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;
using System.Linq;

namespace debug
{
    public static partial class Program
    {
        public static void Main()
        {
            var n = Console.ReadLine().ToLong();
            var ais = Console.ReadLine().ToLongArray();
            var array = new bool[n];
            
            for (var i = n; i > 0; i--)
            {
                var sum = 0;
                var num = 1;
                while (num * i <= n)
                {
                    sum += array[i - 1] ? 1 : 0;
                    num++;
                }

                if (sum % 2 != ais[i - 1])
                {
                    array[i - 1] = true;
                }
            }

            Console.WriteLine(array.Count(x => x));
            if (array.Any(x => x))
            {
                Console.WriteLine(array.Select((x, idx) => new {x, idx}).Where(x => x.x).Select(x => x.idx + 1).JoinToStr());
            }
        }
    }

    public static partial class Program
    {
        //テンプレここから
        private static long GCD(long aaa, long bbb) => bbb == 0 ? aaa : GCD(bbb, aaa % bbb);
        private static long LCM(long aaa, long bbb) => aaa * bbb / GCD(aaa, bbb);
        private static long ToLong(this double ddd) => (long) ddd;
        private static long ToLong(this string str) => long.Parse(str);
        private static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
        private static long[] ToLongArray(this string str, char opr = ' ') => str.Split(opr).ToLong();
        private static long Diff(long aaa, long bbb) => Math.Abs(Math.Max(aaa, bbb) - Math.Min(aaa, bbb));
        private static long Sign(this long iii) => Math.Sign(iii);
        private static bool IsEven(this long iii) => iii % 2 == 0;
        private static readonly int[] Dx = {0, -1, 0, 1};
        private static readonly int[] Dy = {-1, 0, 1, 0};
        public const int MOD = 1000000007;
        public const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const string alphabet = "abcdefghijklmnopqrstuvwxyz";
        public static long ToLong(this char ccc) => ccc.ToString().ToLong();
        public static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);
        public static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);

        public static string JoinToStr(this IEnumerable<long> array, string sep = "")
            => array.Select(xxx => xxx.ToString()).Join(sep);
        public static string JoinToStr(this IEnumerable<int> array, string sep = "")
            => array.Select(xxx => xxx.ToString()).Join(sep);
        
        //テンプレここまで
    }
}