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 Ruby (2.3.3) (judge verdict: Wrong Answer)

items = gets.to_i

arry = gets.split(' ').map(&:to_i)

b = nil
arry.each_with_index do |a, idx|
  b = false

  # i 個目の箱
  idx += 1
  target_idx = []
  items.times { |t_idx| target_idx << t_idx if (t_idx + 1) % idx == 0 }

  # if a == 1
  #   valid_arry = target_idx.map { |t_idx| arry[t_idx] if arry[t_idx] == 1 }.compact
  #   sum = valid_arry.reduce(:+)
  #   if sum != nil && sum % 2 == a
  #     puts valid_arry.size
  #     puts valid_arry.each_with_index.map { |_, t_idx| t_idx + 1 }.join(' ') if a == 1
  #     break;
  #   end
  # else
  #   valid_arry = target_idx.map { |t_idx| arry[t_idx] if arry[t_idx] == 0 }.compact
  #   sum = valid_arry.reduce(:+)
  #   if sum != nil && sum % 2 == a
  #     puts 0
  #     break
  #   end
  # end

  valid_arry = target_idx.map { |t_idx| arry[t_idx] if arry[t_idx] == 1 }.compact
  sum = valid_arry.reduce(:+)
  sum = 0 if sum == nil
  if sum % 2 == a
    puts valid_arry.size
    puts valid_arry.each_with_index.map { |_, t_idx| t_idx + 1 }.join(' ') if a == 1
    break;
  end

  b = true
end

puts '-1' if b