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.*;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.awt.Point;


public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] a = new int[n+1];
        //int[] b = new int[n];
        String[] s = br.readLine().split(" ");
        List<Integer> nums = new ArrayList();
        
        for (int i = 0; i < n; i++) {
            a[i+1] = Integer.parseInt(s[i]);
        }
        
        for (int i = n/2+1; i <= n; i++) {
            if (a[i] == 1) {
                nums.add(i);
            }
        }
        
        //Arrays.sort(b);
        int x = 0;
        for (int i = n/2; i >= 1; i--) {
            x = 0;
            for (int num:nums) {
                if (num%i == 0) x++;
            }
            if (x%2==1) {
                if (a[i] == 1) continue;
                else {
                    System.out.println(-1);
                    return;
                }
            }
            else {
                //System.out.println("bbbbb");
                if (a[i] == 1) {
                    nums.add(i);
                    continue;
                }
                else {
                    continue;
                }
                
            }
        }
        
        System.out.println(nums.size());
        for (int i = 0; i < nums.size(); i++) {
            System.out.print(nums.get(i));
            if (i == nums.size()-1) System.out.printf("\n");
        }
        
    }

    
}