Problem:
Score : 100 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq M), the i-th directed edge goes from Vertex x_i to y_i.
G does not contain directed cycles.

Find the length of the longest directed path in G.
Here, the length of a directed path is the number of edges in it.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq x_i, y_i \leq N

All pairs (x_i, y_i) are distinct.

G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the length of the longest directed path in G.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

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

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;  // cannot be used in GCJ
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    public class Program
    {
        public static IO.StreamScanner scanner = new IO.StreamScanner(Console.OpenStandardInput());

        public static void Main()
        {
            var n = scanner.Integer();
            var m = scanner.Integer();
            var paths = new List<Tuple<int, int>>();
            for (int i = 0; i < m; i++)
            {
                paths.Add(new Tuple<int, int>(scanner.Integer(), scanner.Integer()));
            }
            var ans = GetAns(n, m, paths);
            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }

        public static int GetAns(int n, int m, List<Tuple<int, int>> paths)
        {
            var graph = Enumerable.Range(0, n).Select(v => new List<int>()).ToList();
            foreach (var path in paths)
                graph[path.Item1 - 1].Add(path.Item2 - 1);

            var ret = 0;
            for (int i = 0; i < n; i++)
                ret = Math.Max(ret, Dfs(i, graph));

            return ret;
        }

        static Dictionary<int, int> _dict = new Dictionary<int, int>();
        static int Dfs(int idx, List<List<int>> graph)
        {
            if (_dict.ContainsKey(idx)) return _dict[idx];
            var ret = 0;

            foreach(var c in graph[idx])
            {
                ret = Math.Max(ret, Dfs(c, graph) + 1);
            }

            _dict[idx] = ret;
            return ret;
        }
    }


#if DEBUG

    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {

        }

        public static bool IsEq(IEnumerable<IEnumerable<int>> l1, IEnumerable<IEnumerable<int>> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (!IsEq(l1.ElementAt(i), l2.ElementAt(i))) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<int> l1, IEnumerable<int> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i<l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<double> l1, IEnumerable<double> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (!IsEq(l1.ElementAt(i), l2.ElementAt(i))) return false;
            }
            return true;
        }

        public static bool IsEq(IEnumerable<bool> l1, IEnumerable<bool> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i < l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        public static bool IsEq(double a, double b)
        {
            return Math.Abs(a - b) < 1E-5;
        }
    }


#endif

    // Used in LeetCode
    public class TreeNode
    {
        public int val;
        public TreeNode left;
        public TreeNode right;
        public TreeNode(int x) { val = x; }
    }

    public static class LeetCode
    {
        public static TreeNode ParseBinaryTree(string str)
        {
            var ar = str.Replace("[", "").Replace("]", "").Split(',');

            var nodes = new List<TreeNode>();
            for (int i = 0; i < ar.Length; i++)
            {
                nodes.Add(ar[i] == "null" ? null : new TreeNode(int.Parse(ar[i])));
                var parent = (i + 1) / 2 - 1;

                // if the node class parent property
                //if(parent >= 0)
                //{
                //    nodes.Last().Parent = nodes[parent];
                //}
            }

            for (int i = 0; i < nodes.Count(); i++)
            {
                var l = (i + 1) * 2 - 1;
                var r = (i + 1) * 2;
                if (l >= 0 && l < nodes.Count() && nodes[i] != null) nodes[i].left = nodes[l];
                if (r >= 0 && r < nodes.Count() && nodes[i] != null) nodes[i].right = nodes[r];
            }

            return nodes.First();
        }

        public static IList<IList<int>> ParseLLI(string str)
        {
            var ret = new List<IList<int>>();

            var split = str.Split(']');
            foreach (var s in split)
            {
                var v = s.Replace(",[", "").Replace(", [", "").Replace("[", "");
                if (string.IsNullOrWhiteSpace(v))
                {
                    ret.Add(new List<int>());
                    continue;
                }
                ret.Add(v.Split(',').Select(i => int.Parse(i)).ToList());
            }

            return (IList<IList<int>>)ret;
        }

        public static IList<int> ParseLI(string str)
        {
            str = str.Replace("[", "").Replace("]", "");
            return str.Split(',').Select(v => int.Parse(v)).ToList();
        }
    }

    namespace IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;

        public class Printer : StreamWriter
        {
            static Printer()
            {
                Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
            }

            public static Printer Out { get; set; }

            public override IFormatProvider FormatProvider
            {
                get { return CultureInfo.InvariantCulture; }
            }

            public Printer(Stream stream)
                : base(stream, new UTF8Encoding(false, true))
            {
            }

            public Printer(Stream stream, Encoding encoding)
                : base(stream, encoding)
            {
            }

            public void Write<T>(string format, T[] source)
            {
                base.Write(format, source.OfType<object>().ToArray());
            }

            public void WriteLine<T>(string format, T[] source)
            {
                base.WriteLine(format, source.OfType<object>().ToArray());
            }
        }

        public class StreamScanner
        {
            public StreamScanner(Stream stream)
            {
                str = stream;
            }

            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof;

            public bool IsEndOfStream
            {
                get { return isEof; }
            }

            private byte read()
            {
                if (isEof) return 0;
                if (ptr < len) return buf[ptr++];
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
                isEof = true;
                return 0;
            }

            public char Char()
            {
                byte b;
                do b = read(); while ((b < 33 || 126 < b) && !isEof);
                return (char)b;
            }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }

            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }

            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0;
                byte b;
                var ng = false;
                do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-')
                {
                    ng = true;
                    b = read();
                }
                for (; ; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    ret = ret * 10 + b - '0';
                }
            }

            public int Integer()
            {
                return (isEof) ? int.MinValue : (int)Long();
            }

            public double Double()
            {
                var s = Scan();
                return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
            }

            static T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n)
            {
                return enumerate(n, Char);
            }

            public string[] Scan(int n)
            {
                return enumerate(n, Scan);
            }

            public double[] Double(int n)
            {
                return enumerate(n, Double);
            }

            public int[] Integer(int n)
            {
                return enumerate(n, Integer);
            }

            public long[] Long(int n)
            {
                return enumerate(n, Long);
            }
        }
    }
}