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.chomp.to_i
alist = gets.chomp.split.collect{ |item| item.to_i}
ballList = Array.new(n)
result = Array.new()
n.times do |ni|
  ballList[ni] = 0
end
def set_ball(zo,ni,ballList,n)
  data_r = 0
  data_b = 0
  if ((ni+1)*2) > n
    data_r = zo
    data_b = zo
  else
    
    if ballList[2*(ni+1)-1] == zo
      data_r = 0
      data_b = zo
    else
      data_r = 1
      data_b = zo == 1 ? 0 : 1
    end
  end
  return data_r,data_b
end

(n-1).downto(0) do |ni|
  zeroOne = alist[ni]
  data_r,data_b = set_ball(zeroOne,ni,ballList,n)
  ballList[ni] = data_b
  result.unshift(ni+1) if (data_r == 1)
end


  puts result.size
  puts result.join(" ")