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)

/*
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 * and open the template in the editor.
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/**
 *
 * @author aakas
 */
import java.util.*;
public class Main {
    static int n;
    static int m;
    static ArrayList<Integer>[] adjList;
    static boolean[] v;
    static int[] dp;
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        adjList = new ArrayList[n+1];
        //visited = new boolean[n];
        v = new boolean[n+1];
        dp = new int[n+1];
        for(int i=0;i<=n;i++)
            adjList[i] = new ArrayList<Integer>();
        for(int i=0;i<m;i++)
            adjList[sc.nextInt()].add(sc.nextInt());
        int temp = Integer.MIN_VALUE;
        for(int i=1;i<=n;i++)
        {
            //boolean[] visited = new boolean[n+1];
            temp = Math.max(dfs(i),temp);
        }
        System.out.println(temp);
    }
    public static int dfs(int s)
    {
        //System.out.println("call for "+s+" "+visited[s]);
        //if(visited[s])
          //  return 0;
        if(v[s])
            return dp[s];
        v[s] = true;
        //visited[s] = true;
        for(int i=0;i<adjList[s].size();i++)
        {
            int v = adjList[s].get(i);
            //System.out.println(s+ " -> "+v);
            //if(!visited[v])
            //{
                 dp[s] = Math.max(1+dfs(v),dp[s]);
                 //System.out.println(s+" "+dp[s]);
            
        }
        //System.out.println(s+" "+dp[s]);
        return dp[s];
    }
}