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;

class Program
{
    static List<Tuple<long, int>> f(long n)
    {
        var ans = new List<Tuple<long, int>>();
        for (long i = 2; i * i <= n; i++)
        {
            if (n % i != 0) continue;
            var x = 0;
            while (n % i == 0)
            {
                x++;
                n /= i;
            }
            ans.Add(Tuple.Create(i, x));
        }
        if (n != 1) ans.Add(Tuple.Create(n, 1));
        return ans;
    }

    static void Main(string[] args)
    {
        var n = long.Parse(Console.ReadLine());
        var A = new int[n + 1];
        var s = Console.ReadLine().Split();
        for (int i = 0; i < n; i++) A[i + 1] = int.Parse(s[i]);
        var ans = new int[n + 1];
        var M = 0L;
        for (int i = 1; i <= n; i++)
        {
            var sum = 0;

            foreach (var item in f(i))
            {
                var fst = item.Item1;
                var snd = item.Item2;

                for (int j = 1; j <= snd; j++)
                {
                    sum = (sum + ans[fst * j]) % 2;
                }
            }

            if (A[i] != sum)
            {
                M++;
                ans[i]++;
            }
        }

        Console.WriteLine(M);
        for (int i = 1; i <= n; i++)
        {
            if (ans[i] != 0) Console.Write($"{i} ");
        }
    }
}