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_imports)]
#![allow(non_snake_case)]
use std::io::Read;
use std::io::{stdout, BufWriter, Write};
 
fn main() {
    let mut buf = String::new();
    
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
 
    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();
 
    // 読み込んだStringを空白で分解する
    let mut iter = buf.split_whitespace();
 
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    
    let a : Vec<i64> = (0..n).map(|_|{
        iter.next().unwrap().parse().unwrap()
    }).collect();
    
    const N : usize = 200000;
    let mut buf = [0 ; N];
    
    let mut ball = 0;
    
    let half = n / 2;
    for i in half..n {
        if a[i] == 1 {
            buf[i] = 1;
            ball += 1;
        }
        else if a[i] == 0 {buf[i] = 0;}
        else {
            println!("-1");
            return;
        }
    }
    
    for i in (0..half).rev() {
        let mut sum = 0;
        let index = i + 1;
        
        let mut mul = 2;
        while(mul * index <= n){
            sum += buf[mul * index - 1];
            mul += 1;
        }
        
        if sum % 2 == a[i] {
            buf[i] = 0;
        }else{
            buf[i] = 1;
            ball += 1;
        }
    }
    
    println!("{}", ball);
    for i in 0..n {
        if buf[i] == 1 {
            print!("{} ", i + 1);
        }
    }
    println!(" ");
}