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
m = -1
if n == 0 then
  puts "#{m}"
else
  m = 0
  a = gets.chomp.split(" ").map(&:to_i)
  if a.max == 0 then
    puts "#{m}"
  else
    b = Hash.new
    (1..a.length).reverse_each do |i|
      div = a.length / i
      if div > 1 then
        sum = i.step(a.length, i).inject(0) {|r, j| r + a[j-1]}
        if (sum % 2) == 1 then
          b[i] = 1
        end
      elsif div == 1 then
        if a[i-1] == 1 then
          b[i] = a[i-1]
        end
      end  
    end
    keys = ""
    b.keys.each do |k|
      keys += " " if keys != ""
      keys += k.to_s
    end
    puts keys
    values = ""
    b.values.each do |v|
      values += " " if values != ""
      values += v.to_s
    end
    puts values
  end
end