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)

/*author:anshumanc007
   created on:08/01/2019
            */
//EMBRACE THE STRUGGLE!!!
#include <bits/stdc++.h>
#include <queue>
#include <stack>
using namespace std;


//typedef pair<long long int,long long int> pa;
#define MAX 100005
long long int MOD=1e9+7;
long long int INF=1e18;
stack<long long int> st;
bool visited[MAX];
long long int dp[MAX];
void dfs(vector<long long int >adj[],long long int i)
{
    visited[i]=true;
    long long int j;
    for(auto j:adj[i])
    {
        if(!visited[j])
        dfs(adj,j);
    }
    st.push(i);
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    long long int i,j,k,l,m,n,o,p,q,r,x,y,a,b,mini=INF,maxi=0,cnt=0,W,ans;
    cin>>n>>m;
    vector<long long int>adj[n];
    vector<long long int>adj1[n];
    for(i=0;i<m;i++)
    {
        cin>>x>>y;
        x--;
        y--;
        adj[x].push_back(y);
        adj1[y].push_back(x);
    }
    for(i=0;i<n;i++)
    {
        visited[i]=false;
        dp[i]=0;
    }
    for(i=0;i<n;i++)
    {
        if(!visited[i])
        {
            dfs(adj,i);
        }
    }
    vector<long long int>V;
    while(!st.empty())
    {
        j=st.top();
        st.pop();
        V.push_back(j);
    }
    
  for(j=V.size()-1;j>=0;j--)
{
      i=V[j];
    //  st.pop();
      for(auto k:adj1[i])
      {
          dp[k]=max(dp[k],dp[i]+1);
          if(dp[k]>maxi)
          {
              maxi=dp[k];
          }
      }
  }
    cout<<maxi;
    
    

    
}