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 (3.8.2) (judge verdict: Wrong Answer)

# 1からNまでの数字それぞれの約数を求める
# Nから(大きい値から)見ていき、1であれば入れる
# 数字iを入れた場合、iの約数の数を+1
# それぞれの数はdictで保持する

N = int(input())
A = list(map(int, input().split()))

def divisor(n):
    i = 1
    table = []
    while i * i <= n:
        if n%i == 0:
            table.append(i)
            table.append(n//i)
        i += 1
    table = list(set(table))
    table.sort()
    return table

dic = {}
ans = [0 for _ in range(N)]
for i in range(N):
    tmp = N - i
    if tmp in dic:
        if dic[tmp] % 2 != A[tmp-1]:
            dic[tmp] += 1
            ans[tmp - 1] = 1

    else:
        if A[tmp-1] == 1:
            dic[tmp] = 1
            ans[tmp - 1] = 1
        else:
            dic[tmp] = 0

print(sum(ans))
for i in range(N):
    if ans[i] == 1:
        print(i + 1)