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: Accepted)

#require 'pp'

n = gets.chomp!.to_i
a_n = gets.chomp!.split(" ").map(&:to_i)
a_n.unshift(-1)

memo = {}
1.upto(n) do |i|
    memo[i] = -1
end

n.downto(1) do |baisu|
    x = baisu
    count = 0
    while x <= n
        if memo[x] == 1
            count += 1
        end
        x += baisu
    end
    
    if count % 2 == 0
        memo[baisu] = a_n[baisu]
    else
        memo[baisu] = (a_n[baisu] + 1) % 2
    end
    #pp count
    #pp memo
end

sum = 0
answer = []
memo.each do |k, v|
    if v == 1
        sum += 1
        answer << k
    end
end

puts sum
answer_str = answer.join(" ")
if answer_str != ""
    puts answer_str
end