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: Wrong Answer)

<?php

fscanf(STDIN, "%d", $n);

$array = explode(" ", trim(fgets(STDIN)));

$half = intdiv($n, 2);

for($i=$n-1;$i>$half;$i--){

    if($array[$i] == 1){
        $box[$i+1] = $i+1;
    }

}
$short = intdiv($half, 5);
for($i = $half; $i >$short; $i--){
    $check = ($i+1)*2;
    $flag = 0;
    while($check <= $n){
        $flag = ($flag + isset($box[$check])?1:0)%2;
        $check = $check * 2;
    }
    if(($flag && $array[$i] == 0) || !$flag && $array[$i] == 1){
        $box[$i+1] = $i+1;
    }
}

for($i = $short; $i >0; $i--){
    $check = ($i+1);
    $double = $check*2;
    if(isset($box[$double])){
        $flag = 1;
    }else{
        $flag = 0;
    }
    $loop = $check + $double;
    while($loop <= $n){
        $flag = ($flag + isset($box[$loop])?1:0)%2;
        $loop = $loop + $double;
    }
    if(($flag && $array[$i] == 0) || !$flag && $array[$i] == 1){
        $box[$i+1] = $i+1;
    }
}
if(isset($box)) {
    $m = count($box);
}else{
    $m = 0;
    $p = 1;
}
$num = $m % 2;
if($array[0] == 1){
    if($num == 0){
        $box[1] = 1;
        $m++;
    }
}elseif($num == 1){
    $box[1] = 1;
    $m++;
}

echo $m.PHP_EOL;
if($m == 0){
    echo 0;
}else{
    echo implode(" ", $box);
}