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.Linq;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Convert.ToInt32(Console.ReadLine());
            int[] A = Console.ReadLine().Split().Select(i => Convert.ToInt32(i)).ToArray();
            int[] inOrNull = new int[N + 1];
            int middle = N / 2;
            int count = 0;
            // 半分までは即時決定できる
            for (var i = N; i > middle; i--)
            {
                switch (A[i - 1])
                {
                    case 0:
                        inOrNull[i] = 0;
                        break;
                    case 1:
                        inOrNull[i] = 1;
                        count++;
                        break;
                    default:
                        Console.WriteLine(-1);
                        return;
                }
                A[0] -= inOrNull[i];
            }
            for (var i = middle; i > 1; i--)
            {
                int max = N / i * i;
                while (max != i - 1)
                {
                    A[i - 1] -= inOrNull[max];
                    max /= i;
                }
                switch (A[i - 1])
                {
                    case 0:
                        inOrNull[i] = 0;
                        break;
                    case 1:
                        inOrNull[i] = 1;
                        count++;
                        break;
                    default:
                        Console.WriteLine(-1);
                        return;
                }
                A[0] -= inOrNull[i];
            }
            if (A[0] == 0)
            {
                inOrNull[1] = 0;
            }
            else if (A[0] == 1)
            {
                inOrNull[1] = 1;
                count++;
            }
            else
            {
                Console.WriteLine(-1);
                return;
            }
            Console.WriteLine(count);
            for (var i = 0; i < N; i++)
            {
                if (inOrNull[i] == 1)
                    Console.Write($"{i} ");
            }

        }
    }
}