Problem:
Score : 500 points

Problem Statement

For an integer n not less than 0, let us define f(n) as follows:

f(n) = 1 (if n < 2)

f(n) = n f(n-2) (if n \geq 2)

Given is an integer N. Find the number of trailing zeros in the decimal notation of f(N).

Constraints

0 \leq N \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of trailing zeros in the decimal notation of f(N).

Sample Input 1

12

Sample Output 1

1

f(12) = 12 × 10 × 8 × 6 × 4 × 2 = 46080, which has one trailing zero.

Sample Input 2

5

Sample Output 2

0

f(5) = 5 × 3 × 1 = 15, which has no trailing zeros.

Sample Input 3

1000000000000000000

Sample Output 3

124999999999999995

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

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (unfoldr)

main :: IO ()
main = do
  (n : _) <- map unsafeSignedDecimal . T.words <$> T.getLine :: IO [Int]
  let
    (q, r) = n `divMod` 2
  print $ if r == 0 then f q else 0

f :: Int -> Int
f = sum . unfoldr next
  where
    next k | q == 0 = Nothing
           | otherwise = Just (q, q)
      where
        q = k `div` 5

unsafeSignedDecimal :: T.Text -> Int
unsafeSignedDecimal s = case T.signed T.decimal s of
  Right (n, _) -> n