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)

N = gets.to_i
a = gets.split.map(&:to_i)

box = Array.new(N, 0)

a.reverse[0..(N - 2)].each_with_index do |an, i|
  b = N - i

  v = 0
  (b * 2).step(N, b) do |j|
    v += box[j - 1]
  end

  if an == 1 && v.even?
    box[b - 1] = 1
  elsif an == 0 && v.odd?
    box[b - 1] = 1
  end
end

v = box.inject(:+)

if v == 0 && a[0] == 0
  puts 0
  exit
end

if v.odd?
  if a[0] == 0
    box[0] = 1
    v += 1
  else
    puts '-1'
    exit
  end
else
  if a[0] == 1
    box[0] = 1
    v += 1
  else
    puts '-1'
    exit
  end
end

p v

result = []
box.each_with_index do |d, i|
  result << i + 1 if d == 1
end

puts result.join(' ')