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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace DPG5
{
    class Program
    {
        public static int[] DP;
        public struct root
        {
            public int start;
            public int goal;
        }
        public static List<root> N_List = new List<root>();
        public static List<root> Topo_List = new List<root>();

        public static List<int> Ns = new List<int>();
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            Ns.Add(0);
            for (int i = 1; i <= N; i++)
            {
                Ns.Add(i);
            }
            DP = new int[N + 1];
            int M = int.Parse(input[1]);
            //有向辺の情報をリストに保存する
            for (int i = 0; i < M; i++)
            {
                string[] input_xy = Console.ReadLine().Split(' ');
                root r = new root();
                r.start = int.Parse(input_xy[0]);
                r.goal = int.Parse(input_xy[1]);
                N_List.Add(r);
                DP[r.goal] = 1;
            }
                TopologicalSort(N);
                Console.WriteLine(DP.Max());
        }
        //トポロジカルリストを作る
        //Nはノードの数
        public static void TopologicalSort(int N)
        {
            int counter;
            foreach (int i in Ns)//入力のないノードを検索する
            {
                counter = 0;
                for (int j = 0; j < N_List.Count; j++)
                {
                    if (N_List[j].goal == i)
                    {
                        counter++;
                        break;
                    }
                }
                if (counter == 0)//入力がないノード
                {
                    for (int k = 0; k < N_List.Count; k++)
                    {
                        if (N_List[k].start == i)
                        {
                            Topo_List.Add(N_List[k]);//トポロジカルリストへ出力する
                            DP[N_List[k].goal] = Math.Max(DP[N_List[k].start] + 1, DP[N_List[k].goal]);
                        }
                    }
                }
            }
            foreach (var item in Topo_List)
            {
                N_List.Remove(item);//トポロジカルリストに出力したものはN_Listから削除する
                Ns.Remove(item.start);//検索するノードNsからも削除する
            }
            if (N_List.Count > 0)
            {
                TopologicalSort(N);
            }
        }
    }
}