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.ArrayList;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn=new Scanner(System.in);
		int n=scn.nextInt();
		ArrayList<Integer> al=new ArrayList<>();
		HashSet<Integer> set =new HashSet<>();
		int []arr=new int[n+1];
		for(int i=1;i<=n;i++) {
			int x=scn.nextInt();
			arr[i]=x;
			if(i>=n/2+1&&arr[i]==1) {
				set.add(i);
			}
		}
		for(int j=n/2+1;j>=1;j--) {
			int sum=0;
			for(int i=2;i<=n/2+1;i++) {
				if(i*j<=n) {
					if(set.contains(i*j))
					sum+=1;
				}else {
					break;
				}
			}
			if((sum%2==0&&arr[j]==1)||(sum%2==1&&arr[j]==0)) {
				set.add(j);
			}
		}
		System.out.println(set.size());
		Iterator<Integer> itr=set.iterator();
		while(itr.hasNext()) {
			System.out.print(itr.next()+" ");
		}
	}

}