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.*;

public class Main {

    public static int solve(int i,int dp[],ArrayList<ArrayList<Integer>> arr){
        if(dp[i] != -1) return dp[i];

        int max = 0;
        int leaf = 1;

        for(Integer j : arr.get(i)){
            leaf = 0;
            max = Math.max(max,solve(j,dp,arr));
        }

        return dp[i] = (leaf == 1 ? 0 : 1 + max);
    }

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n,e;
        n = sc.nextInt();
        e = sc.nextInt();

       int dp[] = new int[n+1];
        ArrayList<ArrayList<Integer>> arr = new ArrayList<ArrayList<Integer>>();
        for(int i=0;i<=n;i++) arr.add(new ArrayList<Integer>());

        for(int i=0;i<e;i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
            arr.get(a).add(b);
        }


        for(int i=0;i<=n;i++) dp[i] = -1;
        int ans = 0;
        for(int i=1;i<=n;i++){
            ans = Math.max(ans,solve(i,dp,arr));
        }
        System.out.print(ans);

    }
}