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: Runtime Error)


import numpy as np
n = int(input())
a = np.array(list(map(int, input().strip().split())))

b = np.zeros((n))




from numpy.linalg import solve

c = np.zeros((n,n))
for i in range(n):

    j = 1
    while (i+1) * j <= n:
        c[i][(i+1) * j-1] = 1
        j += 1

#print(c)
b = solve(c,a)
#print(b)

'''
for i in range(n):
    b[i] = a[i]

#print(b)

if n % 2 == 0:
    p = int(np.ceil(n/2))
else:
    p = int(np.ceil(n/2)-1)
#print(p)

for i in reversed(range(p+1)):
    for j in reversed(range(1,int(n/(i+1)))):
        #print(i,j)
        b[i] -= b[(i+1)*(j+1)-1]

'''


b = b.astype(int)

#print(b)

flag = True
for i in range(n):
    if b[i] < 0:
        flag = False
        break

if flag:
    print(str(b).replace('[','').replace(']','').replace(' 0',''))

else:
    print(-1)