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: Runtime Error)

import java.util.*;

public class Main
{
  static int n;
  static Integer[] memo;
  static ArrayList<Integer>[] G;
  public static void main(String[] args)
  {
	Scanner in = new Scanner(System.in);
    n = in.nextInt();
    int m = in.nextInt();
    G = new ArrayList[n];
    for (int i = 0; i < n; i++)
      G[i] = new ArrayList<>();
    for (int i = 0; i < m; i++)
      G[in.nextInt()-1].add(in.nextInt()-1);
    
    int max = 0;
    for (int i = 0; i < n; i++)
      if (memo[i] == null)
        max = Math.max(max, dp(i));
    System.out.println(max);
    in.close();
  }
  
  public static int dp(int at)
  {
    if (memo[at] != null)
      return memo[at];
    int ans = 0;
    for (int i : G[at])
      ans = Math.max(ans, 1+dp(i));
    return memo[at] = ans;
  }
}