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-->@harshrajani460
 *     codeforces round-567
 *
 */
#include<bits/stdc++.h>
using namespace std;
#define FAST ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
#define pb push_back
#define ff first
#define ss second
#define sz size()
#define mp make_pair
#define pe(x) cout<< x << endl ;
#define deb(x) cout<<#x<<" : "<<x<<endl;
#define debug(x,y) cout<<#x<<" : "<<x<<"\t"<<#y<<" : "<<y<<endl;
#define el endl
#define M 998244353 
#define int long long
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define ROR(i,a,b) for(int i=a;i>=b;i--)
const int N = 1e5 + 5;
int dp[N];
void dfs(vector<vector<int> > &v,vector<bool> &vis,int x)
{
    vis[x]=true;
    for(int i=0;i<v[x].size();i++)
    {
        if(!vis[v[x][i]])
        dfs(v,vis,v[x][i]);
        
        dp[x]=max(dp[x],1+dp[v[x][i]]);
    }
}
int32_t main() 
{ 
   int n,m;
   cin>>n>>m;
   vector<vector<int> > v(n+1);
   vector<bool> vis(n+1,false);
   //memset(vis,false,sizeof(false));
   memset(dp,0,sizeof(dp));
   FOR(i,0,m)
   {
       int x,y;
       cin>>x>>y;
       v[x].pb(y);
   }
   FOR(i,1,n+1)
   {
       if(!vis[i])
       dfs(v,vis,i);
   }
   int ans=0;
   FOR(i,1,n+1)
   ans=max(ans,dp[i]);
   cout<<ans;
   
}