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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Deque;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());

		String str[] = br.readLine().split(" ");
		int a[] = new int[n + 1];

		for (int i = 0; i < n; i++) {
			a[i + 1] = Integer.parseInt(str[i]);
		}

		int dp[] = new int[n + 10];

		ArrayList<Integer> list = new ArrayList<>();
		for (int i = n; i >= 1; i--) {
			int sum = 0;
			for (int j = i; j <= n; j += i) {
				sum += dp[j];
			}
			if (sum % 2 != a[i]) {
				dp[i]++;
				list.add(i);
			}
		}

		Collections.sort(list);

		System.out.println(list.size());
		if (list.size() != 0) {
			System.out.print(list.get(0));
			for (int i = 1; i < list.size(); i++) {
				System.out.print(" " + list.get(i));
			}
			System.out.println();
		}
	}

	public static final ArrayList<Integer> divisor(final int n) {
		final ArrayList<Integer> list = new ArrayList<>();

		for (int i = 1; i * i <= n; i++) { // √n
			if (n % i == 0) {
				list.add(i); // a x b
				if (i != n / i) {
					list.add(n / i); // b x a (逆向き)
				}
			}
		}
		return list;
	}
}