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.Scanner;
public class Main {
	
	static int []cnt;
	static int []a;
	static ArrayList<Integer>ans;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = Integer.parseInt(sc.next());
		
		a = new int [n];
		cnt = new int [n];
		
		for(int i = 0 ;i < n ;i++) {
			a[i] = Integer.parseInt(sc.next());
		}
		
		ans = new ArrayList<Integer>();
		
		for(int i = n-1 ; i >= 0 ;i--) {
			if(cnt[i] % 2 != a[i] ) {
				gcd(n,i+1);
				ans.add(i+1);
			}
		}
		
			System.out.println(ans.size());
			for(int i = 0 ;i < ans.size() ;i++) {
				System.out.println(ans.get(i));
			}
		}
	
	
	static void gcd(int n,int k) {
		for(int i = 2; k * i <= n ;i++) {
			if(cnt[k*i-1]%2 != a[k*i-1]) {
				cnt[k*i-1]++;
				if(!ans.contains(k*i)) {
				ans.add(k*i);
				}
			}
		}
	}

}