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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        String nStr = Long.toString(n);
        long result = 0; // nが奇数の時は常に0個
        if(n%2 == 0) {
            // 途中に出てくる10の倍数の数字の、末尾の0の個数の合計
            int len = nStr.length();
            long[] dp = new long[len+1];
            dp[0] = 0;
            // 10の位の数字から見始める
            for(int i=1; i<len; i++) {
                int digit = Integer.parseInt(nStr.substring(len-i-1, len-i));
                result += digit*dp[i-1] + digit * i;
                dp[i] = (dp[i-1]*10) + (9*i);
            }
        }
        System.out.println(result);
    }
}