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)

# 後ろから判定してエラトステネスっぽく更新していく

n = int(input())
arr = list(map(int, input().split()))
boxes = [0 for _ in range(n)]

for i in range(n, 0, -1):
    # print("i = {}".format(i))
    tmp = 0
    for j in range(i - 1, n, i):
        # print("j = {}".format(j))
        tmp += arr[j]
        tmp %= 2
    # print("tmp = {}".format(tmp))
    if arr[i - 1] != tmp:
        arr[i - 1] += 1
        arr[i - 1] %= 2
        boxes[i - 1] += 1

ans = list(filter(lambda v: v[1] > 0, enumerate(boxes)))
print(len(ans))
if len(ans) > 0:
    ans = list(map(lambda x: str(x[0] + 1), ans))
    print(" ".join(ans))