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;
using System.Text;
using System.Threading.Tasks;

    class Program_D
    {
        static bool[] ans;
        static int N;
        static bool Solve(bool[] a, int s)
        {
            // check
            bool check = true;
            for (var idx = 1; idx <= N; idx++)
            {
                bool n = false;
                for (var idx2 = idx; idx2 <= N; idx2 += idx)
                {
                    n ^= a[idx2];
                }

                if (a[idx] != n) 
                {
                    check = false;
                    break;
                }
            }
            if (check)
            {
                ans = new bool[N+1];
                a.CopyTo(ans, 0);
                return true;
            }

            for ( var idx = s + 1; idx <= N; idx++)
            {
                if (a[idx]) continue;
                var aa = new bool[N+1];
                a.CopyTo(aa, 0);
                aa[idx] = true;
                if (Solve(aa, idx)) return true;
            }

            return false;
        }
        static void Main(string[] args)
        {

            N = Int32.Parse(Console.ReadLine());
            var a = new bool[N+1];
            var aaa = Console.ReadLine().Split(' ');
            for (var i = 0; i < N; i++)
            {
                a[i+1] = aaa[i] == "1";
            }

            if (!Solve(a, 1))
            {
                Console.WriteLine(-1);
                return;
            }


            var nn = ans.Count(__ => __);
            Console.WriteLine(nn);
            var sb = new StringBuilder();
            for (var i = 0; i <= N; i++)
            {
                if (!ans[i]) continue;

                if (sb.Length > 0) sb.Append(" ");
                sb.Append(i);
            }
            Console.WriteLine(sb.ToString());

        }
    }