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 <iostream>
using namespace std;

const int MAX_N = 2 * (10 * 10 * 10 * 10 * 10);

int a[MAX_N];
int b[MAX_N];

int main() {
    int N;
    cin >> N;
    for (int i = 0; i < N; ++i) {
        cin >> a[i];
    }
    int non_zero = 0;
    for (int i = N - 1; i >= 0; --i) {
        int a_i = a[i];
        int q = N / (i+1);
        int b_s = 0;
        for (int j = 2; j <= q; j++) {
            b_s += b[(i+1)*j - 1];
        }
        if ((b_s & 0x1) == a_i) {
            b[i] = 0;
        } else {
            b[i] = 1;
            non_zero++;
        }
    }
    cout << non_zero << "\n";
    if (non_zero >= 1) {
        int i;
        for (i = 0; i < N; ++i) {
            int b_i = b[i];
            if (b_i != 0) {
                cout << (i+1);
                break;
            }
        }
        for (; i < N; ++i) {
            int b_i = b[i];
            if (b_i != 0) {
                cout << " " << (i+1);
            }
        }
        cout << "\n";
    }
    return 0;
}