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 static java.lang.Math.max;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.Locale;
import java.util.Scanner;

public class Main {

	final static int INF = Integer.MAX_VALUE;
	static boolean[][] conn;
	static int[] memo;
	static int n;

	public static void main(String[] args) {
		Locale.setDefault(Locale.ENGLISH);
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		solve(in, System.out);
		in.close();
	}

	protected static void solve(Scanner in, PrintStream out) {
		n = in.nextInt();
		int m = in.nextInt();
		conn = new boolean[n + 1][n + 1];
		for (int j = 0; j < m; j++)
			conn[in.nextInt()][in.nextInt()] = true;
		int ret = solveLine();
		out.printf(Locale.ENGLISH, "%s%n", ret);
	}

	private static int solveLine() {
		int ans = 0;
		for (int i = 1; i <= n; i++) {
			memo = new int[n + 1];
			Arrays.fill(memo, -1);
			ans = max(ans, lp(i));
		}
		return ans;
	}

	private static int lp(int pos) {
		if (memo[pos] >= 0) return memo[pos];
		int ans = 0;
		for (int i = 1; i <= n; i++) {
			if (conn[pos][i]) {
				ans = max(ans, 1 + lp(i));
			}
		}
		return memo[pos] = ans;
	}

}