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: Accepted)

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

#define FAST {ios::sync_with_stdio(false); cin.tie(NULL);}
#define pb push_back
#define fi first
#define se second
#define f(i,a,b) for(int i=a;i<b;i++)

vector<vector<int>> grid;
vector<int> visited,len; 
//visited: -1 ; 0-discovered; 1-assigned

void dfs(int node){
	if(grid[node].size() == 0){
		visited[node] = 0;
		return;
	}

	int elem = INT_MIN;
	for(auto p: grid[node]){
		if(visited[p] == -1)
			dfs(p);
		elem = max(elem, visited[p]);
	}

	visited[node] = max(visited[node], elem+1);
}

int main(){

    FAST
	
	int n,m;
	cin>>n>>m;

	grid = vector<vector<int>> (n+1);
	
	for(int i=0;i<m;i++){
		int u,v;
		cin>>u>>v;
		grid[u].pb(v);
	}

	visited = vector<int> (n+1,-1);
	
	for(int i=1;i<=n;i++)
	{
		if(visited[i] == -1)
		{
			dfs(i);
		}
	}

	int ans = INT_MIN;
	for(auto elem: visited){
		ans = max(ans,elem);
	}
	cout<<ans<<"\n";
    return 0;
}