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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

class Main
{
    static int dp[];
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String s[]=br.readLine().split(" ");
        List<List<Integer>> list=new ArrayList<>();
        int n=Integer.parseInt(s[0]);
        for(int i=0;i<=n;i++)
            list.add(new ArrayList<>());
        int m=Integer.parseInt(s[1]);
        for(int i=0;i<m;i++)
        {
            String str[]=br.readLine().split(" ");
            int a=Integer.parseInt(str[0]);
            int b=Integer.parseInt(str[1]);
            list.get(a).add(b);
        }
        dp=new int[n+2];
        Arrays.fill(dp,-1);
        int max=0;
        for(int i=1;i<=n;i++)
        {
            max=Math.max(max,dfs(list,i));
        }
        System.out.println(max);


    }

    private static int dfs(List<List<Integer>> list, int index) {
        int max=0;
        if(dp[index]!=-1)
            return dp[index];
        for(int i=0;i<list.get(index).size();i++)
        {
            max=Math.max(max,1+dfs(list,list.get(index).get(i)));
        }
        return dp[index]= max;
    }


}