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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Monad
import Control.Monad.ST
import Data.List
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as MV

main = do
    n <- head . unfoldr BS.readInt <$> BS.getLine
    a <- UV.fromList . unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
    let ans = foldl' (\x y -> sub4 y a x) V.empty (reverse [0.. UV.length a - 1])
    if length ans == 0
    then print 0
    else putStrLn $ (unwords . V.toList . V.map show) ans

sub4 :: Int -> UV.Vector Int -> V.Vector Int -> V.Vector Int
sub4 i ls s | ns        = runST $ do
                            s_ <- V.thaw s
                            s_ <- MV.grow s_ 1
                            MV.write s_ (MV.length s_ - 1) (i + 1)
                            V.freeze s_
            | otherwise = s
    where b = ls UV.! i
          ns = V.length (V.filter (\x -> x `mod` (i + 1) == 0) s) `mod` 2 /= b