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>

#define all(x) x.begin(),x.end()
#define pb(x) emplace_back(x)
#define forn(i,N) for(int i=0;i<N;i++)

using namespace std;
using ll=long long int;
using ld=long double;
using vi=vector<int>;
using vll=vector<ll>;
using vd=vector<double>;
int ctoi(char c) {return c-'0';}

const int mxn=1e5+5;
vector<vector<int>> g(mxn,vector<int>());
vi visited(mxn);
vi memo(mxn);
int N,M;

int dp(int c) {
  if(g[c].size()==0) {
    return 0;
  }
  int ans=0;
  visited[c]=1;
  for(auto& x: g[c]) {
    if(!visited[x]) {
      if(memo[x]==0)
        ans=max(ans,memo[x]=dp(x)+1);
      else
        ans=max(ans,memo[x]);
    }
  }
  visited[c]=0;
  return ans;
}

int main() {
//freopen("input.txt","rt",stdin);
ios::sync_with_stdio(false);
cin.tie(nullptr);

cin>>N>>M;
forn(i,M) {
  int x,y;
  cin>>x>>y;
  g[x].pb(y);
}
int mxans=0;
for(int i=1;i<=N;i++) {
  int d=dp(i);
  mxans=max(mxans,d);
}
cout<<mxans<<endl;
return 0;
}