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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
namespace G
{
    class Program
    {
        static int lp=0;
        static int dp1(List<List<int>> nn,int i, int N,int[] dp)
        {
            int lp=0;
            if(nn[i].Count == 0)
            {
                return dp[i];
            }
            for (int j = 0; j < nn[i].Count; j++)
            {
                dp[nn[i][j]] = Math.Max(dp[nn[i][j]], dp[i] + 1);
                lp = dp1(nn, nn[i][j], N, dp);
            }
            return lp;
        }
        static void Main(string[] args)
        {
            string[] NM = Console.ReadLine().Split(' ');
            int N = int.Parse(NM[0]);int M = int.Parse(NM[1]);
            int[] rute = new int[N+1];
            List<List<int>> nn = new List<List<int>>();
            for(int i=0;i<N;i++)
            {
                nn.Add(new List<int>());
            }
            for(int i=0;i<M;i++)
            {
                string[] xy = Console.ReadLine().Split(' ');
                int x = int.Parse(xy[0]);int y = int.Parse(xy[1]);
                nn[--x].Add(--y);
                
            }
            int nMax = 0;
            for (int i = 0; i < N; i++)
            {
                int result = dp1(nn, i, N, rute);
                if(nMax < result) { nMax = result; }
            }
            Console.WriteLine(nMax);
        }
    }
}