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.util.*;
public class Main {
 public static void main(String args[]) {
	 Scanner sc =new Scanner(System.in);
	 int N = sc.nextInt();
	 int data[]=new int[N+1];
	 int ans[] =new int[N+1];
	 int max =0;
	 int max1=0;
	 int aa=0;
	 ArrayList<Integer> ar =new ArrayList<Integer>();
	 ArrayList<Integer> arans =new ArrayList<Integer>();
	 boolean flag=false;
	 for(int i=1;i<N+1;i++) {
		 data[i]=sc.nextInt();
		 aa +=data[i];
	 }
	 
	 for(int t=1;t<N+1;t++) {
		 if(aa==0||flag==true) break;
		 
	 for(int i=1;i<N+1; i++) {
		 
		 if(i%t==0) {
			 ans[t] += data[i];
			 if(data[i]>0) {
			 ar.add(i);
			 }
		 }
		
		 if(i==N) {
			 if(ans[t]%2==t) {
				 flag=true;
				 max =ans[t];
				 arans.clear();
				 for(int j=0;j<ar.size();j++) {
					 int tt= ar.get(j);
					 arans.add(tt);
					 
				 }
				
				 
			 }
			 ar.clear(); 
		 }
		 
		
	 }
	 }
	 
	 if(aa == 0) {
		 System.out.println( "0");
     }else if(flag==false) {
		 System.out.println("-1");
	 }else {
	 System.out.println(max);
	 for(int i=0;i<arans.size();i++) {
		System.out.println(arans.get(i));
	 }
	 
	 }
		 

	 
 }
}