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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

//package compilers;

import java.util.Queue;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.*;

public class Main {
	private static Map<Integer,Boolean> map;
	private static List<Integer> ans;
    private static void dfs(int i, Set<Integer>[] arr) {
    	if(map.containsKey(i))
    		return;
    	map.put(i,true);
		for(int j: arr[i]) {
			//System.out.println(j);
			dfs(j,arr);
		}
		ans.add(i);
    }
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int m=in.nextInt();
		Set<Integer> []arr=new Set[n+1];
		int x,y;
		for(int i=1;i<=n;i++)
			arr[i]=new HashSet();
		//Map<Integer,Integer> ma=new HashMap();
		while(m>0) {
		       x=in.nextInt();
			   y=in.nextInt();
			   arr[x].add(y);
			  
			   m--;
		}
		//Stack<Integer> s=new Stack();
		/*
		 * for(int i=1;i<=n;i++) { System.out.print(i + "-> "); for(int j:arr[i]) {
		 * System.out.print(j+ " "); } System.out.println(); }
		 */
		map=new HashMap();
		//s.push(1);
		 ans=new ArrayList();
		  for(int i=1;i<=n;i++) {
			  dfs(i,arr);
		}
		  int dp[]=new int[n];
		  Collections.reverse(ans);
		  
		  for(int i=1;i<ans.size();i++) {
			  for(int j=0;j<i;j++) {
				  if(arr[ans.get(j)].contains(ans.get(i)))
					  dp[i]=Math.max(dp[i],dp[j]+1);
			  }
		  }
		  
		  int max=0;
		  
		  for(int i=0;i<n;i++) {
			  //System.out.print(dp[i] + " ");
			  max=Math.max(max, dp[i]);
		  }
		  System.out.println(max);
		
		
		
	}

}