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.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class Program
	{
		static int[] dp;

		static List<List<int>> graph;

		static void Main(string[] args)
		{
			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int n = vs[0];
			int m = vs[1];
			graph = new List<List<int>>();
			for (int i = 0; i < n; i++) {
				graph.Add(new List<int>());
			}
			for (int i = 0; i < m; i++) {
				int[] tmp = Console.ReadLine().Split().Select(int.Parse).ToArray();
				graph[tmp[0] - 1].Add(tmp[1] - 1);
			}

			//for (int i = 0; i < graph.Count; i++) {
			//	System.Diagnostics.Debug.Write($"{i + 1}:");
			//	for (int j = 0; j < graph[i].Count; j++) {
			//		System.Diagnostics.Debug.Write($"{graph[i][j] + 1}, ");
			//	}
			//	System.Diagnostics.Debug.WriteLine("");
			//}

			dp = new int[n];
			for (int i = 0; i < dp.Length; i++) {
				dp[i] = -1;
			}

			int ans = 0;
			for (int i = 0; i < dp.Length; i++) {
				ans = Math.Max(ans, Compute(i));
			}
			Console.WriteLine(ans);
		}

		static int Compute(int v)
		{
			if (dp[v] != -1) {
				return dp[v];
			}
			int ans = 0;
			foreach (int nv in graph[v]) {
				ans = Math.Max(ans, Compute(nv) + 1);
			}
			//System.Diagnostics.Debug.WriteLine($"{v + 1}={ans}");
			return dp[v] = ans;
		}

	}
}