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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define ll long long int
void dfs(vector<vector<ll>> graph,vector<bool> &visited,vector<ll> &dp,ll Node){
    visited[Node] = true;
    for(int i=0;i<graph[Node].size();i++){
        if(!visited[graph[Node][i]]){
            dfs(graph,visited,dp,graph[Node][i]);
        }
        dp[Node] = max(dp[Node],1+dp[graph[Node][i]]);
    }
    
}
int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
   ll N,M;
   cin>>N>>M;
   vector<vector<ll>> graph(N+1);
   for(int i=0;i<M;i++){
       int temp,temp1;
       cin>>temp>>temp1;
       graph[temp].push_back(temp1);
   }
   vector<ll> dp(N+1,0);
   vector<bool> visited(N+1,false);
   for(int i=1;i<=N;i++){
       if(!visited[i]){
           dfs(graph,visited,dp,i);
       }
   }
   ll ans = INT_MIN;
   for(int i=1;i<=N;i++){
       ans = max(ans,dp[i]);
   }
   cout<<ans;
   
  
}