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)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class G
{
	public static void Main()
	{
		(new Solver()).Solve();
	}
}


public class Solver
{
	private int N;
	private int M;
	private List<int>[] adj;
	private int[] memo;

	public Solver()
	{
		N = GetInt();
		M = GetInt();
		adj = Enumerable.Range(0, N).Select(_ => new List<int>()).ToArray();
		for(int i = 0; i < M; i++)
		{
			int x = GetInt() - 1;
			int y = GetInt() - 1;
			adj[x].Add(y);
		}
		memo = Enumerable.Repeat(-1, N).ToArray();
	}

	public void Solve()
	{
		Console.WriteLine(Enumerable.Range(0, N).Select(x => rec(x)).Max());
	}

	private int rec(int v)
	{
		if(memo[v] != -1)
			return memo[v];

		int max = -1;
		foreach(int u in adj[v])
			max = Math.Max(max, rec(u));

		memo[v] = max + 1;
		return memo[v];
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}