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: Accepted)

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

static class CodeJam
{
    static int[] Solve(int M, int[] B)
    {
        var factors = new int[M];
        var balls = new List<int>();
        for (int i = M; i > 0; --i)
        {
            if (factors[i - 1] % 2 != B[i - 1])
            {
                balls.Add(i);
                for (int j = 1; j * j <= i; ++j)
                {
                    if (j * j == i)
                    {
                        ++factors[j - 1];
                    }
                    else if (i % j == 0)
                    {
                        ++factors[j - 1];
                        ++factors[i / j - 1];
                    }
                }
            }
        }
        return balls.ToArray();
    }

    static void Main(string[] args)
    {
        int M = int.Parse(Console.ReadLine());
        int[] B = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var ans = Solve(M, B);
        if (ans != null)
        {
            Console.WriteLine(ans.Length);
            Console.WriteLine(string.Join(" ", ans));
        }
        else
        {
            Console.WriteLine(-1);
        }
    }
}