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;
using System.Text;
using static System.Console;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        int[] NM = ReadLineParseIntArray();
        int N = NM[0];
        int M = NM[1];
        int[] dp = new int[N];
        Queue<int> zeroDegrees = new Queue<int>();
        List<int>[] Gragh = new List<int>[N];
        int[] dig = new int[N];
        for (int i = 0; i < N; i++)
            Gragh[i] = new List<int>();
        for(int i = 0; i < M; i++)
        {
            int[] xy = ReadLineParseIntArray();
            xy[0]--;
            xy[1]--;
            Gragh[xy[0]].Add(xy[1]);
            dig[xy[1]]++;
        }

        for(int i = 0; i < N; i++)
        {
            if (dig[i] == 0)
                zeroDegrees.Enqueue(i);
        }
        while(zeroDegrees.Count != 0)
        {
            int v = zeroDegrees.Dequeue();
            foreach (var nv in Gragh[v])
            {
                dig[nv]--;
                if (dig[nv] == 0)
                {
                    zeroDegrees.Enqueue(nv);
                    dp[nv] = Max(dp[nv], dp[v] + 1);
                }
            }
        }
        int ans = 0;
        for (int i = 0; i < N; i++)
            ans = Max(ans, dp[i]);
        WriteLine(ans); 
    }
    static int[] ReadLineParseIntArray() => ReadLine().Split(' ').Select(int.Parse).ToArray();
}