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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(let ((n (read))
      (a (make-array 1 :element-type 'integer
                       :initial-element 0  
                       :adjustable t
                       :fill-pointer 1))
      (ans (make-array 0 :element-type 'integer
                         :adjustable t
                         :fill-pointer 0))
      (ans-c 0))
     (dotimes (i n)
       (vector-push-extend (read) a))
     (loop for i from n downto 1
           do (loop for j from 2 upto n
                    while (<= (* i j) n)
                    do (setf (aref a i) (logxor (aref a i) (aref a (* i j)))))
              (if (= (aref a i) 1) (progn (incf ans-c)
                                          (vector-push-extend i ans))))
     (format t "~A~%" ans-c)
     (if (not (= 0 ans-c)) (format t "~{~A~%~}" (coerce ans 'list))))