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: Time Limit Exceeded)

require 'prime'

class Integer
  # 全ての約数を配列で返す
  def divisor_list
    return [1] if self == 1
    Prime.prime_division(self).map do |d|
      Array.new(d[1] + 1).map.with_index { |element, i| d[0] ** i }
    end.inject { |p, q| p.product(q) }.map do |a|
      [a].flatten.inject(:*)
    end.sort
  end
end

n = gets.to_i
numbers = gets.split(" ").map(&:to_i)
# 箱にボールを入れる時、全ての約数にメモをする
memo = Array.new(n + 1, 0)
answers = []
# 上から順番に箱に入れる
n.downto(1) do |i|
  # 自身の倍数に入れられたボールの数を2で割り、余りが箱に書かれた整数と一致する場合はボールを入れない
  if memo[i] % 2 == numbers[i - 1]
    next
  # 一致しない場合はボールを入れる
  else
    answers << i
    # また、全ての約数にメモをする
    i.divisor_list.each do |divisor|
      memo[divisor] += 1
    end
  end
end
puts answers.size
puts answers.join(" ") if answers.size != 0