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)

						//		package Dynamic;
import java.io.*;
import java.util.*;
class Main
{
    static public void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//        int t=Integer.parseInt(br.readLine());
//        while(t-->0)
//        {
        	int n=Integer.parseInt(br.readLine());
        	int ar[]=new int[n];
        	StringTokenizer st=new StringTokenizer(br.readLine());
        	//TreeSet<Integer> tt=new TreeSet<>();
        	int i=0;
        	HashSet<Integer> h=new HashSet<>();
        	while(i<n)
        	{
        		ar[i]=Integer.parseInt(st.nextToken());
        		if(ar[i]==1)
        			h.add(i+1);
        		i++;
        	}
        	if(h.size()>1)
        	{
        		System.out.println("-1");
        		System.exit(0);
        	}
        	HashSet<Integer> hh=new HashSet<>();
        	int ff=0;
        	o:
        	for(int x=1;x<=n;x++)
        	{
        		if(ar[x-1]==1)
        		{
        			int c=0;
        			
        			for(int y=x;y<=n;y+=x)
        			{
        				if(h.contains(y))
        				{
        					c++;
        					hh.add(y);
        				}
        				if(c==2)
        				{
        					ff++;break o;
        				}
        			}
        		}
        		else
        		{
        			
        			for(int y=x;y<=n;y+=x)
        			{
        				if(h.contains(y))
        				{
        					ff++;
        					break o;
        				}
        			}
        		}
        	}
        	if(ff!=0)
        		System.out.println("-1");
        	else
        	{
        		System.out.println(hh.size());
        		for(int xx:hh)
        			System.out.print(xx+" ");
        	}
        		
    }
}