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: Wrong Answer)

import java.util.*;

public class Main {
	final int MOD = 100000000;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;
	final int LEN = 100000;
	Scanner sc = new Scanner(System.in);


	void doIt() {
		int N = sc.nextInt();
		int M = sc.nextInt();
		ArrayList<Integer>[] link = new ArrayList[N];
		for(int i = 0; i < N; i++) 
			link[i] = new ArrayList<>();
		for(int i = 0; i < M; i++) 
			link[sc.nextInt() - 1].add(sc.nextInt() - 1);
		int dp[] = new int[N];
		for(int i = 0; i < N; i++) {
			for(int j : link[i]) {
				dp[j] = dp[i] + 1;
			}
		}
		for(int i = 0; i < N; i++) {
			for(int j : link[i]) {
				dp[j] = Math.max(dp[j], dp[i] + 1);
				//System.out.println(dp[j]);
			}
		}
		int max = 0;
		for(int i = 0; i < N; i++) {
			max = Math.max(max, dp[i]);
		}
		System.out.println(max);
		//System.out.println(Arrays.toString(dp));
		
		
	}
	public static void main(String[] args) {
		new Main().doIt();
	}
}