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.BitSet;
import java.util.Scanner;
import java.util.stream.Collectors;

class Solver {
    void solve(Scanner sc) {
        int N = sc.nextInt();
        BitSet a = new BitSet(N);
        for (int i = 0; i < N; i++) {
            a.set(i, sc.nextInt() == 1);
        }

        BitSet box = new BitSet(N);
        for (int n = N; n > 0; n--) {
            int sum = 0;
            for (int i = n; i < N; i += n) {
                if (box.get(i - 1)) {
                    sum++;
                }
            }
            if ((sum % 2 == 0) == a.get(n - 1)) {
                box.set(n - 1);
            }
        }

        System.out.println(box.cardinality());
        System.out.println(box.stream().map(i -> i + 1).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
    }
}

class Main {
    public static void main(String... args) {
        Scanner in = new Scanner(System.in);

        new Solver().solve(in);

        in.close();
    }
}