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.Collections;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
namespace Collections
{
	class program
	{
		static void Main(string[] args)
		{
			// 入力
			int N = Int32.Parse(Console.ReadLine());
			//string[] input = Console.ReadLine().Split(' ');
			int[] a = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();

			// 大きい方からボールを入れるかどうか決めていく
			int[] box = new int[N+1];
      int num = 0;
			StringBuilder sb = new StringBuilder();
			for(int i=N; i>0; i--)
			{
				// iの倍数の数が1個の場合、input[i-1]が0→入れない 1→入れる
				//Console.WriteLine(i + " " + N/i);
				if(N/i == 1)
				{
					if(a[i-1] == 1)
          {
            	box[i] = 1;
              sb.Append(i+ " ");
              num++;
          }

				}
				else
				{
					// iの倍数の数が2個以上の場合、iの倍数の箱に入っているボールの個数を数える...
					int ball = 0;
					for(int j=i, k=2; j<=N; j = i*k, k++)
					{
						//Console.WriteLine(i + "check " + j + " is " + box[j] );
						ball += box[j];
					}
					if(a[i-1] != ball%2)
          {
            box[i] = 1;
            sb.Append(i+ " ");
            num++;
          }

				}
			}

			Console.WriteLine(num + "");
			if(num > 0)
			{
				Console.WriteLine(sb.ToString());
			}
    }
	}
}