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;

namespace question4
{
    class Program
    {
        static void Main(string[] args)
        {

            int flag = 1;

            int n = int.Parse(Console.ReadLine());
            string[] str = Console.ReadLine().Split(' ');
            string[] ans = str;
            int half = (n / 2) + 1;

            /*
            for (int i = (n-1); i >=half; i--)
            {
                ans[i] = str[i];
            }
            */
            for (int i = n - 1; i >= 0; i--)
            {
                if (i > (n / 2 - 1))
                {
                    ans[i] = str[i];
                }
                else
                {
                    ans[i] = (int.Parse(str[i]) ^ int.Parse(str[(i + 1) * 2 - 1])).ToString();

                }

            }

            int m = 0;

            string b = "";
            for (int i = 0; i < n; i++)
            {
                if (ans[i] == "1")
                {
                    m += 1;
                    b = b + (i + 1).ToString() + " ";
                }
            }
            /*
            for (int i = 1; i < (n/2+1); i++)
            {
                int delta = (n / i);
                int count = 0;
                for (int j=1;j< (delta+1); j++)
                {
                    count += int.Parse(ans[i * j-1]);

                }
                if (count%2 != int.Parse(str[i-1])) flag = 0;                
            }
            */
            if (flag == 1)
            {
                Console.WriteLine(m);
                Console.WriteLine(b);

            }
            else Console.WriteLine("-1");
            Console.ReadLine();
        }
    }
}