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

namespace ABC134D
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var a = input.NextInt(n);
            var b = new int[n];

            for (int i = n - 1; i >= 0; i--)
            {
                if (a[i] != 0)
                {
                    // 自分の倍数の箱にすでに入っている数の和を求める
                    var sum = 0;
                    for (int j = i; j < n; j += i + 1)
                    {
                        sum += b[j];
                    }

                    if (sum % 2 == 0)
                    {
                        b[i] = 1;
                    }
                }
            }

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

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        /// <summary>
        /// 値を書き換え可能なTuple（ぐらいのイメージ）
        /// </summary>
        public class Pair<T, U> : IComparable<Pair<T, U>>, IEquatable<Pair<T, U>>
            where T : IComparable<T>
            where U : IComparable<U>
        {
            public T V1 { get; set; }
            public U V2 { get; set; }

            public Pair(T v1, U v2)
            {
                this.V1 = v1;
                this.V2 = v2;
            }

            public Pair(Pair<T, U> src) : this(src.V1, src.V2) { }

            public int CompareTo(Pair<T, U> other)
            {
                var r = this.V1.CompareTo(other.V1);
                if (r == 0) r = this.V2.CompareTo(other.V2);

                return r;
            }

            public bool Equals(Pair<T, U> other)
                => (other != null && this.CompareTo(other) == 0);

            public override string ToString()
                => $"{V1} {V2}";

            public override bool Equals(object obj)
                => Equals(obj as Pair<T, U>);

            public override int GetHashCode()
            {
                var hashCode = 1989511945;
                hashCode = hashCode * -1521134295 + V1.GetHashCode();
                hashCode = hashCode * -1521134295 + V2.GetHashCode();
                return hashCode;
            }

            public static bool operator ==(Pair<T, U> a, Pair<T, U> b)
            {
                if (object.ReferenceEquals(a, null))
                {
                    return object.ReferenceEquals(b, null);
                }

                return a.Equals(b);
            }

            public static bool operator !=(Pair<T, U> a, Pair<T, U> b)
                => !(a == b);
            public static bool operator <(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) < 0;
            public static bool operator <=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) <= 0;
            public static bool operator >(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) > 0;
            public static bool operator >=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) >= 0;
        }

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim()
                    .Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    queue.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any()
                => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read())
                {
                    return "";
                }

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                {
                    if (!Read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}