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: Accepted)

#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <utility>
#include <string>

using namespace std;

int main() {
	int n;
	cin >> n;

	vector<int> a(n+1, 0);
	for (int i = 1; i <= n; i++) {
		cin >> a[i];
	}

	vector<int> ball(n+1, 0);
	vector<int> ans;
	for (int i = n; i >= 1; i--) {
		if (ball[i] % 2 == a[i]) {
			continue;
		}

		ans.emplace_back(i);
		for (int j = 1; j * j <= i; j++) {
			if (i % j == 0) {
				ball[j]++;
				if (j * j != i) {
					ball[i/j]++;
				}
			}
		}
	}

	cout << ans.size() << endl;
	for (int i = 0; i < ans.size(); i++) {
		if (i != 0) {
			cout << " ";
		}
		cout << ans[i];
	}
	cout << endl;
	return 0;
}