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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    static class Node{
        List<Node> next=new ArrayList<>();
    }

    public static void main(String[] args) {
        Scanner sc  = new Scanner(System.in);
        int N = sc.nextInt();// vertex
        int M = sc.nextInt(); // edges
        Node[] nodes = new Node[N];
        for (int i = 0; i < M ; i++) {
            int x  = sc.nextInt();
            int y  = sc.nextInt();
            if(nodes[x-1]==null){
                nodes[x-1]= new Node();
            }
            if(nodes[y-1]==null){
                nodes[y-1]= new Node();
            }
            Node node = nodes[x-1];
            node.next.add(nodes[y-1]);
        }


        int max =0;
        for (int i = 0; i < N  ; i++) {
//            System.out.println(nodes[i]);
            if(nodes[i] != null ){
                int res = longest(nodes[i],0);
//                System.out.println("i="+i+"  path="+res);
                if(res>max) max = res;
            }
        }

        System.out.println(max);
    }

    static int longest(Node root ,int  path){

        List<Node> list = root.next;
        if(list.size()==0) return path;
        int max =0;
        for(Node node: list){
            int pth = longest( node , path +1);
            if(pth>max) max = pth;
        }
        return max;
    }
}