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: Accepted)

def multiple_factors(i, N):
  factors = []
  for index in range(0, N//i):
    factors.append(int((index+1)*i))
  return factors
  
def assign_ball(factors, blist, ai, b_add_index):
  sum_b = 0
  for index in range(len(factors)-1, 0, -1):
    sum_b += blist[factors[index]-1]
  
  if ai != sum_b%2:
    blist[factors[0]-1] = 1
    b_add_index.append(str(factors[0]))
  return blist, b_add_index

      
N = int(input())
alist = list(map(int, input().split()))
blist = [0 for i in range(N)]
b_add_index = []
for i in range(N-1,-1, -1):
  factors = multiple_factors(i+1, N)
  blist, b_add_index = assign_ball(factors, blist, alist[i], b_add_index)

if sum(blist)%2 != alist[0]:
  print(-1)
else:
  print(len(b_add_index))
  print(" ".join(b_add_index))