题目描述
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.
Examples
Input
3
1 0 0
Output
1
1
Input
5
0 0 0 0 0
Output
0
输入格式
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输出格式
见题面