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 Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
a_list = list(map(int, input().split()))

a_count = len(a_list)

boll_list = [0] * n

for rev_index, a in enumerate(reversed(a_list)):
    index = a_count - rev_index - 1
    if (a + 1) * 2 > a_count:
        boll_list[index] = a_list[index]
    else:
        divide_max = a_count // (index + 1)
        total = 0
        for i in range(divide_max):
            total += boll_list[i]
        total = total % 2
        if a_list[index] != total:
            boll_list[index] = 1

if (1 in boll_list):
    output_list = []
    for index, i in enumerate(boll_list):
        if i == 1:
            output_list.append(str(index + 1))
    print(' '.join(output_list))
else:
    print('0')