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 PHP (5.6.30) (judge verdict: Accepted)

<?php  
  fscanf(STDIN,"%d",$n);
  $input = preg_split("/ /",trim(fgets(STDIN)));
  $flag = 0;
  for($i=1;$i<=$n;$i++){
    $a[$i] = $input[$i-1];
    $box[$i] = ceil($n/$i);
  }
  for($i=$n;$i>=1;$i--){
    if($box[$i]==1){
      $b[$i]=$a[$i];
    }else{
      $count = 0;
      for($j=$i*$box[$i];$j>=$i;$j=$j-$i){
        if($b[$j]==1){
          $count++;
        }
      }
      if($count%2==$a[$i]){
        $b[$i]=0;
      }else{
        $b[$i]=1;
      }
    }
  }
  $m = 0;
  $ans = array(0);
  for($i=1;$i<=$n;$i++){
    if($b[$i]==1){
      $m++;
      array_push($ans,$i);
    }
  }

  echo($m."\n");
  if($m>0){
    for($i=1;$i<=$m;$i++){
      echo($ans[$i]." ");
    }
  }