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;
using System.Collections.Generic;

public static class Program {
    public static void Main() {
        int[]nm=Console.ReadLine().Split().Select(int.Parse).ToArray();
        int n=nm[0];
        int m=nm[1];
        List<int>[]graph=Enumerable.Range(0,n).Select(_=>new List<int>()).ToArray();
        for(int i=0;i<m;i++){
            int[]uv=Console.ReadLine().Split().Select(int.Parse).ToArray();
            graph[uv[0]-1].Add(uv[1]-1);
        }

        int[]dp=new int[n];
        bool[]ckd=new bool[n];
        Action<int>dfs=null;
        dfs=(int x)=>{
            foreach(int y in graph[x]){
                if(!ckd[y])dfs(y);
                dp[x]=Math.Max(dp[x],dp[y]+1);
            }
        };
        for(int i=0;i<n;i++){
            if(!ckd[i])dfs(i);
        }
        int ans=0;
        for(int i=0;i<n;i++){
            ans=Math.Max(ans,dp[i]);
        }
        Console.WriteLine(ans);
    }
}