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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
  static void Main()
  {
    int N = int.Parse(Console.ReadLine());
    string[] A = ("0 " + Console.ReadLine()).Split(' ');  // 1-indexed に
    var result = new List<int>();
    
    for (int i = N; i >= 1; i--)
    {
      // 後ろから見る
      int a = int.Parse(A[i]);
      int c = 0;
      int i_multiple = i * 2;
      
      // iの倍数の箱にすでに入っている球の数 := c
      while(i_multiple <= N)
      {
        if (result.Contains(i_multiple))
          c++;
        i_multiple += i;
      }
      
      // a と c の偶奇が一致して居ない場合、i の箱に球を入れる
      if ((a + c) % 2 == 1)
        result.Add(i);
    }
    
    Console.WriteLine(result.Count);
    Console.WriteLine(string.Join(" ", result));
    
  }
}