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.Text;
using System.Collections.Generic;
using System.ComponentModel;
using System.Linq;
using System.Threading.Tasks;
using System.IO;

class Solve
{
	const int mod = 1000000007;
	static void Main(string[] args)
	{
		var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
		Console.SetOut(sw);

		int N = int.Parse(Console.ReadLine());
		var A = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

		int[] ball = new int[N];


		for (int i = N; i >= 1; i--)
		{
			int sum = 0;
			int num = 1;
			while (num * i <= N)
			{
				if (ball[num * i - 1] == 1)
				{
					sum++;
				}
				num++;
			}
			if (sum % 2 == A[i - 1])
			{
				ball[i - 1] = 0;

			}
			else { ball[i - 1] = 1; }
		}
		int bsum = 0;
		for (int i = 0; i < N; i++)
		{
			bsum += ball[i];
		}
		if (bsum == 0) { Console.WriteLine(0); }
		else
		{
			Console.WriteLine(bsum);
			for (int i = 0; i < N; i++)
			{
				if (ball[i] == 1)
				{
					Console.Write(i + 1 + " ");
				}
			}
		}


		Console.Out.Flush();
	}
}