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;

namespace abc134_d
{
  class Program
  {
    static void Main(string[] args)
    {
      var n = CIn.ReadInt();
      var a = CIn.ReadIntArray(n);

      var m = 0;
      var b = new List<int>();

      var isPut = new bool[n];

      for (var i = n; i >= 1; i--)
      {
        var mod = false;

        for (var j = i * 2; j <= n; j += i)
        {
          mod ^= isPut[j - 1];
        }

        isPut[i - 1] = a[i - 1] == 1 ^ mod;
      }

      for (var i = 0; i < n; i++)
      {
        if (isPut[i])
        {
          m++;
          b.Add(i + 1);
        }
      }

      Console.WriteLine(m);
      Console.WriteLine(string.Join(" ", b));
    }
  }

  class CIn
  {
    private static readonly Queue<string> fieldBuffer = new Queue<string>();

    public static string Read()
    {
      if (fieldBuffer.Count == 0)
      {
        foreach (var field in Console.ReadLine().Split())
        {
          fieldBuffer.Enqueue(field);
        }
      }

      return fieldBuffer.Dequeue();
    }

    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());

    public static string[] ReadStringArray(long n)
    {
      var array = new string[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = Read();
      }

      return array;
    }

    public static int[] ReadIntArray(long n)
    {
      var array = new int[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadInt();
      }

      return array;
    }

    public static long[] ReadLongArray(long n)
    {
      var array = new long[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadLong();
      }

      return array;
    }
    public static double[] ReadDoubleArray(long n)
    {
      var array = new double[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadDouble();
      }

      return array;
    }
  }
}