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: Time Limit Exceeded)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS

readInt = fst . fromJust . BS.readInt
getInt = readInt <$> BS.getLine

main = do
    n <- getInt
    let ns = f n
    let p2 = sum $ map (check 2) ns
    let p5 = sum $ map (check 5) ns
    print $ min p2 p5


f n | n <= 1 = [1]
    | otherwise = n : f (n - 2)

check x n | n `mod` x == 0 = 1 + check x (n `div` x)
          | otherwise = 0