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 Data.Bits
import Data.List
import Control.Monad
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as VM
import Control.Monad.ST

divisor :: Int -> [Int]
divisor n = sub 1
  where
    sub i | i > (ceiling (sqrt $ fromIntegral n)) = []
          | n `mod` i == 0 = i : (n `div` i) : (sub (i+1))
          | otherwise = sub (i+1)

main :: IO ()
main = do
  n <- readLn :: IO Int
  as' <- map read.words <$> getLine :: IO [Int]

  let as = V.fromList as'
      nums = runST $ do
        vec <- VM.replicate n False

        fmap (filter (> 0)) $ forM [n,n-1..1] $ \i -> do
          let ai = as V.! (i-1)
          b <- VM.read vec (i-1)
          if b && ai == 1 || (not b) && ai == 0 then return (-1)
            else do
              forM_ (divisor i) $ \d -> do
                b0 <- VM.read vec (d-1)
                if b0 then VM.write vec (i-1) False else VM.write vec (i-1) True
              return i

  print $ length nums
  forM nums $ \k -> do
    putStr $ (show k) ++ " "
  putStrLn ""