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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);

		int N = Integer.parseInt(in.readLine());
		String[] tokens = in.readLine().split(" ");
		int[] a = new int[N];
		for (int i = 0; i < N; ++i) {
			a[i] = Integer.parseInt(tokens[i]);
		}
		int[] b = new int[N];
		Arrays.fill(b, 0);

		for (int i = N - 1; i >= 0; --i) {
			int count = 0;
			for (int j = 2; j * (i + 1) <= N; ++j) {
				count += a[j * (i + 1) - 1];
			}
			if (count == a[i]) {
				b[i] = 0;
			} else {
				b[i] = 1;
			}
		}
		List<Integer> indexes = new ArrayList<>();
		for (int i = 0; i < N; ++i) {
			if (b[i] > 0) {
				indexes.add(i + 1);
			}
		}
		System.out.println(indexes.size());
		if (indexes.size() > 0) {
			StringBuilder strBuilder = new StringBuilder();
			strBuilder.append(Integer.toString(indexes.get(0)));
			for (int i = 1; i < indexes.size(); ++i) {
				strBuilder.append(" " + (indexes.get(i)));
			}
			System.out.println(strBuilder.toString());
		}

	}
}