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>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<iostream>
#define ios   ios_base::sync_with_stdio(false);  cin.tie(0);    cout.tie(0);
typedef   long long int ll;
using namespace std;
const int N=1e5+5;
#define fi first
#define se second
#define pb push_back
#define endl "\n"
ll n,m;
vector<ll> adj[N];
ll cnt[N];
ll ans;
ll dfs(ll u)
{
    ll &g=cnt[u];
    if(g!=-1)
    return g;
    g=0;
    for(auto f : adj[u])
    {
        g=max(g,dfs(f)+1);
    }
    return g;
}
int main()
{
   cin>>n>>m;
   for(ll i=1;i<=n;++i)
   cnt[i]=-1;
   for(ll i=0;i<m;++i)
   {
       ll u,v;cin>>u>>v;
       adj[u].pb(v);
       //adj[v].pb(u);
   }
   for(ll i=1;i<=n;++i)
   {
       if(cnt[i]==-1)
       {
           ans=max(ans,dfs(i));
       }
   }
   //cout<<endl;
   //for(ll i=1;i<=n;++i)
   //cout<<cnt[i]<<" ";
   cout<<ans;
}