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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
using namespace std;

int main() {

    int n;

    cin >> n;

    vector<int> v(n + 1);

    vector<int> ans(n + 1, 0);

    for(int i = 1; i <= n; ++i)
        cin >> v[i];

    bool isTrue = true;

    for(int i = n; i >= 0; --i) {

        if(i > n / 2 && v[i]) {
            ans[i] = v[i];
            for(int j = 1; j * j < i; ++j)
                if(i % j == 0)
                    ans[j] ^= 1;
                
        }
        else {
            ans[i] = v[i] ^ ans[i];
            for(int j = 1; j * j < i; ++j) 
                    if(i % j == 0) 
                        ans[j] ^= ans[i];
              
        }

   }

    if(isTrue) {
        int count = 0;
        for(int i = 1; i <= n; ++i)
            count += ans[i];
        cout << count << endl;
        for(int i = 1; i <= n; ++i)
            if(ans[i] == 1)
                cout << i << " ";
        if(count)
            cout << endl;
    }
    else {
        cout << -1 << endl;
    }

    return 0;

}