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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.io.*;
import java.lang.*;

 class Main{

    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static StringBuilder sb = new StringBuilder("");
    static StringTokenizer stk = new StringTokenizer("");
    // static long[][] dp ;
    static Map<Integer,ArrayList<Integer>> adjList = new HashMap<>();
    static int N = 0;
    static int M = 0;
    static long maxValue = 0;

    public static  void main(String args[]){
        try{
            stk = new StringTokenizer(bf.readLine());
             N = Integer.parseInt(stk.nextToken());
             M = Integer.parseInt(stk.nextToken());
            //  dp =  new long[N+1][N+1];

            for(int i=0;i<M;i++){
                stk = new StringTokenizer(bf.readLine());
                int from = Integer.parseInt(stk.nextToken());
                int to = Integer.parseInt(stk.nextToken());

                if(adjList.containsKey(from)){
                    adjList.get(from).add(to);
                }else{
                    ArrayList<Integer> al = new ArrayList<>();
                    al.add(to);
                    adjList.put(from,al);
                }
            }

            solver();

        }catch(Exception e){
            e.printStackTrace();
        }
    }

    public static void solver(){
        for(int i=1;i<=N;i++){
            dfs(i,i,1);
            // System.out.println("doing dfs from "+i+" value "+maxValue);
            // printMatrix()
        }
        System.out.println(maxValue);
    }

  

    public static void dfs(int src, int origin ,long length){
        if(adjList.get(src) == null || adjList.get(src).size() == 0){
            return ;
        }

        //check where things are starting 
        for(int i=0;i < adjList.get(src).size();i++){
            // dp[src][adjList.get(src).get(i)] = Math.max(dp[src][adjList.get(src).get(i)],1);
            // dp[origin][adjList.get(src).get(i)] = Math.max(dp[origin][adjList.get(src).get(i)] , length );
            maxValue = Math.max(maxValue , length);
            dfs(adjList.get(src).get(i),origin,length+1);
        }   
    }

}