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: Wrong Answer)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

N = int(input())
a = list(map(int, input().split()))

# N = 6
# a =  [0, 0, 0, 1, 0, 1]
# ans: [1,    3, 4,    6]

# N = 6
# a =  [1, 1, 0, 1, 0, 1]
# ans: [1, 2, 3, 4,    6]

b = [0 for _ in range(N)]


for i in range(N - 1, 0 , -1):
    # i は 5 から 1 までイテレートする
    # print('i', i)
    # print('a', a[::i][1:])
    # print('b', b[i::i+1])
    # print("")
    if (sum(a[::i][1:]) + sum(b[i::i+1])) % 2 == 0:
        b[i] = 0
    else:
        b[i] = 1

if a[0] == 0:
    b[0] = (sum(b[1:])) % 2
else:
    # print('kotti', sum(b[1:]))
    b[0] = (sum(b[1:]) + 1) % 2

# print('a', a)
# print('b', b)

s = sum(b)
print(s)
if s != 0:
    # print(*b[:last_index(b, 1) + 1])
    print(*[x + 1 for x in range(N) if 0 < b[x]])