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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long
int mod = 2019;
int INF = (int)2e18;

signed main() {
    int N;
    cin >> N;
    vector<int> a(N + 1, 0);
    for (int i = 1; i <= N; i++) cin >> a[i];
    vector<vector<int>> equid(200000 + 1, {1});
    for (int i = 2; i <= N; i++) {
        for (int j = i; j <= N; j += i) equid[j].push_back(i);
    }
    vector<int> count(N + 1, 0);
    for (int i = N; i >= 1; i--) {
        if (i > N / 2) {
            if (a[i] == 1) {
                for (int j = 0; j < equid[i].size(); j++) {
                    count[equid[i][j]]++;
                }
            }
        } else {
            if (count[i] % 2 != a[i]) {
                for (int j = 0; j < equid[i].size(); j++) {
                    count[equid[i][j]]++;
                }
            }
        }
    }
    vector<int> ans;
    for (int i = 1; i <= N; i++) {
        if (count[i] % 2 != a[i]) {
            cout << -1 << endl;
            return 0;
        } else {
            if (count[i] % 2 == 1) ans.push_back(i);
        }
    }
    cout << ans.size() << endl;
    for (int i = 0; i < ans.size(); i++) {
        if (i == N - 1) cout << ans[i] << endl;
        else cout << ans[i] << " ";
    }
}