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: Time Limit Exceeded)

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <stack>
#include <queue>
#include <set>
#include <map>

using namespace std;

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,a,n) for(int i=a;i<n;i++)

typedef long long ll;

void Main()
{
    int n; cin >> n;
    int a[200010];
    rep(i, n) cin >> a[i + 1];
    int res[200010];
    int cnt = 0;
    for (int i = n; i > 0; --i) {
        int other = 0;
        for (int j = i + 1; j <= n; ++j) {
            if (j % i == 0 && res[j] == 1) {
                ++other;
            }
        }
        if (a[i] == 0) {
            if (other % 2 == 0) {
                res[i] = 0;
            } else {
                res[i] = 1;
                ++cnt;
            }
        } else {
            if (other % 2 == 0) {
                res[i] = 1;
                ++cnt;
            } else {
                res[i] = 0;
            }
        }
    }
    cout << cnt << endl;
    rep(i, n)
    {
        if (res[i + 1] == 1) {
            cout << (i + 1);
            if (i == n - 1) {
                cout << endl;
            } else {
                cout << " ";
            }
        }
    }
}

int main()
{
    cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	Main();
}