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: Accepted)

#include <bits/stdc++.h>
using namespace std;
int vis[100005],dis[100005],fin[100005];
vector<int> v[100005];
set<int> t;

int dfs(int u){
    vis[u]=1;
    int inter=0;
    for(int i=0;i<v[u].size();i++){
        if(!vis[v[u][i]]){
            dis[v[u][i]]=dis[u]+1;
            inter=dfs(v[u][i]);
            fin[u]=max(fin[u],inter);
        }else{
            fin[u]=max(fin[u],fin[v[u][i]]-dis[v[u][i]]+1+dis[u]);    
        }
    }
    if(t.find(u)!=t.end()){
        fin[u]=dis[u];
        return dis[u];    
    }
    
    else{
        return fin[u];
    }
}


int main() {
	int n,m;
	cin>>n>>m;
	int x,y;
	for(int i=0;i<n;i++){
	    t.insert(i+1);
	}
	for(int i=0;i<m;i++){
        cin>>x>>y;
	    auto pos2=t.find(x);
	    if(pos2!=t.end())
	        t.erase(x);
            
        v[x].push_back(y);
	   
	}
	int ans=0;
	for(int i=1;i<=n;i++){
	    if(!vis[i]){
	        dis[i]=0;
	        ans=max(ans,dfs(i));
	    }
	}
	cout<<ans;
	
	return 0;
}