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.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();    
    int[] a = new int[N+1];
    for (int i = 1; i <= N; i++) {
      a[i] = sc.nextInt();
    }
    
    int[] box = new int[N+1];
    
    // N -> N/2
    for (int i = N; i > N/2; i--) {
      box[i] = a[i];
    }
    // N/2 -> 1
    for (int i = N/2; i >= 1; i--) {
      int sum = 0;
      int j = 2;
      while (j*i <= N) {
        sum += box[j*i];
        j++;
      }
      if (sum % 2 == a[i]) {
        box[i] = 0;
      } else {
        box[i] = 1;
      }
    }
    
    int M = 0;
    StringBuilder builder = new StringBuilder();
    for (int i = 1; i <= N; i++) {
      if (box[i] == 1) {
        M++;
        builder.append(i).append(' ');
      }
    }
    
    System.out.println(M);
    System.out.println(builder.toString());
 }
}