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;

namespace ConsoleApp_CS
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = CIn.ReadLong();
            var a = CIn.ReadIntArray(n);
            var b = new List<long>();
            var m = 0;

            for (var i = n - 1; i >= 0; i--)
            {
                if (a[i] > 0)
                {
                    var t = n / a[i];
                    var s = (long)0;
                    for (var j = 1; j < t; j++)
                    {
                        s += a[n - (a[i] * j)];
                    }
                    if (s / 2 != a[i])
                    {
                        m++;
                        b.Add(i + 1);
                    }
                }
            }
            b.Sort();
            Console.WriteLine(m);
            foreach (var item in b)
            {
                Console.Write("{0} ", item);
            }
            Console.WriteLine();

        }
    }

        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;
            }
        }
    }