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>
 #include<stdio.h> 
  	
 using namespace std;
 int dp[1000000];
 

 int maxi(int a,int b){
 if (a>b)
 return a;
 else 
 return b;}
 void dfs(int t ,vector<int>a[1000000],vector<bool>visited,int n)
 {
	visited[t]=true;
	 for(int i=0;i<a[t].size();i++)
	 {
		 if (dp[a[t][i]]<dp[t]+1){
			 
			dp[a[t][i]]=dp[t]+1;
		 
		 dfs(a[t][i],a,visited,n);
	 }
		   
			
		     
		}
		
		
  
 
}

	
 
 int main()
 { 
 
 int k=0;

int n,e,x,y;
cin>>n>>e;
vector<int>a[1000000];
 vector<bool>visited(n+1,false);
for(int i=0;i<e;i++){
cin>>x>>y;
a[x].push_back(y);
}
for(int i=1;i<=n;i++)
a[0].push_back(i);


     dfs(0,a,visited,n);
    
    for(int i=0;i<=n;i++)
    k=maxi(k,dp[i]);
    cout<<k-1;
}