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: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        
        Point[] points = new Point[n];
        for (int i = 0; i < n; i++) {
            points[i] = new Point(i);
        }
        
        while (m-- > 0) {
            int parent = sc.nextInt() - 1;
            int child = sc.nextInt() - 1;
            points[parent].addChild(points[child]);
        }
        
        int max = 0;
        for (int i = 0; i < n; i++) {
            int length = getLength(0, points[i]);
            max = Math.max(max, length);
        }
        
        System.out.println(max);
    }
    
    public static class Point {
        int name;
        List<Point> children;
        int generationLength = -1;
        
        Point(int name) {
            this.name = name;
            this.children = new ArrayList<Point>();
        }
        
        void addChild(Point p) {
            this.children.add(p);
        }
    }
    
    public static int getLength(int depth, Point p) {
        int length = 0;
        
        boolean alreadyKnown = p.generationLength != -1;
        if (alreadyKnown) {
            return depth + p.generationLength;
        }
        
        if (p.children.isEmpty()) {
            length = depth;
        } else {
            for (Point child : p.children) {
                int l = getLength(depth + 1, child);
                length = Math.max(length, l);
            }
        }
        
        p.generationLength = length - depth;
        
        return length;
    }
}