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.Linq;
using System.Collections.Generic;
using System.Text;

namespace atcoderBeginnerContest134
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Convert.ToInt32(Console.ReadLine());
            int[] A = Console.ReadLine().Split().Select(x => Convert.ToInt32(x)).ToArray();

            bool[] mrk = new bool[N + 1]; 
            int[] balls = new int[N + 1];
            int m = 0;
            for (int i = 1; i <= N; ++i)
            {
                for (int j = i; j <= N; j += i)
                    mrk[j] = true;

                if (mrk[i])
                {
                    if (1 == A[i - 1])
                    {
                        ++m;
                        balls[i] = 1;
                    }
                }else
                if (mrk[i] && A[i - 1] == 1)
                {
                    Console.WriteLine("-1");
                    return;
                }

            }

            Console.WriteLine(m);
            StringBuilder stringBuilder = new StringBuilder();
            for (int i = 1; i <= N; ++i)
                if (balls[i] > 0)
                    stringBuilder.Append(i + " ");
            Console.WriteLine(stringBuilder.ToString());
        }
    }
}