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.util.*;

public class Main{

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        Map<Integer, List<Integer>> graph = new HashMap<>();
        int n = sc.nextInt();

        for (int i = 1; i <= n; i++) {
            graph.put(i, new ArrayList<>());
        }


        int m = sc.nextInt();
        for (int i = 0; i < m; i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();

            List<Integer> edges = graph.get(x);
            edges.add(y);
        }
        int maxPath = 0;
        for (int i = 1; i <= n; i++) {
            maxPath = Math.max(maxPath, maxPath(graph, i));
        }

        System.out.println(maxPath);
    }

    private static int maxPath(Map<Integer, List<Integer>> graph, int i) {
        List<Integer> edges = graph.get(i);
        if(edges == null || edges.isEmpty()) {
            return 0;
        }

        int max = 0;
        for (int edge: edges) {
            int path = maxPath(graph, edge);
            max = Math.max(path, max);
        }

        max++;
        return max;
    }
}