Problem:
Score : 200 points

Problem Statement

Takahashi loves numbers divisible by 2.

You are given a positive integer N. Among the integers between 1 and N (inclusive), find the one that can be divisible by 2 for the most number of times. The solution is always unique.

Here, the number of times an integer can be divisible by 2, is how many times the integer can be divided by 2 without remainder.

For example,

6 can be divided by 2 once: 6 -> 3.

8 can be divided by 2 three times: 8 -> 4 -> 2 -> 1.

3 can be divided by 2 zero times.

Constraints

1 ≤ N ≤ 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

7

Sample Output 1

4

4 can be divided by 2 twice, which is the most number of times among 1, 2, ..., 7.

Sample Input 2

32

Sample Output 2

32

Sample Input 3

1

Sample Output 3

1

Sample Input 4

100

Sample Output 4

64

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE FlexibleContexts, OverloadedStrings #-}
import Control.Applicative
import Control.Monad
import qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)
import Text.Printf
import Debug.Trace
import Data.List (sort)

f n = length $ takeWhile (\x -> x `mod` 2 == 0) $ iterate (`div`2) n

main = do
  [n] <- getInts
  let xs = sort $ take (n+1) $ iterate (\(x,y)->(f (y+1),y+1)) (0,0)
  print $ snd $ last xs
  
-- util
getInts :: IO [Int]
getInts = map (fst . fromJust . B.readInt) . B.words <$> B.getLine