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: Runtime Error)

# describe Abc134D do
#   context 'test' do
#     it 'sample' do
#       expect(Abc134D.calc(3, [1, 0 ,0])).to match([1, [1]])
#       expect(Abc134D.calc(5, [0, 0, 0, 0, 0])).to match([0, []])
#     end
#   end
# end

class Abc134D
  def self.input()
    n = STDIN.gets.to_i
    b_array = STDIN.gets.split(/\s/).map(&:to_i)
    [n, b_array]
  end

  def self.output(m, result_array)
    puts m
    puts result_array.join(' ')
  end

  def self.calc(n, b_array)
    box = b_array
    mod_box = box.map {|x| x % 2}
    m = mod_box.sum
    result_array =
        mod_box
            .map.with_index {|x, i| {index: i + 1, x: x}}
            .select {|o| o[:x] == 1}
            .map {|o| o[:index]}
    [m, result_array]
  end

  def self.main()
    n, b_array = input()
    m, result_array = calc(n, b_array)
    output(m, result_array)
  end
end

if __FILE__ == $0
  Abc134D.main
  exit
end