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;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main()
	{
		int N = GetInt();
		int[] a = new int[N + 1];
		for(int i = 1; i <= N; i++)
			a[i] = GetInt();

		long[] sum = new long[N + 1];
		int[] b = new int[N + 1];
		int M = 0;
		for(long i = N; i > 0; i--)
		{
			if(sum[i] % 2 == a[i])
				continue;

			b[i] = 1;
			M++;
			var divisors = getDivisors(i);
			foreach(long divisor in divisors)
				sum[divisor]++;			
		}

		
		Console.WriteLine(M);
		if(M == 0)
			return;

		var sb = new StringBuilder();
		for(int i = 1; i <= N; i++)
			if(b[i] == 1)
				sb.AppendFormat($"{i} ");
		Console.WriteLine(sb);
	}

	private static List<long> getDivisors(long N)
	{
		List<long> divisors = new List<long>();
		
		long floorSqrtN = (long)Math.Sqrt(N);
		for(long i = 1; i < floorSqrtN; i++)
		{
			if(N % i == 0)
			{
				divisors.Add(i);
				divisors.Add(N/i);
			}
		}
		if(floorSqrtN * floorSqrtN == N)
			divisors.Add(floorSqrtN);
		
		return divisors;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}