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)

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE BinaryLiterals #-}
{-# LANGUAGE BangPatterns #-}

-- Default Imports

import Control.Monad
import Control.Monad.ST
import Control.Monad.Trans.Class

import qualified Control.Monad.Reader as Reader
import Control.Monad.Reader (Reader, ReaderT, runReader, runReaderT)

import qualified Data.Array.MArray as MArray
import qualified Data.Array.ST as STArray
import Data.Array.ST (STArray, STUArray, runSTArray, runSTUArray)
import Data.Ix (Ix)

import qualified Data.Bits as Bits
import Data.Bits ((.&.), (.|.))

import qualified Data.ByteString.Char8 as BS
import Data.ByteString.Char8 (ByteString)

import qualified Data.Char as Char
import qualified Data.List as List
import qualified Data.Map as Map
import Data.Map (Map)
import qualified Data.Maybe as Maybe

import qualified Data.Vector as Vector
import qualified Data.Vector.Generic as GVector
import qualified Data.Vector.Unboxed as UVector

import Numeric

import Debug.Trace
-- ----------

-- Custom Import Here


-- ----------

-- Default Definitions

type Vector = Vector.Vector
-- type GVector = GVector.Vector
type UVector = UVector.Vector

readIntToList :: ByteString -> [Int]
readIntToList = List.unfoldr (fmap (second $ BS.dropWhile Char.isSpace) . BS.readInt)

readToList :: Read a => ByteString -> [a]
readToList = List.unfoldr $ fmap (mapTaken . mapRemain) . span' (not . Char.isSpace)
	where
		mapTaken  = first $ read . BS.unpack
		mapRemain = second $ BS.dropWhile Char.isSpace
		span' pred s
			| BS.null taken = Nothing
			| otherwise     = Just (taken, remain')
			where
				(taken, remain) = BS.span pred s
				remain' = BS.dropWhile Char.isSpace remain

readToListN :: Read a => Int -> ByteString -> [a]
readToListN n = take n . readToList

readIntToUVector :: ByteString -> UVector.Vector Int
readIntToUVector = UVector.unfoldr (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

readIntToUVectorN :: Int -> ByteString -> UVector.Vector Int
readIntToUVectorN n = UVector.unfoldrN n (fmap stripRemain . BS.readInt)
	where stripRemain = second $ BS.dropWhile Char.isSpace

first :: (a -> a') -> (a, b) -> (a', b)
first f (a, b) = (f a, b)

second :: (b -> b') -> (a, b) -> (a, b')
second f (a, b) = (a, f b)

average :: Fractional a => [a] -> a
average xs = sum xs / (fromIntegral . length) xs

-- ----------

fs :: [Int]
fs = [2 * (5 ^ n) | n <- [1..100], 2 * (5 ^ n) <= 1000000000000000000]

-- dfacto100 :: Int -> Int
-- dfacto100 n
-- 	| n == 0    = 12
-- 	| n < 50    = n `div` 10
-- 	| otherwise = n `div` 10 + 1
--
dfacto :: Int -> Int
dfacto n
	| n `mod` 2 /= 0 = 0
	| otherwise = sum $ map (n `div`) fs

main :: IO ()
main = do
	n <- readLn
	print $ dfacto n