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: Accepted)

# from sys import exit, stderr
# from inspect import currentframe
# def debug(*args):
#     names = {id(v):k for k,v in currentframe().f_back.f_locals.items()}
#     print(', '.join(names.get(id(arg),'???')+' = '+repr(arg) for arg in args), file=stderr)
#     return
N = int(input())
a = [int(_) for _ in input().split()]
b = set()
out = []
n = 0
for i in range(N-1, -1, -1):
    if a[i] == 1:
        out.append(i + 1)
        n += 1
        # print(i+1)
        for f in range(1, int((i+1)**0.5)+1):
            if (i+1)%f == 0:
                a[f-1] = 0 if a[f-1] == 1 else 1
                if f != (i+1)//f and f != 1:
                    a[(i+1)//f-1] = 0 if a[(i+1)//f-1] == 1 else 1
    # debug(a)
print(n)
# print(b)
if len(out) > 0:
    for i in range(len(out)):
        print(out[i], end=" ")
    print()