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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  
fscanf(STDIN, "%d", $qua);
$a = explode(" ", trim(fgets(STDIN)));
$boolean_result = True;
for ($i = 0; $i < 2 ** $qua; $i++){
  $binary = decbin($i);
  $binary = str_pad($binary, $qua, 0, STR_PAD_LEFT);
  $binary_array = str_split($binary);
  //毎回$boolean_resultをTrueに戻す。
  $boolean_result = True;
  $boolean = True;
  for ($k = 1; $k <= $qua; $k++){
    $sum = 0;
    for ($l = $k; $l <= $qua; $l += $k){
      $sum += $binary_array[$l - 1];
    }
    // $aの中身はstringなので、!==ではなく、!=
    if($sum % 2 != $a[$k - 1]){
      $boolean = False;
      break;
    }
  }
  //以上で条件を満たすかどうか判定終了。条件を満たす場合、次のif構文内で入れ方を出力。
  //満たさない場合、変数$boolean_resultにFalseを格納。
  if($boolean){
    $sum_in = 0;
    for ($k = 0; $k < $qua; $k++){
      $sum_in += $binary_array[$k];
    }
    echo $sum_in."\n";
    $bool_space = False;
    for ($k = 0; $k < $qua; $k++){
      if ($binary_array[$k] == 1 and $bool_space === True){
        echo " ".($k + 1);
      }
      if ($binary_array[$k] == 1 and $bool_space === False){
        echo $k + 1;
        $bool_space = True;
      }
    }
    echo "\n";
    break;
  } else {
    $boolean_result = False;
  }
}
if ($boolean_result === False) {
  echo -1;
}