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)

# -*- coding: utf-8 -*-
N=int(input())
a=list(map(int,input().split()))
seta=set()

for i in range(N//2,N):
    if a[i]==1:
        seta.add(i+1)
        
for i in range(3,N+1):
    if N//i+1<N//(i-1):
        for j in range(N//i+1,N//(i-1)+1):
            m=2
            asum=0
            while j*m<=N:
                if j*m in seta:
                    asum=asum+1
                m=m+1
            if asum%2!=a[j-1]:
                seta.add(j)
    else:
        j=N//i+1
        m=2
        asum=0
        while j*m<=N:
            if j*m in seta:
                asum=asum+1
            m=m+1
        if asum%2!=a[j-1]:
            seta.add(j)

asum=0
for n in range(2,N+1):
    if n in seta:
        asum=asum+1
if asum%2!=a[0]:
        seta.add(1)

print(len(seta))
if len(seta)!=0 and len(seta)==1:
    print(list(seta)[0])
elif len(seta)!=0:
    print(" ".join(list(seta)))