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 (2.7.1) (judge verdict: Wrong Answer)

require 'prime'

N=gets.to_i
array=gets.chomp.split(" ").map(&:to_i)

def _divisors(primes, k)
    Enumerator.new do |y|
      if primes.size == k
        y << 1
      else
        p, e = primes[k]
        _divisors(primes, k + 1).each {|d|
          (e + 1).times {|e1|
            y << p ** e1 * d
          }
        }
      end
    end
end
  
def divisors(n)
    _divisors(Prime.prime_division(n), 0).to_a.sort
end

b_array=Array.new(N,0)
N.downto(1) do |i|
    next if array[i-1] == b_array[i-1]

    ds = divisors(i)
    ds.each do |d|
        b_array[d-1] = (b_array[d-1] + 1)%2
    end
end

m = 0
rets = []
b_array.each_with_index do |b,index|
    if b != 0
        m += 1
        rets.push(index+1)
    end
end
puts m
puts rets.join(" ") if m > 0