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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace CSharpSample01
{


    class Program
    { 
        static List<int> TopologicalSort(int N, List<int>[] g, int[] into)
        {
            List<int> L = new List<int>();
            Stack<int> st = new Stack<int>();

            for(int i = 1; i <= N; i++)
            {
                if(into[i] == 0)
                {
                    st.Push(i);
                }
            }

            while (st.Count != 0)
            {
                int from = st.Pop();
                L.Add(from);
                foreach (int to in g[from])
                {
                    into[to]--;
                    if (into[to] == 0)
                    {
                        st.Push(to);
                    }
                }

            }
            
            return L;
        }


        static int Solve(int N, List<int>[] g, int[] into)
        {
            List<int> L = TopologicalSort(N, g, into);
            int[] dp = new int[N + 1];

            int max_length = 0;

            foreach(var from in L)
            {
                foreach(var to in g[from])
                {
                    dp[to] = Math.Max(dp[to], dp[from] + 1);
                    max_length = Math.Max(max_length, dp[to]);
                }
            }

            return max_length;
        }
        
        
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);

            List<int>[] g = new List<int>[N + 1];
            int[] into = new int[N + 1];

            for(int i = 1; i <= N; i++)
            {
                g[i] = new List<int>();
            }
            
            for(int i = 0; i < M; i++)
            {
                input = Console.ReadLine().Split(' ');
                int x = int.Parse(input[0]);
                int y = int.Parse(input[1]);
                g[x].Add(y);
                into[y]++;
            }

            Console.WriteLine(Solve(N, g, into));
        }
    }
}