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 {
	static long dist[] = new long[100010];
	static int connect[][] = new int[100010][2];
	static int point;
	static int side;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		point = sc.nextInt();
		side = sc.nextInt();
		for(int i = 0; i < side; i ++) {
			connect[i][0] = sc.nextInt() - 1;
			connect[i][1] = sc.nextInt() - 1;
		}

		for(int i = 0; i < point; i ++) {
			dist[i] = -1;
		}

		long max = 0;
		for(int i = 0; i < point; i ++) {
			max = Math.max(max, get(i));
		}
		System.out.println(max);
	}
	public static long get(int index) {
		if(dist[index] == -1) {
			dist[index] = 0;
			for(int i = 0; i < side; i ++) {
				if(connect[i][0] == index) {
					dist[index] = Math.max(dist[index], get(connect[i][1]) + 1);
				}
			}
		}
		return dist[index];
	}
}