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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import math


def is_prime(n):
    if n == 1:
        return 1, 1

    for k in range(2, int(math.sqrt(n)) + 1, 2):
        if n % k == 0:
            return k, n // k

    return 1, n


N = int(input())
A = list(map(int, input().split()))
B = [0] * N

for i in range(N - 1, 1, -1):
    a = A[i]
    b = B[i]
    B[i] = (b % 2) ^ a

    p, q = is_prime(i + 1)
    B[p - 1] += b + B[i]
    B[q - 1] += b + B[i]


B[0] = A[0] ^ (sum(B) % 2)


S = []
for i, b in enumerate(B):
    if b == 1:
        S.append(str(i + 1))

if len(S) == 0:
    print(0)
else:
    print(len(S))
    print(' '.join(S))