout(0);

    if box_num_list.len() == 0 {
        cout.add(0, '\n');
    } else {
        cout.add(box_num_list.len(), '\n');
        cout.add_from_iterator(&mut box_num_list.iter(), box_num_list.len(), ' ', '\n');
    }

    cout.flush();
}