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;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
			int[] a = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
			int[] b = new int[N];
			List<int> ans = new List<int>();
			for (int i = N - 1; i >= 0; i--) {
				int n = i + 1;
				if (b[i] % 2 != a[i]) {
					ans.Add(n);
					int j = 0, div = 0, mod = 0;
					do {
						j++;
						div = n / j;
						mod = n % j;
						if (mod == 0 && j < div) {
							b[j - 1]++;
							b[div - 1]++;
						}
					} while (j < div);
				}
			}
			Console.WriteLine(ans.Count);
			for (int i = 0; i < ans.Count; i++) {
				if (i > 0) {
					Console.Write(" ");
				}
				Console.Write(ans[i]);
			}
			Console.WriteLine("");
		}
	}
}