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)

module Main
  ( main
  )
where

import           Control.Applicative
import           Control.Monad
import           Data.List
import           Data.Array
import           Data.Char
import           Data.Bits
import qualified Data.ByteString.Char8 as BS
import Data.Maybe

parse = fst . fromJust
parseInt = parse . BS.readInt
parseInteger = parse . BS.readInteger
readInt = parseInt <$> BS.getLine
readInteger = parseInteger <$> BS.getLine
readIntList = map parseInt . BS.words <$> BS.getLine

main = do
  n <- readInteger
  print $ if n `mod` 2 == 1 then 0 else count n 10 5

count n d m
  | n < d = 0
  | otherwise = n `div` d + count n (d * m) m