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 (7.4.4) (judge verdict: Wrong Answer)

<?php

[$N] = fscanf(STDIN, "%d");

$array = fscanf(STDIN, str_repeat("%d", $N));
$half = intdiv($N,2)-1;
$ans = array_fill(0,$N,-1);

for($i=$N;$i>0;$i--){
    $start = intdiv($N, $i) * $i;
    $sum = 0;
    for($j = $start; $j>= $i; $j-=$i){
        if($j === $i){
            $ans[$i-1] = $array[$i-1] ^ $sum;
        }else{
            $sum += $ans[$j-1];
        }
    }
}

$sum = 0;
$list = [];
foreach($ans as $key => $value){
    if($value === 1){
        $sum++;
        $list[] = $key+1;
    }
}

echo $sum.PHP_EOL;
echo implode(" ", $list);