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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.math.*;
 
public class Main
{
    static int dp[];
    static boolean visited[];

    static int dfs(int node,ArrayList<Integer> l[]){
        visited[node]=true;
        int ret=1;
        for(Integer child : (l[node])){
            if(visited[child])
                ret=Math.max(1+dp[child],ret);
            else
                ret=Math.max(1+dfs(child,l),ret);
        }

        return dp[node]=ret;
    }
    public static void process()throws IOException
    {
        int n=ni(),m=ni();
        ArrayList<Integer> l[]=new ArrayList[n+1];
        visited=new boolean[n+1];

        for(int i=1;i<=n;i++) l[i]=new ArrayList<>();

        for(int i=1;i<=m;i++)
            l[ni()].add(ni());         
        dp=new int[n+1];

        for(int i=1;i<=n;i++){
            if(!visited[i])
                dfs(i,l);
        }

        int res=1;
        for(int i : dp) res=Math.max(res, i);
        pn(res-1);
    }
 
 
    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new FastReader();
 
        long s = System.currentTimeMillis();
        int t=1;
        //t=ni();
        while(t-->0)
            process();
 
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static int ni()throws IOException{return Integer.parseInt(sc.next());}
    static long nl()throws IOException{return Long.parseLong(sc.next());}
    static double nd()throws IOException{return Double.parseDouble(sc.next());}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    
    static long mod=(long)1e9+7l;
 
    static<T> void r_sort(T arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            T temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){ 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next(){ 
            while (st == null || !st.hasMoreElements()){ 
                try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        } 
  
        String nextLine(){ 
            String str = ""; 
            try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
            return str; 
        } 
    } 
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}