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)

N = int(input())
a = list(map(int, input().split()))
dp = [0] * (N + 1)
for i in range(N, 0, -1):
  #print(i)
  if i > N // 2:
    dp[i] = a[i - 1]
  else:
    j = 3
    dp[i] = dp[2 * i] ^ a[2 * i - 1]
    if i <= N // 3:
      dp[i] = dp[3 * i] ^ a[3 * i - 1]
      if i <= N // 6:
        dp[i] = dp[6 * i] ^ a[6 * i - 1]
      while i * j <= N:
        dp[i] = dp[i] ^ dp[i * j]
        j += 2
        if j % 3 == 0:
          j += 2
    else:
      while i * j <= N:
        dp[i] = dp[i] ^ dp[i * j]
        j += 2
    dp[i] = dp[i] ^ a[i - 1]
M = 0
res2 = ""
#print(dp)
for i, v in enumerate(dp):
  if v == 1:
    M += 1
    res2 += str(i) + " "
print(M)
print(res2)