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
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            List<int>[] Node = new List<int>[N + 1];
            int[] dp = new int[N + 1];
            List<int> T_List = new List<int>();//トポロジカルリスト
            for (int i = 0; i < N + 1; i++)
            {
                Node[i] = new List<int>();
            }
            int M = int.Parse(input[1]);
            //有向辺の情報をリストに保存する
            int[] indeg = new int[N + 1];
            for (int i = 0; i < M; i++)
            {
                string[] input2 = Console.ReadLine().Split(' ');
                Node[int.Parse(input2[0])].Add(int.Parse(input2[1]));// １→２，３　２→４　３→２，４を各リストに記録する
                indeg[int.Parse(input2[1])]++;//各ノードへの入力辺の数
                dp[int.Parse(input2[1])] = 1;
            }
            while (T_List.Count < N)//トポロジカルリストを作る　T_List
            {
                for (int i = 1; i <= N; i++)
                {
                    if (indeg[i] == 0)//入力がないノードが見つかったら
                    {
                        T_List.Add(i);
                        foreach (int item in Node[i])//出力先への辺を削除
                        {
                            indeg[item]--;
                        }
                        indeg[i] = -1;//訪問済みの印
                        break;
                    }
                }
            }
            int ans = 0;
            foreach (var start in T_List)//トポロジカルリストの順番に処理する
            {
                foreach (var goal in Node[start])
                {
                    dp[goal] = Math.Max(dp[start] + 1, dp[goal]);
                    if (ans < dp[goal])
                    {
                        ans = dp[goal];
                    }
                    if (ans == M)//すべての辺の数に達したら、それ以上は大きい答えはないのでブレイク
                    {
                        break;
                    }
                }
                if (ans == M)
                {
                    break;
                }
            }
            Console.WriteLine(ans);
        }
    }
}