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)

# ABC 134 D - Preparing Boxes
# https://atcoder.jp/contests/abc134/tasks/abc134_d

n = gets.chomp.to_i
a = gets.chomp.split(/ /).map(&:to_i)

class Box
  def initialize(a, index, balls_count)
    @a = a
    @index = index
    @balls_count = balls_count
  end

  attr_reader :a, :index
  attr_accessor :balls_count
  # setter checked : Bool
end

boxes = a.map.with_index { |element, i| Box.new(element, i + 1, 0) }
boxes.reverse.each_cons(2) do |boxes|
  box_large, box_small = boxes
  box_large.balls_count = (box_large.a == box_small.a ? 0 : 1)
end

balls_count_all = boxes.map(&:balls_count)
balls_count_sum = balls_count_all.reduce(0) { |acc,i| acc + i}

if (balls_count_sum.even? && boxes.first.a == 0) || (balls_count_sum.odd? && boxes.first.a == 1)
  puts balls_count_all.select(&:positive?).size
  boxes_not_empty = boxes.select { |box| box.balls_count.positive? }
  if !boxes_not_empty.empty?
    puts boxes_not_empty.map(&:index).join(' ')
  end
else
  puts "-1"
end