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)

#![allow(unused_mut, unused_macros, unused_variables, unused_assignments, non_snake_case, unused_imports, dead_code)]

use std::collections::{HashMap, BinaryHeap, BTreeMap};

// [Rustで競技プログラミングの入力をスッキリ記述するマクロ - Qiita]
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 から拝借
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    // ABC128-C-Switches用に拡張
    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, $t);
        (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    }};
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

// 可愛い可愛い、お手製のライブラリ達
macro_rules! p {
    ($t:expr) => {
        println!("{}", $t);
    };
}
macro_rules! debug {
    ($t:expr) => {
        println!("{:?}", $t);
    };
}
fn gcd(a:usize, b:usize) -> usize {
    if b == 0 {return a};
    gcd(b, a % b)
}
fn lcm(a:usize, b:usize) -> usize {
    a / gcd(a, b) * b
}

use std::cmp::max;

// エントリーポイント
fn main() {
    input! {
        N:usize,
        A:[usize; N],
    }
    let mut numbers = vec![0; N + 1];
    for n in (1..N + 1).rev() {
        let mut xor = 0;
        let mut i = n + n;
        while i <= N {
            xor ^= numbers[i];
            i += n;
        }
        numbers[n] = A[n - 1] ^ xor;
    }
    let mut result = Vec::new();
    for (i, n) in numbers.iter().skip(1).enumerate() {
        if *n == 1usize {result.push(i + 1);}
    }
    p!(result.len());
    for r in result {
        p!(r);
    }
}