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

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] in = new int[n];
		List<Integer>[] es = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			es[i] = new ArrayList<>();
		}

		for (int i = 0; i < m; i++) {
			int x = sc.nextInt() - 1;
			int y = sc.nextInt() - 1;
			es[x].add(y);
			in[y]++;
		}

		int answer = 0;
		for (int i = 0; i < n; i++) {
			if (in[i] != 0) continue;
			answer = Math.max(answer, dfs(i, es));
		}

		System.out.println(answer);
	}

	private static int dfs(int v, List<Integer>[] es) {
		if (es[v].size() == 0) return 0;
		int a = 0;
		for (int e = 0; e < es[v].size(); e++) {
			a = Math.max(dfs(es[v].get(e), es), a);
		}
		return a + 1;
	}
}