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;

class Program
{
    static int N;
    static int[] A;
    static int[] anser;

    static void Main(string[] args)
    {
         N = GetInputInt();
         A = GetInputsInt();
         anser = new int[N+1];

        List<int> aList = new List<int>();

        int n2 = N / 2 +1;
        for (int i = N; i >= n2; i--)
        {
            anser[i] = A[i-1];
            if (anser[i] == 1) aList.Add(i);
        }
        for (int i = n2-1; i > 0; i--)
        {
            anser[i] = A[i-1];

            int total = anser[i];
            int numTotal = i * 2;

            while(numTotal <= N)
            {
                total += anser[numTotal];
                numTotal += i;
            }
            if(anser[i] == total % 2)
            {
               if (anser[i] == 1) aList.Add(i);
            }
            else
            {
                Console.WriteLine(-1);
                return;
            }
        }

        Console.WriteLine(aList.Count);
        if (aList.Count > 0) {
            for (int i = 0; i < aList.Count-1; i++)
            {
                Console.Write(aList[i] + " ");
            }
            Console.Write(aList[aList.Count-1]);
        }
        Console.ReadKey();
    }

    

    public static int GetInputInt()
    {
        return int.Parse(Console.ReadLine());
    }
    public static int[] GetInputsInt()
    {
        return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    }
    public static List<int> GetInputsIntList()
    {
        return Console.ReadLine().Split(' ').Select(int.Parse).ToList();
    }
    public static long[] GetInputsLong()
    {
        return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
    }

}