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.*;
class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int N=sc.nextInt();
		int[] A=new int[N+1];
		A[0]=0;
		for(int i=1;i<=N;i++){
			A[i]=sc.nextInt();
		}
		int[] dp=new int[N+1];
		
		if(A[N]==0){
			dp[N]=0;
		}else{
			dp[N]=1;
		}
		
		for(int i=N-1;i>=1;i--){
			int sum=0;
			for(int j=i+1;j<=N;j++){
				if(j%i==0&&dp[j]==1)
				sum++;
			}
			if(sum%2==A[i]){
				dp[i]=0;
			}else{
				dp[i]=1;
			}
		}
		int count=0;
		for(int i=1;i<=N;i++){
			if(dp[i]==1)
				count++;
		}
		
		if(count==0){
			System.out.println(0);
			System.out.println(0);
		}else{
			System.out.println(count);
			for(int i=1;i<=count;i++){
				if(dp[i]==1){
					System.out.print(i);
					System.out.print(" ");
				}
			}
		}
	}
}