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)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.List (unfoldr)
import Control.Monad
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as BS

solve :: Int -> U.Vector Int -> U.Vector Int
solve !n v = U.create $ do
  result <- UM.replicate (n + 1) 0
  forM_ [n,n-1..1] $ \i -> do
    s <- sumM [ UM.read result j | j <- [2*i..n] ]
    UM.write result i ((s + v U.! (i-1)) `rem` 2)
  return result

main = do
  n <- readLn
  xs <- U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let result = U.filter (\(i,v) -> v > 0) $ U.indexed $ solve n xs
  print $ U.length result
  U.forM_ result $ \(i,_) -> print i

sumM :: (Monad m, Num a) => [m a] -> m a
sumM = foldM (\s a -> (s +) <$> a) 0