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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public class ABC
{
    //          long[] sp = Console.ReadLine().Split().Select(long .Parse).ToArray();
    //          int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
    public static void Main()
    {
        long n = long.Parse(Console.ReadLine());
        long[] A = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long[] stuckBalls = new long[n];
        long[] answer = new long[n];
        for (long i = n - 1; i >= 0; --i)
        {
            long lookingBoxNumber = i + 1;
            // n/i+1 個の影響がある
            long affects = n / lookingBoxNumber;

            if (stuckBalls[i] % 2 != A[i])
            {
                for (long dividing = 1; dividing * dividing <= lookingBoxNumber; ++dividing)
                {
                    if (lookingBoxNumber % dividing == 0)
                    {
                        
                        if (dividing * dividing != lookingBoxNumber)
                        {
                            stuckBalls[dividing - 1]++;
                            stuckBalls[lookingBoxNumber / dividing - 1]++;
                        }
                        else
                        {
                            stuckBalls[dividing - 1]++;
                        }
                    }
                }
            }
            

        }
        for (int i = 0; i < n; i++)
        {
            answer[i] = stuckBalls[i] % 2;
        }
        Console.WriteLine(answer.Sum());
        string output = "";
        for (int i = 0; i < n; i++)
        {
            if (answer[i] == 1) output += (i+1)+" ";
        }
        if (output.Trim() != "")
        {
            Console.WriteLine(output.Trim());
        }
    }




}