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.Linq;

class G
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var h = read();
		var rs = new int[h[1]].Select(_ => read()).ToArray();
		var map = rs.ToLookup(r => r[0], r => r[1]);
		var map_r = rs.ToLookup(r => r[1], r => r[0]);

		var q = Enumerable.Range(1, h[0]).Where(i => !map_r.Contains(i)).ToList();
		var c = -1;
		for (; q.Any(); c++)
		{
			var ps = q.ToArray();
			q.Clear();

			foreach (var p in ps)
				foreach (var np in map[p])
					if (!q.Contains(np)) q.Add(np);
		}
		Console.WriteLine(c);
	}
}