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{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int M = sc.nextInt();
    Map<Integer, ArrayList<Integer>> map = new HashMap<>();
    for(int i = 0; i < M; i++){
      int x = sc.nextInt();
      int y = sc.nextInt();
      if(!map.containsKey(x)){
        map.put(x, new ArrayList<Integer>());
      }
      List<Integer> list = map.get(x);
      list.add(y);
    }
    int[] memo = new int[N+1];
    Arrays.fill(memo, -1);
    System.out.println(solve(map, memo));
  }
  
  public static long solve(Map<Integer, ArrayList<Integer>> map, int[] memo){
    long max = -1L;
    for(int i = 1; i <=memo.length; i++){
      max = Math.max(max, saiki(map, i, memo));
    }
    return max;
  }
  
  public static long saiki(Map<Integer, ArrayList<Integer>> map, int n, int[] memo){
    if(!map.containsKey(n)){
      return 0;
    }
    if(memo[n] != -1){
      return memo[n];
    }
    List<Integer> list = map.get(n);
    long max = -1L;
    for(int i : list){
      max = Math.max(max, saiki(map, i, memo));
    }
    return max+1;
  }
}