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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC148.E();
        }

        class ABC148
        {
            public static void A()
            {
                Console.WriteLine(6 / Read.Int() / Read.Int());
            }
            public static void B()
            {
                var N = Read.Int();
                var S = Read.Str();
                var T = Read.Str();
                Console.WriteLine(String.Join("", Enumerable.Range(0, N).Select(i => S[i] + "" + T[i])));
            }
            public static void C()
            {
                var A = Read.Long();
                var B = Read.Long();
                Console.WriteLine(A * B / Util.GCD(A, B));
            }
            public static void D()
            {
                var N = Read.Int();
                var A = Read.IntN();
                int next = 1;
                for(int i = 0; i < N; ++i)
                {
                    if (A[i] == next) { next++; }
                }
                Console.WriteLine(next == 1 ? -1 : N - (next - 1));
            }
            public static void E()
            {
                var N = Read.Long();
                if (N % 2 == 1) { Console.WriteLine(0);return; }
                N /= 2;
                long count = 0;
                while (N > 0)
                {
                    count += N / 5;
                    N /= 5;
                }
                Console.WriteLine(count);
            }
            public static void F()
            {
                var N = Read.Int();
                var u = Read.Int();
                var v = Read.Int();
                var ADJ = Read.AdjacencyList(N, N - 1);
                var distU = Graph.CalcDistance(ADJ, N, u);
                var distV = Graph.CalcDistance(ADJ, N, v);
                int max = 0;
                for(int i = 1; i <= N; ++i)
                {
                    if (distV[i] > distU[i])
                    {
                        max = Math.Max(max, distV[i]);
                    }
                }
                Console.WriteLine(max - 1);
            }
        }
        class Util
        {
            public static long GCD(long a, long b)
            {
                while (b > 0)
                {
                    var c = a % b;
                    a = b;
                    b = c;
                }
                return a;
            }

        }
        class Graph
        {
            public static int[] CalcDistance(Dictionary<int, HashSet<int>> adj, int N, int start)
            {
                var dist = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
                dist[start] = 0;
                Queue<int> queue = new Queue<int>();
                queue.Enqueue(start);
                while (queue.Count > 0)
                {
                    var v = queue.Dequeue();
                    foreach(var w in adj[v])
                    {
                        if (dist[w] < 0)
                        {
                            dist[w] = dist[v] + 1;
                            queue.Enqueue(w);
                        }
                    }
                }
                return dist;
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}