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)

import java.io.*;
import java.util.*;
public class Main{
	public static int n, m;
	public static List<Integer> adj[];
	public static int dist[];
    public static void main(String[] args) throws IOException{
    	FastScanner sc = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    	n = sc.nextInt();
    	m = sc.nextInt();
    	dist = new int[n];
    	adj = new ArrayList[n];
    	for(int i=0; i<n; i++) {
    		adj[i] = new ArrayList<>();
    	}
    	for(int i=0; i<m; i++) {
    		int a = sc.nextInt()-1;
    		int b = sc.nextInt()-1;
    		adj[a].add(b);
    	}
    	for(int i=0; i<n; i++) {
    		if(dist[i]!=0) continue;
    		dfs(i, 0);
    	}
    	int max = 0;
    	for(int i=0; i<n; i++) {
    		max = Math.max(max, dist[i]);
    	}
    	out.println(max);
    	out.close();
    }
    public static void dfs(int start, int cnt) {
    	dist[start] = cnt;
    	for(int i:adj[start]) {
    		if(dist[i]>cnt+1) continue;
    		dfs(i, cnt+1);
    	}
    }
    public static class FastScanner {
    	BufferedReader br;
    	StringTokenizer st;

    	public FastScanner(String s) {
    		try {
    			br = new BufferedReader(new FileReader(s));
    		} catch (FileNotFoundException e) {
    			e.printStackTrace();
    		}
    	}

    	public FastScanner() {
    		br = new BufferedReader(new InputStreamReader(System.in));
    	}
    	
    	String nextToken() {
    		while (st == null || !st.hasMoreElements()) {
    			try {
    				st = new StringTokenizer(br.readLine());
    			} catch (IOException e) {
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}

    	String nextLine() {
    		st = null;
    		try {
    			return br.readLine();
    		} catch (IOException e) {
    			e.printStackTrace();
    		}
    		return null;
    	}

    	int nextInt() {
    		return Integer.parseInt(nextToken());
    	}

    	long nextLong() {
    		return Long.parseLong(nextToken());
    	}

    	double nextDouble() {
    		return Double.parseDouble(nextToken());
    	}
    }
}