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++14 (GCC 5.4.1) (judge verdict: Accepted)



//longest path in a directed graph
#include<bits/stdc++.h>
using namespace std;
int dp[100001];  //dp[i]= len of longest path starting at node i;

vector<int>Graph[100001];
int solve(int src)
{
    if(dp[src]!=-1)
    return dp[src];
    
    int bestchild=0;
     bool leaf=1;
     for(int child:Graph[src])  //O(M)
     {
         leaf=0;
         bestchild=max(bestchild,solve(child));
     }
     return dp[src]=leaf?0:1+bestchild;



}





int main()
{
    int n,m;
    cin>>n>>m;
    memset(dp,-1,sizeof dp);
  
    for(int i=0;i<m;i++)
    {
        int u,v;
        cin>>u>>v;
        Graph[u].push_back(v);
    }
    int ans=0;
    for(int i=1;i<=n;i++)   //O(N)
    ans=max(ans,solve(i));
    cout<<ans;
    return 0;

}