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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public int[] Sarray() { return ReadLine().Split().Select(int.Parse).ToArray(); }
        static public List<int> Slist() { return ReadLine().Split().Select(int.Parse).ToList(); }

        static int N;
        static int[,] Move;
        static int[,] dp;
        static void Main(string[] args)
        {
            var NM = Sarray();
            var N = NM[0];
            var M = NM[1];
            var outpath = new List<int>[N];
            var inpath = new List<int>[N];
            for (var i = 0; i < N; ++i)
            {
                outpath[i] = new List<int>();
                inpath[i] = new List<int>();
            }
            for (var i = 0; i < M; ++i)
            {
                var t = Sarray();
                outpath[t[0] - 1].Add(t[1] - 1);
                inpath[t[1] - 1].Add(t[0] - 1);
            }
            var srs = new List<int>();
            for (var i = 0; i < N; ++i)
            {
                if (!inpath[i].Any())
                    srs.Add(i);
            }
            var dp = new int[N];
            foreach (var v in srs)
            {
                var q = new Queue<int>();
                q.Enqueue(v);

                while (q.Any())
                {
                    var vw = q.Dequeue();
                    foreach (var op in outpath[vw])
                    {
                        if (dp[op] < dp[vw] + 1)
                        {
                            dp[op] = dp[vw] + 1;
                            q.Enqueue(op);
                        }
                    }
                }
            }
            WriteLine(dp.Max());
        }
    }
}