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.