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: Runtime Error)

#include <iostream>
#include <string>
#include <fstream>
#include <vector>
#include <algorithm>
#include <utility>
#include <set>
#include <queue>
#include <map>
#include <cmath>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;

int main() {

    
    int n;
    cin >> n;
    vector<int> a(n);
    
    for (int i = 0; i < n; ++i)
    {
        cin >> a[i];
    }
    
    vector<vector<int>> div(1e5 + 1, vector<int>());
    
    for (int i = 1; i <= 1e5; ++i)
    {
        for (int j = i; j <= 1e5; j += i)
        {
            div[i].push_back(j);
        }
    }
    vector<int> ans(n + 1, 0);
    vector<int> ret;
    
    for (int i = n; i >= 1; --i)
    {
        int sum = 0;
        for (int j = 0; j < div[i].size(); ++j)
        {
            if (div[i][j] == i || div[i][j] > n)
            {
                break;
            }
            sum += ans[div[i][j]];
        }
        sum %= 2;
        if ((sum == 1 && a[i - 1] == 1) || (sum == 0 && a[i - 1] == 0))
        {
            ans[i] = 0;
        }
        else
        {
            ans[i] = 1;
            ret.push_back(i);
        }
    }
    
    sort(ret.begin(), ret.end());
    cout << ret.size() << endl;
    for (int i = 0; i < ret.size(); ++i)
    {
        if (i == ret.size() - 1)
        {
            cout << ret[i] << endl;
            break;
        }
        cout << ret[i] << " ";
    }
    
    return 0;
}