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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCorder
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }
        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var a = cin.ReadIntArray(N);
            int[] b = new int[N];
            for(int i = 0; i < N; i++)
            {
                b[i] = 0;
            }
            var sum = 0;
            for(int i = N; i > (N+ 1) / 2; i--)
            {
                if(a[i-1] == 0)
                {
                    b[i-1] = 0;
                    for (int j = 1; j <= (N + 1) / 2; j++)
                    {
                        if (i % j == 0)
                        {
                            b[j - 1] = 0;
                        }
                    }
                }
                else
                {
                    b[i-1] = 1;
                    for (int j = 1; j <= (N+1) / 2; j++)
                    {
                        if (i % j == 0)
                        {
                            b[j - 1] = 1;
                        }
                    }
                }
            }
            for(int i = (N+1)/2; i > 0; i--)
            {
                if (a[i - 1] == 0)
                {
                    b[i - 1] = 0;
                    for (int j = 1; j <= (i+1)/2; j++)
                    {
                        if (i % j == 0)
                        {
                            b[j - 1] = 0;
                        }
                    }
                }
                else
                {
                    b[i - 1] = 1;
                    for (int j = 1; j <= (i + 1) / 2; j++)
                    {
                        if (i % j == 0)
                        {
                            b[j - 1] = 1;
                        }
                    }
                }
            }
            for(int i = 0; i < N; i++)
            {
                if(b[i] == 1)
                {
                    sum++;
                }
            }
            WriteLine(sum);
            for(int i = 0; i < N; i++)
            {
                if (b[i] == 1)
                {
                    WriteLine(i+1);
                }
            }
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}