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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static int LoadInt() { return int.Parse(Console.ReadLine()); }
        static int[] LoadIntArray() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray(); }

        static void Main(string[] args)
        {
            var N = LoadInt();
            var array = LoadIntArray();
            var flag = new int[N];
            // ケツから決める（N/2までは決定的）
            for(var i=N-1; i>=N/2; i--)
            {
                flag[i] = array[i];
            }
            for(var i=N/2-1; i>=0; i--)
            {
                var tmp = 0;
                for(var j=i; j<N; j+=i+1)
                {
                    tmp += flag[j];
                }
                if((tmp%2 == 0 && array[i]==1) || (tmp%2==1 && array[i]==0))
                {
                    flag[i] = 1;
                }
            }
            var result = Enumerable.Range(0, N).Where(x => flag[x] == 1).Select(x => x + 1).ToList();
            Console.WriteLine(result.Count);
            if (result.Count > 0)
            {
                Console.WriteLine(string.Join(" ", result));
            }
        }
    }
}