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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.PrintWriter;
import java.util.*;

public class Main {
    PrintWriter out = new PrintWriter(System.out);
    final long mod = 1000000000+7;
    ArrayList<Integer>[] tree;
    long ans = 1;
    int n,k;
    public static void main(String[] args) {
        Main main = new Main();
        System.out.println(main.solve());
    }
    long solve(){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n+1], b = new int[n+1];
        for(int i=1;i<=n;i++) a[i]=sc.nextInt();
        for(int i=n;i>=1;i--){
            int sum = 0;
            for(int j=2*i;j<=n;j+=i) sum += b[i];
            if(sum%2!=a[i]) b[i] = 1; // otherwise no need to change status quo
        }
        List<Integer> ans = new LinkedList<>();
        for(int i=1;i<=n;i++){
            if(b[i]>0) ans.add(i);
        }
        out.println(ans.size());
        for(int i:ans){
            out.print(String.format("%d ",i));
        }
        out.flush();
        System.exit(0);
        return -1;
    }
}