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: Accepted)

using System;
using static System.Console;
using System.Collections.Generic;

namespace dp
{
    class Program
    {
        static void Main(string[] args)
        {
            var nm = ReadLine().Split(' ');
            var n = int.Parse(nm[0]);
            var m = int.Parse(nm[1]);

            var pathList = new List<int>[n + 1];
            for (var i = 0; i < m; ++i)
            {
                var xy = ReadLine().Split();
                var x = int.Parse(xy[0]);
                var y = int.Parse(xy[1]);
                if (pathList[x] == null)
                {
                    pathList[x] = new List<int>();
                }
                pathList[x].Add(y);
            }

            var dp = new int[n + 1];
            for (var i = 0; i <= n; ++i)
            {
                dp[i] = -1;
            }
            var max = 0;
            for (var i = 1; i <= n; ++i)
            {
                max = Math.Max(max, Rec(i, pathList, dp));
            }
            Console.WriteLine(max);
        }
        private static int Rec(int start, List<int>[] pathList, int[] dp)
        {
            if (dp[start] > -1)
            {
                return dp[start];
            }
            var max = 0;
            if (pathList[start] != null)
            {
                foreach (var next in pathList[start])
                {
                    max = Math.Max(max, Rec(next, pathList, dp) + 1);
                }
            }
            dp[start] = max;
            return max;
        }
    }
}