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;

public class MainClarss
{
	public const long Giri = 1000000007;
	
	public static void Main(string[] args)
	{
		int n = int.Parse(Console.ReadLine());
		string[] sbs = Input();
		int[] bs = new int[n];
		int[] kekka = new int[n];
		
		for(int i = 0; i < n; i++)
		{
			bs[i] = int.Parse(sbs[i]);
		}
		
		//半分埋める
		int max = n-1;
		int cnt = 0;
		while(max > 0)
		{
			//Console.WriteLine("max"+max);
			for(int i = max; i >= max/2 && i >= 0; i--)
			{
				//Console.WriteLine(i);
				if(i*2>=n)
				{
					//baisuu jyanai
					if(bs[i] == 1)
					{
						kekka[i] = 1;
						cnt++;
					}
				}
				else
				{
					int allwa = 0;
					for(int j = i; j < n; j += Math.Max(1,i))
					{
						allwa = kekka[j] % 2;
					}
					if(allwa != bs[i])
					{
						kekka[i]=1;
						cnt++;
					}
				}
			}
			max = max / 2;
		}
		
		//Console.WriteLine("cnt:"+cnt);
		Console.WriteLine(cnt);
		
		//Console.WriteLine("ppp;"+ppp);
		//Console.WriteLine(ppp);
		
		/////syuituryopku

		StringBuilder strb = new StringBuilder();
		int c = 0;
		for(int i = 0; i < n; i++)
		{
			if(kekka[i]==0)
				continue;
			strb.Append(string.Format("{0} ", i+1));
			c++;
		}
		
		
		Console.WriteLine(strb.ToString().Trim());
	}
	
	public static long GCD(long a, long b)
	{
		if(b == 1)
			return a;
		long p = b / a;
		return GCD(a, b - a*p);
	}
	
	public static string[] Input()
	{
		return Console.ReadLine().Split(' ');
	}

	
	public static int Clamp(int val, int max, int min = 0)
	{
		return Math.Min(max, Math.Max(min, val));
	}

}