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 Data.Array.IO
import Data.Bits
import Data.List
import Debug.Trace

main = do
    n <- read <$> getLine
    a <- map read <$> words <$> getLine
    a <- newListArray (1, n) a
    r <- solve n a
    r <- getElems r
    putStrLn $ show $ length r
    putStrLn $ intercalate " " $ map show $ r

solve :: Int -> IOArray Int Int -> IO (IOArray Int Int)
solve n a = do
    forM_ [n, n - 1 .. 1] $ \i -> do
        b <- readArray a i
        let s = (floor . sqrt . fromIntegral) i
        forM_ [1 .. s] $ \j -> do
            if i /= 1 && i `mod` j == 0 then do
                c <- readArray a j
                writeArray a j (b `xor` c)
                if j /= 1 && (j /= s || i /= s * s) then do
                    c <- readArray a (i `div` j)
                    writeArray a (i `div` j) (b `xor` c)
                else return ()
            else return ()
    return a