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.io.*;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;
public class Main{
    static int[] memo;
    static ArrayList<Integer>[] adjlist;
    public static void main(String[] args) throws IOException {
        scanner sc = new scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        int m = sc.nextInt();

        adjlist = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            adjlist[i] = new ArrayList<>();
        }

        for (int i = 0; i < m; i++)
            adjlist[sc.nextInt()-1].add( sc.nextInt()-1);

        memo = new int[n];
        Arrays.fill(memo,-1);
        int max = 0;
        for (int i = 0; i < n; i++) {
            if (memo[i] == -1)
                dp(i);

            max = Math.max(memo[i],max);
        }
        out.println(max);
        out.flush();

    }

    static int dp(int i){

        if (memo[i] != -1)
            return  memo[i];

        int max = 0;
        for (int nxt: adjlist[i]) {
            max = Math.max(max,dp(nxt)+1);
        }
        return memo[i] = max;
    }
}
class scanner{
    StringTokenizer st;
    BufferedReader br;
    public scanner(InputStream s){
        br = new BufferedReader(new InputStreamReader(s));
    }
    public scanner (String s) throws FileNotFoundException { br = new BufferedReader(new FileReader(s));}

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
        return  Long.parseLong(next());
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public boolean ready() throws IOException {
        return br.ready();
    }
}