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;
using System.Collections.Generic;
namespace Collections
{
	class program
	{
		static int[] box;
		static int N;
		static string[] input;
		static List<HashSet<int>> div;
		static void Main(string[] args)
		{
			// 入力
			//string[] input = Console.ReadLine().Split(' '); // N, a
			N = Int32.Parse(Console.ReadLine());
			input = Console.ReadLine().Split(' ');

			// 1~Nの約数リストを作る
			div = new List<HashSet<int>>();
			div.Add(new HashSet<int>());
			div.Add(new HashSet<int>());
			div.Add(new HashSet<int>());//1,2,3は約数がないので先に作る
			for(int i=4; i<=N; i++)
			{
				div.Add(getDiv(i));
			}

			// 大きい方からボールを入れるかどうか決めていく
			box = new int[N+1];
			for(int i=N; i>0; i--)
			{
			//Console.WriteLine(i + "のはこの中身は "+ box[i] + " aiは " + input[i-1] );
				if(box[i]%2 == Int32.Parse(input[i-1]))
				{
					//box[i] = box[i]%2;
					box[i] = 0;
				}
				else
				{
					//box[i] = (box[i] + 1)%2;
					box[i] = 1;
				}
				// i以下の約数のボックスにボールを一つずつ入れていく
				// ボールを入れた場合
				if(box[i] == 1)
				{
					HashSet<int> d = div[i-1];
					// 1には必ず入れる
					box[1] += 1;
					foreach(var a in d)
					{
						box[a] += 1;
					}
				}
			}
			int num = 0;
			string ret = "";
			for(int i=1; i<=N; i++)
			{
				if(box[i]==1)
				{
					num ++;
					ret += i + " ";
				}
			}

			Console.WriteLine(num + "");
			if(num > 0)
			{
				Console.WriteLine(ret);
			}
    }
		static HashSet<int> getDiv(int i)
		{
			// iの約数を列挙する
			HashSet<int> ret = new HashSet<int>();
			for(int d = 2; d<=i/2; d++)
			{
				if(i%d==0)
				{
					// 初めて割り切れた時
					List<int> p = new List<int>(div[i/d-1]);
					// 例えば24/2 = 12
					// "2"+ "12" + 12の約数リストをまるっとコピー + 各要素に*2したものが約数のリストになる・・・はず
					ret.Add(d);
					ret.Add(i/d);
					for(int j=0; j<p.Count; j++)
					{
							ret.Add(p[j]);
							ret.Add(p[j]*d);
					}
					break;
				}
			}

			return ret;
		}
	}
}