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[] a = new int[n];
		for(int i=0; i<n; i++){
			a[i] = sc.nextInt();
		}
		
		int[] ans = new int[n];
		for(int i=n-1; 0<=i; i--){
			int j = i;
			int total = 0;
			int count = 2;
			j = (j+1)*count;
			while(j<ans.length-1){
				total += ans[j-1];
				count++;
				j = (j+1)*count;
			}
			if(total%2 == 0){
				if(a[i] == 0) ans[i] = 0;
				else ans[i] = 1;
			} else {
				if(a[i] == 1) ans[i] = 1;
				else ans[i] = 1;
			}
		}
		int ansC = 0;
		List<Integer> ansA = new ArrayList<>();
		for(int i=0; i<ans.length; i++){
			if(ans[i] == 1) {
				ansC++;
				ansA.add(i);
			}
		}
		System.out.println(ansC);
		for(int i: ansA){
			System.out.print((i+1)+" ");
		}

	}
}