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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
 
class Program {
    static List<int>[] Sub;
    static int[] Salary;
    
    
    static void Main(string[] args){
        var N = int.Parse(Console.ReadLine());
        var A  = Console.ReadLine().Split().Select(a => long.Parse(a)).ToArray();
        
        var B = new long[N+1];
        for(int i = (N/2)+1;i <= N;i++){
            B[i] = A[N-1];
        }
        
        
        for(int i = (N/2);i > 0;i--){
           var tmp = i;
           var sum = 0L;
           while(tmp <= N){
               sum += B[tmp];
               tmp *= 2;
           }
           
           if(sum%2 != A[i-1]){
               B[i] = 1;
           }
        }
       var C = new long[N];
       Array.Copy(B, 1, C, 0, B.Length - 1);
       Console.WriteLine(String.Join(" ",C));
    }
         
}