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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ll_s long
#define mod 1000000007
#define forn(i,start,lim) for(ll i=start;i<lim;i++)
#define forn_d(i,start,lim) for(ll i=start;i>=lim;i--)
#define f first
#define s second
#define pb push_back
#define pf push_front
#define mp make_pair
#define debug1(a) cout<<"------\n"<<#a<<" = "<<a<<endl<<"------"<<endl
#define debug2(a,b) cout<<"--------------\n"<<#a<<" = "<<a<<" ; "<<#b<<" = "<<b<<endl<<"--------------"<<endl
#define debug3(a,b,c) cout<<"----------------------\n"<<#a<<" = "<<a<<" ; "<<#b<<" = "<<b<<" ; "<<#c<<" = "<<c<<endl<<"----------------------"<<endl
#define sz(a) (ll)(a.size())
#define debug4(a) cout<<"chu "<<a<<endl
#define endl "\n"

void get_topo(int s, vector<vector<ll>> &adj, vector<bool> &v, vector<ll> &topological_sort){
  v[s]=true;
  for(auto it:adj[s]){
    if(!v[it]){
      get_topo(it,adj,v,topological_sort);
    }
  }
  topological_sort.push_back(s);
}

int main()
{
  ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  ll t;
  // cin>>t;
  t=1;
  while(t--){
    ll n,m;
    cin>>n>>m;
    vector<vector<ll>> adj(n+1);
    vector<bool> v(n+1);
    vector<ll> topological_sort, dp(n+1);
    forn(i,0,m){
      ll x,y;
      cin>>x>>y;
      adj[x].pb(y);
    }
    for(int i=1;i<=n;i++){
      if(!v[i]){
        get_topo(i,adj,v,topological_sort);
      }
    }
    reverse(topological_sort.begin(),topological_sort.end());
    ll ans=0;
    for(auto i:topological_sort){
      for(auto it:adj[i]){
        dp[it] = max(dp[it],dp[i]+1);
      }
      // debug2(i,dp[i]);
      ans=max(ans,dp[i]);
    }
    cout<<ans<<endl;

  }
  return 0;
}