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: Accepted)


import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final int[] boxes = new int[n];
        final int[] answerChoice = new int[n];

        for (int i = 0; i < n; i++) {
            boxes[i] = scanner.nextInt();
        }

        for (int i = n - 1; i >= 0; i--) {
            if (i > n / 2) {
                answerChoice[i] = boxes[i];
                continue;
            }

            int sum = 0;
            for (int j = 2 * i + 1; j < n; j += i + 1) {
                sum += answerChoice[j];
            }

            if (sum % 2 == boxes[i]) {
                answerChoice[i] = 0;
            } else {
                answerChoice[i] = 1;
            }
        }

        final List<String> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (answerChoice[i] == 1) {
                list.add(Integer.toString(i + 1));
            }
        }

        System.out.println(list.size());
        if (list.size() != 0)
            System.out.println(String.join(" ", list));
    }
}