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: Time Limit Exceeded)

import math

N = int(input())
ak = list(map(int, input().split()))
rng_N = range(1,N+1)
li_ball = [0]*N 
s_ans = ''

for i in range(N-1, math.floor(N/2)-1, -1):
    #print(i)
    li_ball[i] = ak[i]
    if ak[i] == 1:
        li_ball[i] = 1
        s_ans += str(i+1)+'\n'
    
#print(li_ball)

for i in range(math.floor(N/2)-1, 0, -1):
    #print(i)
    
    li = [li_ball[r-1] for r in rng_N if r % (i+1) == 0][1:]
    #print(li)
    if sum(li)%2 != ak[i]:
        li_ball[i] = 1
        s_ans += str(i+1)+'\n'
        
    #print(li_ball)
    
if sum(li_ball)%2 != ak[0]:   
    li_ball[0] = 1
    s_ans += '1'
#print(li_ball)

print(sum(li_ball))
print(s_ans)