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

namespace AtCoder
{
    public class MainClass
    {
        public static void Main(string[] args)
        {
            if (args.Length > 0 && args[0] == "debug")
            {
                var inputs = new[] { @"
3
1 0 0
				", @"
5
0 0 0 0 0
				", @"

				", @"

				" };

                foreach (var str in inputs)
                {
                    var text = str.Trim();
                    if (text.Length == 0) continue;
                    var reader = new System.IO.StringReader(text);
                    Console.SetIn(reader);
                    Main2(args);
                    Console.WriteLine();
                    Console.WriteLine("----------------------------------");
                    Console.WriteLine();
                }
            }
            else
                Main2(args);
        }

        public static void Main2(string[] args)
        {
            checked
            {
                var N = int.Parse(Console.ReadLine());
                var A = Console.ReadLine().Split(' ')
                   .Select(byte.Parse)
                   .ToList();

                var boxes = new BitArray(N);

                for (int i = N - 1; i >= 0; --i)
                {
                    int count = 0;
                    for (int j = (i + 1) * 2 - 1; j < N; j += i + 1)
                    {
                        if (boxes[j]) ++count;
                    }

                    if ((count % 2) != A[i]) boxes[i] = true;
                }

                var res = new List<int>();
                for (int i = 0; i < N; i++)
                {
                    if (boxes[i]) res.Add(i + 1);
                }

                Console.WriteLine(res.Count);
                Console.WriteLine(res.MkString());
            }
        }

    }

    public static class EnumerablePlus
    {
        ///<summary>出力文字列に変換。</summary>
        public static string MkString<T>(this IEnumerable<T> list)
        {
            return list.Aggregate(
                new System.Text.StringBuilder(),
                (a, b) => ((a.Length > 0) ? a.Append(' ') : a).Append(b)
                ).ToString();
        }

        ///<summary>添字付きfor。</summary>
        public static void ForEach<T>(this IEnumerable<T> list, Action<T, int> a)
        {
            int i = 0;
            foreach (var item in list)
            {
                a(item, i);
            }
        }

        ///<summary>指定回数デリゲートを呼び出す。</summary>
        public static IEnumerable<T> Repeat<T>(int n, Func<T> f)
        {
            for (int i = 0; i < n; i++)
            {
                yield return f();
            }
        }
    }

    public static class MathPlus
    {
        ///<summary>約数。順番は不定。</summary>
        public static List<long> Divisor(long n)
        {
            var list = Prime(n).
                GroupBy(id => id).
                Select(pair => new { prime = pair.Key, power = pair.Count() }).
                ToList();

            var result = list.Aggregate(new List<long>(), (left, pair) =>
            {
                var list2 = Enumerable.
                    Range(0, pair.power + 1).
                    Aggregate(new List<long>(), (res, l) =>
                    {
                        var next = res.Count > 0 ? res.Last() * pair.prime : 1L;
                        res.Add(next);
                        return res;
                    });

                if (left.Count == 0) return list2.ToList();

                return list2.
                    SelectMany(l => left.Select(m => l * m)).
                    ToList();
            });

            return result;
        }

        ///<summary>順列の数。</summary>
        public static long Permutation(long n, long r)
            => Factorial(n, r);

        ///<summary>組合せの数。</summary>
        public static long Combination(long n, long r)
        {
            if (r == 0) return 1;

            return Factorial(n, r) / Factorial(r);
        }

        ///<summary>階乗。カウントも指定可能。</summary>
        public static long Factorial(long a, long count = long.MaxValue)
        {
            long res = 1;

            for (long i = 0; a > 0 && i < count; i++)
            {
                checked { res *= a; }
                --a;
            }

            return res;
        }

        ///<summary>素因数分解。昇順。</summary>
        public static List<long> Prime(long a)
        {
            var res = new List<long>();

            for (long b = 2, c = (long)Math.Ceiling(Math.Sqrt(a)); b <= c; ++b)
            {
                while (a % b == 0)
                {
                    res.Add(b);
                    a = a / b;
                }
            }

            return res;
        }

        ///<summary>最小公倍数。</summary>
        public static long Lcm(IEnumerable<long> list)
        {
            return list.Aggregate((a, b) => Lcm(a, b));
        }

        ///<summary>最小公倍数。</summary>
        public static long Lcm(long a, long b)
        {
            return checked(a * b) / Gcd(a, b);
        }

        ///<summary>最大公約数。</summary>
        public static long Gcd(IEnumerable<long> list)
        {
            return list.Aggregate((a, b) => Gcd(a, b));
        }

        ///<summary>最大公約数。</summary>
        public static long Gcd(long a, long b)
        {
            if (a < b)
                Gcd(b, a);

            while (b != 0)
            {
                var rem = a % b;
                a = b;
                b = rem;
            }

            return a;
        }
    }
}