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>
#define M 1000000007
#define pb push_back
#define ll long long int
using namespace std;

void dfs(vector<int> g[],int i,int vis[],stack<int> &s)
{
	vis[i] = 1;
	for(auto it : g[i])
	{
		if(vis[it])
			continue;
		dfs(g,it,vis,s);
	}
	s.push(i);
}


int main()
{
	int n,m;
	cin>>n>>m;
	vector<int> g[n];
	int i;
	for(i = 0;i<m;i++)
	{
		int x,y;
		cin>>x>>y;
		x--;y--;
		g[x].pb(y);
	}
	int vis[n]={0};
	stack<int> s;
	for(i=0;i<n;i++)
	{
		if(vis[i])
			continue;
		dfs(g,i,vis,s);
	}
	vector<int> v;
	while(!s.empty())
	{
		v.pb(s.top());
		s.pop();
	}
	int ans[n] = {0};
	int maxs = 0;
	for(i=n-1;i>=0;i--)
	{	
		ans[v[i]] = 0;
		for(auto it : g[v[i]])
		{
			ans[v[i]] = max(ans[v[i]],1+ans[it]);
		}
		maxs = max(maxs,ans[v[i]]);
	}
	cout<<maxs;
	return 0;

}