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 {

    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();
        }

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

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

    private ArrayList<Integer>[] adj;

    private void addEdge(int u, int v) {
        adj[u].add(v);
    }

    public static void main(String[] args) {
        Main main = new Main();
        FastReader scanner = new FastReader();
        int N = scanner.nextInt();

        main.adj = new ArrayList[N];
        for (int i = 0; i < N; i++) {
            main.adj[i] = new ArrayList<>();
        }

        int M = scanner.nextInt();
        for (int i = 0; i < M; i++) {
            main.addEdge(scanner.nextInt() - 1, scanner.nextInt() - 1);
        }

        int max = 0;
        int[] DP = new int[N];
        for (int i = 0; i < N; i++) {
            main.DFS(new boolean[N], i, DP);
        }
        for (int i = 0; i < N; i++) {
            max = Math.max(max, DP[i]);
        }
        System.out.println(max);
    }

    private void DFS(boolean[] visited, int n, int[] DP) {
        visited[n] = true;
        for (Integer ix : adj[n]) {
            if (!visited[ix]) {
                DFS(visited, ix, DP);
            }
            DP[n] = Math.max(DP[n], 1 + DP[ix]);
        }
    }

}