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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.math.*;
public class Main {
    public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter ou = new PrintWriter(System.out);
		int n = Integer.parseInt(sc.next());
		boolean[] a = new boolean[n];
		Arrays.fill(a , false);
		for(int i = 0 ; i < n ; i++) if(Integer.parseInt(sc.next()) == 1) a[i] = true;
		boolean[] q = new boolean[n];
		Arrays.fill(q , false);
		int yono;
		for(int i = n - 1 ; i >= 0 ; i--){
			yono = 0;
			for(int j = i ; j < n ; j += i + 1){
				if(q[j]) yono++;
			}
			if(yono % 2 == 1) a[i] = true;
		}
		yono = 0;
		for(int i = 0 ; i < n ; i++) if(a[i]) yono++;
		ou.println(yono);
		if(yono != 0){
			yono = 0;
			for(int i = 0 ; i < n && a[i]; i++){
				if(yono == 0){
					ou.print(i + 1);
					yono++;
				}else ou.print(" " + (i + 1));
			}
			ou.println();
		}
		ou.flush();
	}
}