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 DPG9
{
    class Program
    {
        static List<int>[] Node;
        static int[] dp;
        static int[] indeg;
        static int ans = 0;
        static void Main(string[] args)
        {
            //List<int> T_List = new List<int>();//トポロジカルリスト
            int[] input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);//新しい入力処理の書き方
            int N = input[0];
            Node = new List<int>[N];
            dp = new int[N];
            for (int i = 0; i < N; i++)
            {
                Node[i] = new List<int>();
            }
            indeg = new int[N];
            //リストのほうが処理時間がかかった
            int M = input[1];
            int[] input2;//for文の外で宣言した方が少しだけ速い
            for (int i = 0; i < M; i++)
            {
                input2 = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);//新しい入力処理の書き方
                Node[input2[0] - 1].Add(input2[1] - 1);// 出力先を各リストに記録する　ノード番号を０番からに変更した
                indeg[input2[1] - 1]++;//各ノードへの入力辺の数
                dp[input2[1] - 1] = 1;
            }
            for (int i = 0; i < N; i++)
            {
                if (indeg[i] == 0)//入力がないノードが見つかったらdpを計算する
                {
                    indeg_Handle(i, N);
                    break;
                }
            }
            Console.WriteLine(ans);
        }
        static void indeg_Handle(int i, int N)
        {
            indeg[i] = -1;//訪問済みの印
            foreach (var item in Node[i])
            {
                dp[item] = Math.Max(dp[i] + 1, dp[item]);
                ans = Math.Max(ans, dp[item]);
                indeg[item]--;//出力先への辺を削除
            }
            for (int j = 0; j < N; j++)
            {
                if (indeg[j] == 0)
                {
                    indeg_Handle(j, N);
                    break;
                }
            }
        }
    }
}