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.Linq;
using System.Collections.Generic;

namespace AtCoder.DP
{
    class EDPC_G
    {
        public static void Main()
        {
            var nm = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var n = nm[0];
            var m = nm[1];

            var nodes = new List<int>[n];
            var inN = new int[n];

            for (int i = 0; i < m; i++)
            {
                var xy = Console.ReadLine().Split(' ').Select(s => int.Parse(s) - 1).ToArray();
                if (nodes[xy[0]] == null)
                    nodes[xy[0]] = new List<int>();
                if (nodes[xy[1]] == null)
                    nodes[xy[1]] = new List<int>();
                nodes[xy[0]].Add(xy[1]);
                inN[xy[1]]++;
            }

            var queue = new Queue<int>();
            for (int i = 0; i < n; i++)
                if (nodes[i] != null && inN[i] == 0)
                    queue.Enqueue(i);

            int startN = queue.Count;

            var sorted = new List<int>();
            while (queue.Any())
            {
                var i = queue.Dequeue();
                sorted.Add(i);

                foreach (var j in nodes[i])
                {
                    inN[j]--;
                    if (inN[j] == 0)
                        queue.Enqueue(j);
                }
            }

            var longestParitial = new int[n];
            for (int i = sorted.Count - 1; i >= 0; i--)
            {
                if (!nodes[sorted[i]].Any())
                    continue;
                longestParitial[sorted[i]] = nodes[sorted[i]].Max(j => longestParitial[j]) + 1;
            }

            var longest = 1;
            for (int i = 0; i < startN; i++)
                if (longest < longestParitial[sorted[i]])
                    longest = longestParitial[sorted[i]];

            Console.WriteLine(longest);
        }
    }
}