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: Accepted)

import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;

class Main{
	static int[] dp;
	static LinkedList<Integer>[] graph;
	static int rec(int v) {
		if(dp[v] != -1) return dp[v];

		int ret = 0;
		for(int u : graph[v]) {
			ret = Math.max(ret, rec(u) + 1);
		}
		return dp[v] = ret;
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		while(sc.hasNext()) {
			int N = sc.nextInt(), M = sc.nextInt();
			graph = new LinkedList[N];
			for(int i = 0; i < N; i++) graph[i] = new LinkedList<Integer>();
			for(int i = 0; i < M; i++) {
				int x = sc.nextInt(), y = sc.nextInt();
				graph[x - 1].add(y - 1);
			}
			dp = new int[N];
			Arrays.fill(dp, -1);
			int ans = 0;
			for(int i = 0; i < N; i++) ans = Math.max(ans, rec(i));
			System.out.println(ans);
		}
	}
}