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.io.*;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
    static final int MOD = 2;

    public static void main(final String[] args) throws Exception {
        final Scanner sc = new Scanner(System.in);
        int N;
        N = sc.nextInt();
        int[] a = new int[(int)(N)];
        for(int i = 0 ; i < N ; i++){
                a[i] = sc.nextInt();
        }

        final Solver solver = new Solver();
        solver.solve(N, a);
    }
}

class Solver {
    public void solve(int N, int[] a) {
        int[] ans = new int[N];
        List<Integer> balls = new ArrayList<>();
        for (int i = N - 1; i >= 0; i--) {
            int s = sum(N, ans, i) % 2;

            boolean put = s != a[i];
            if (put) {
                ans[i] = 1;
                balls.add(i + 1);
            }
            else {
                ans[i] = 0;
            }
        }

        System.out.println(balls.size());
        System.out.println(
                balls.stream()
                        .map(String::valueOf)
                        .collect(Collectors.joining(" "))
        );
    }

    private int sum(int N, int[] a, int cur) {
        int step = cur + 1;
        int sum = 0;
        for (int i = cur + step; i < N; i+=step) {
            sum = a[i];
        }
        return sum;
    }
}