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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int m = cin.Int();
			var to = Helper.List(n, x => new List<int>());
			var from = Helper.List(n, x => new List<int>());
			for (int i = 0; i < m; i++) {
				int x = cin.Int() - 1;
				int y = cin.Int() - 1;
				to[x].Add(y);
				from[y].Add(x);
			}

			var d = Helper.Array(n, x => 0);
			var q = new Queue<Edge>();
			for (int i = 0; i < n; i++) {
				if (from[i].Count == 0) {
					q.Enqueue(new Edge { V = i, D = 0 });
				}
			}

			while (q.Count > 0) {
				var cur = q.Dequeue();
				if (d[cur.V] > cur.D) {
					continue;
				}

				foreach (int next in to[cur.V]) {
					if (d[next] < cur.D + 1) {
						d[next] = cur.D + 1;
						q.Enqueue(new Edge { V = next, D = cur.D + 1 });
					}
				}
			}

			int ans = d.Max();
			Console.WriteLine(ans);
		}

		struct Edge
		{
			public int V { get; set; }
			public int D { get; set; }
		}
	}

	public static class Helper
	{
		public static void UpdateMin32<T>(T array, int index, int value) where T : IList<int>
			=> array[index] = Math.Min(array[index], value);
		public static void UpdateMax32<T>(T array, int index, int value) where T : IList<int>
			=> array[index] = Math.Max(array[index], value);
		public static void UpdateMin64<T>(T array, int index, long value) where T : IList<long>
			=> array[index] = Math.Min(array[index], value);
		public static void UpdateMax64<T>(T array, int index, long value) where T : IList<long>
			=> array[index] = Math.Max(array[index], value);

		public static T[] Array<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToArray();
		public static List<T> List<T>(int n, Func<int, T> init)
			=> Enumerable.Range(0, n).Select(x => init(x)).ToList();
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}