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;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
            int[] A = new int[N];
            string[] str = Console.ReadLine().Split(' ');
            for(int i = 0; i < N; i++)
            {
                A[i] = int.Parse(str[i]);
            }
            int M = 0;
            int[] TMP = new int[N];
            int[] B = new int[N];

            for(int i = N; i > 0; i--)
            {
                int j = 1,count = 0;
                while (i*j <= N)
                {
                    if (B[i*j -1] == 1) count++;
                    j++;
                }
                if ((count + A[i - 1]) % 2 == 0) B[i - 1] = 0;
                else
                {
                    TMP[M] = i;
                    M++;
                    B[i - 1] = 1;
                }
            }

            Console.WriteLine(M);
            //for (int i = 0; i < M - 1; i++) Console.Write($"{B[i]} ");
            for (int i = 0; i < M - 1; i++) Console.Write($"{TMP[i]} ");
            if(M > 0) Console.WriteLine(TMP[M - 1]);
            Console.ReadLine();

		}
	}
}