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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
int a[1000000];
int ret[1000000];
int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int n;
    cin>>n;
    vector<int> vec;
    for (int i=1;i<=n;i++)cin>>a[i];
    for (int i=n;i>=1;i--) {
        int sum = 0;
        for (int j=i;j<=n;j+=i)sum+=ret[j];
        if ((sum%2)!=a[i]){
            ret[i]=1;
            vec.push_back(i);
        }
    }
    for (int i=1;i<=n;i++) {
        int sum = 0;
        for (int j=i;j<=n;j+=i)sum+=ret[j];
        if ((sum%2)!=a[i]) {
            cout<<-1<<endl;
            return 0;
        }
    }
    cout<<vec.size()<<endl;
    for (auto x:vec)cout<<x<<' ';

}