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: Time Limit Exceeded)

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];
       int[] B = new int[N+1];
       int cnt=0;
       for(int i = 0; i<N; i++) {
       	A[i] = sc.nextInt();
       }
       
       for(int i = N-1; i>=0; i--) {
    	   if(A[i]==1) {
			   B[cnt]=i+1;
			   cnt++;
    		   for(int j=i;j>=0;j--) {
    			   if((i+1)%(j+1)==0) {
    				   if(A[j]==0) {
    					   A[j]=1;
    				   }else {
    					   A[j]=0;
    				   }
    			   }
    		   }
    	   }
       }
       
       System.out.println(cnt);
       for(int i=0;i<cnt;i++) {
    	   System.out.print(B[i] + " ");
       }
       
   }
}