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.lang.reflect.Array;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

class Graph {
    ArrayList<Integer>[] graph;

    @SuppressWarnings("unchecked")
    Graph(int n) {
        graph = new ArrayList[n];
        for(int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }
    }
    public void addEdge(int u, int v) {
        graph[u].add(v);
    }
    public ArrayList<Integer> neighbors(int u) {
        return graph[u];
    }
}

public class Main {
    static Graph g;
    static boolean[] visited;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), m = in.nextInt();

        g = new Graph(n);
        visited = new boolean[n];

        for(int i = 0; i < m; i++) {
            int u = in.nextInt(), v = in.nextInt();
            u--; v--;
            g.addEdge(u, v);
        }
        int mx = 0;
        for(int i = 0; i < n; i++) {
            if(!visited[i]) {
                mx = Math.max(mx, go(i));
                visited[i] = true;
            }
        }

        System.out.println(mx - 1);
    }

    private static int go(int u) {
        int ans = 0;
        visited[u] = true;
        for (int v : g.neighbors(u)) {
            ans = Math.max(ans, go(v));
        }
        return ans + 1;
    }

}