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: Accepted)

<?php
# 入力
fscanf(STDIN, '%d', $n);
$a = array_merge([0], array_map('intval', explode(" ", trim(fgets(STDIN)))));
$b = [];
$result = [];
for ($i = $n; $i > 0; $i--) {
    $sum = 0;
    for ($j = 2; $i * $j <= $n; $j++) {
        if (isset($b[$i * $j])) {
            $sum++;
        }
    }
    if ($sum % 2 != $a[$i]) {
        $b[$i] = true;
        $result[] = $i;
    }
}
$cnt = count($b);
echo $cnt.PHP_EOL;
if ($cnt > 0) {
    echo implode(" ", $result).PHP_EOL;
}
?>