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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

using Graph = vector<vector<int>>;
vector<bool> seen;

int dfs(Graph& G, int v){
  seen.at(v) = true;
  
  for(auto next : G[v]){
    if(!seen.at(next)){
      return dfs(G,next) + 1;
    }
  }
  return 1;
}

int main(){
  int N,M;
  cin >> N >> M;
  ios::sync_with_stdio(false);
  Graph G(N);
  
  for(int i=0;i<M;i++){
    int s,t;
    cin >> s >> t;
    G[s-1].push_back(t-1);
  }

  vector<int> ans(N);
  for(int i=0;i<N;i++){
    seen.assign(N,false);    
    ans.at(i) = dfs(G,i);
  }
  
  int max = -1;
  for(int i=0;i<N;i++){
    if(ans.at(i) > max){
      max = ans.at(i);
    }
  }
  
  cout << max << endl;
  
  return(0);
}