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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        var n = int.Parse(Console.ReadLine());
        int[] aa = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int[] a = new int[n + 1];
        a[0] = 0;
        for (int i = 0; i < aa.Length; i++)
        {
            a[i + 1] = aa[i];
        }

        int[] tmp = new int[n + 1];
        for (int i = a.Length - 1; i > 0; i--)
        {
            var t = 0;
            for (int k = i; k < tmp.Length; k += i)
            {
                t += tmp[k];
            }

            if (a[i] == 1 && t % 2 == 0) tmp[i]++;
            else if (a[i] == 0 && t % 2 == 1) tmp[i]++;
        }

        // for (int i = 0; i < tmp.Length; i++)
        // {
        //     long t = 0;
        //     for (int k = i + 1; k - 1 < tmp.Length; k += (i + 1))
        //     {
        //         t += a[k - 1];
        //     }
        //     if (t % 2 != a[i])
        //     {
        //         var ans = -1;
        //         Console.WriteLine(ans);
        //         return;
        //     }
        //}

        var m = tmp.Where(x => x == 1).Count();
        Console.WriteLine(m);
        for (int i = 1; i < tmp.Length; i++)
        {
            if (tmp[i] == 1) Console.Write(i + " ");
        }
    }
}