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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var scanner = bufio.NewScanner(os.Stdin)

func nextLine() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	i, e := strconv.Atoi(nextLine())
	if e != nil {
		panic(e)
	}
	return i
}

func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		num = nextInt()
		nums = append(nums, num)
	}
	return
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func sumSlice(nums []int) int {
	sum := 0
	for _, n := range nums {
		sum += n
	}
	return sum
}

func binarySearch(target int, list []int) int {
	left := 0
	right := len(list) - 1
	mid := (left + right) / 2

	for {
		if list[mid] < target {
			left = mid + 1
		} else {
			right = mid
		}
		mid = (left + right) / 2
		if left >= right {
			break
		}
	}
	return mid
}

func main() {
	scanner.Split(bufio.ScanWords) // switch to separating by space
	// scanner.Buffer([]byte{}, 1000000009) // switch to read large size input
	N := nextInt()
	v := 2
	count := 0

	for N > v {
		v *= 5
		count += N / v
	}

	if N%2 == 1 {
		count = 0
	}

	fmt.Println(count)
}