p02972 AtCoder Beginner Contest 134 - Preparing Boxes
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.

Examples

Input

3
1 0 0


Output

1
1


Input

5
0 0 0 0 0


Output

0
```python
N = int(input())
A = list(map(int, input().split()))
B = [0]*(N+1)
x = []
 
for n in range(N):
  i = N-n
  BB = B[::i]
  if (sum(BB))%2 == A[i-1]:
    B[i] = 0
  else:
    B[i] = 1
    x.append(str(i))
  
print(len(x))
print(' '.join(x))
```