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: Runtime Error)

import java.util.Scanner;

public class Main {
	static int n;
	static int c = 0;
	static int[] a = new int[100000];
	static int[] b = new int[100000];

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = Integer.parseInt(sc.next());
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sc.next()) % 2 == 0 ? 0 : 1;
		}

		System.out.println();
		if (preparingBoxes()) {
			if (c > 0) {
				System.out.print(b[0]);
				for (int i = 1; i < n; i++) {
					if (b[i] != 0)
						System.out.print(" " + b[i]);
				}
			} else {
				System.out.println("0");
			}
		} else {
			System.out.println("-1");
		}

		sc.close();
	}

	static boolean preparingBoxes() {
		int sum = 0;
		for (int i = n - 1; i >= 0; i--) {
			for (int j = 0; j < n; j++) {
				if ((j + 1) % (i + 1) == 0) {
					sum += b[j];
				}
			}
			if (sum % 2 != a[i]) {
				b[i]++;
				c++;
			}
			sum = 0;
		}
		return true;
	}

}