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 Kotlin (1.0.0) (judge verdict: Accepted)

//DFSテンプレート
fun main(args: Array<String>) {
    val N = nextLong()
    tailrec fun g1(n: Long, p: Long): Long {
        if (n == 0L) return 0
        return (n / p) + g1(n / p, p)
    }
    tailrec fun g2(n: Long, p: Long): Long {
        if (n % 2 == 1L) {
            return g1(n, p) - g2(n - 1, p)
        }
        var res = g1(n / 2, p)
        if (p == 2L) res += n / 2
        return res
    }
    val ans =  Math.min(g2(N,2), g2(N,5))
    println(ans)
}
fun next() = readLine()!!
fun nextLong() = next().toLong()