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
While ($line = fgets(STDIN) ) {
    $a[] = trim($line);
}
$stdin = explode(" ", "0 ".$a[1] );
$ans = array_fill(0, $a[0]+1, 0);

$ans_M = 0;
for($key=$a[0]; $key>0; $key--){
  $sum = 0;
  for($ai=$key; $ai<=$a[0]; $ai+=$key){
    $sum += $ans[$ai];
  }
  if($stdin[$key]==$sum%2){
    $ans[$key]=0;
  }else{
    $ans[$key]=1;
    $ans_M++; 
  }
}

//回答表示
if($ans_M%2 != $stdin[1]){
  echo -1;
}else{
  echo $ans_M,PHP_EOL;
  for($i=1; $i<=$a[0]; $i++){
    if($ans[$i]==1){
      echo $i." ";
    }
  }
}