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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Silviase
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    Scanner in = new Scanner(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    ABC134DPreparingBoxes solver = new ABC134DPreparingBoxes();
    solver.solve(1, in, out);
    out.close();
  }

  static class ABC134DPreparingBoxes {

    public void solve(int testNumber, Scanner in, PrintWriter out) {
      int n = in.nextInt();
      boolean[] bool = new boolean[n];
      int[] array = new int[n];
      int cnt = 0;
      ArrayList<Integer> al = new ArrayList<>();
      for (int i = 0; i < n; i++) {
        bool[i] = false;
        array[i] = in.nextInt();
      }

      for (int i = n - 1; i >= 0; i--) {
        int tmpcnt = 0;
        for (int j = i * 2; j < n; j++) {
          if (bool[j]) {
            tmpcnt = (tmpcnt + 1) % 2;
          }
        }
        if (tmpcnt != array[i]) {
          bool[i] = true;
        }
      }

      for (int i = 0; i < n; i++) {
        if (bool[i]) {
          cnt++;
          al.add(i + 1);
        }
      }
      out.println(cnt);
      for (int i = 0; i < al.size(); i++) {
        out.println(al.get(i));
      }
    }

  }
}