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: Time Limit Exceeded)

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

void dfs(int u, vector <int> adj[], vector <int> &dp, vector <bool> vis)
{
  int i,j;
  vis[u] = true;
  for(i=0;i<adj[u].size();i++)
  {
    if(vis[adj[u][i]] == false)
      dfs(adj[u][i],adj,dp,vis);
    dp[u] = max(dp[u],1+dp[adj[u][i]]);
  }
}

int main()
{
  int n,m,i,j,u,v;
  cin >> n >> m;
  vector <int> adj[n+1];
  for(i=0;i<m;i++)
  {
    cin >> u >> v;
    adj[u].push_back(v);
  }
  vector <int> dp(n+1,0);
  vector <bool> vis(n+1,false);
  int ans =-1;
  for(i=1;i<=n;i++)
  {
    if(vis[i] == false)
      dfs(i,adj,dp,vis);
    ans = max(ans,dp[i]);
  }
  cout << ans << endl;
  return 0;
}