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: Time Limit Exceeded)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String[] line = scanner.nextLine().split(" ");
        int numVertices = Integer.parseInt(line[0]);
        int numEdges = Integer.parseInt(line[1]);

        Map<Integer, List<Integer>> graph = new HashMap<>();
        for (int i = 0; i < numEdges; i++) {
            line = scanner.nextLine().split(" ");
            int from = Integer.parseInt(line[0]);
            int to = Integer.parseInt(line[1]);
            graph.putIfAbsent(from, new ArrayList<>());
            graph.get(from).add(to);
        }

        int[] max = new int[numVertices + 1];
        boolean[] visited = new boolean[numVertices + 1];
        for (int i = 1; i <= numVertices; i++) {
            if (!visited[i]) {
                dfs(graph, i, 0, max, visited);
            }
        }

        int ans = 0;
        for(int num : max) {
            ans = Math.max(ans, num);
        }
        System.out.println(ans);
    }

    private static void dfs(Map<Integer, List<Integer>> graph, int start, int count, int[] max, boolean[] visited) {
        visited[start] = true;
        max[start] = 0;
        if (graph.containsKey(start)) {
            for (int child : graph.get(start)) {
                dfs(graph, child, count, max, visited);
                max[start] = Math.max(max[start], 1 + max[child]);
            }
        }
    }
}