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; 
using E = System.Linq.Enumerable; 

class Program { 
     const long beki = 1000000007;
     static void Main(string[] args) {
     //入力を受け取る 
    var N = int.Parse(Console.ReadLine()); 
     int[] A = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
     int[] B = new int[N+1];
     int[] ANS = new int[N];
     for(int i = 0; i < N ;i++){
         B[i+1] = A[i];
     }
     var M = 0;
     
     //N^2logN→間に合わなくないか？
     //logN回の繰り返し
     for(int i = 1;Math.Pow(2,i-1) <=N;i++){
         int waru = (int) Math.Pow(2,i-1);
         int start = N/waru;
         int end   = start/2;
         //最大でもN/2回
         for(int j = start;j > end;j--){
             //倍数の累積和をとる
             var cumusum = 0;
             //N/i回繰り返すつまり最大でN回
             for(int k = i;k > 1;k--){
                 cumusum += B[k*j];
             }
             //累積和との差に応じてボールを入れるかどうかを調べる
             if(cumusum%2 !=(B[j]+cumusum)%2){
                 M ++;
                 ANS[j-1] = 1;
             }else{
                 ANS[j-1] = 0;
             }
         }
     }
     
     
     if(M==0|| M==-1){
         Console.WriteLine(-1);
     }else{
         Console.WriteLine(-1);
     }
     
       }
      
     }