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: Wrong Answer)


	#include <bits/stdc++.h>
	#include <cstdio>
	#include <cstring>
	#include <cmath>
	#include <cstring>
	#include <chrono>
	#include <complex>
	#define endl "\n"
	#define ll long long int
	#define vi vector<int>
	#define vll vector<ll>
	#define vvi vector < vi >
	#define pii pair<int,int>
	#define pll pair<long long, long long>
	#define mod 1000000007
	#define inf 1000000000000000001;
	#define all(c) c.begin(),c.end()
	#define mp(x,y) make_pair(x,y)
	#define mem(a,val) memset(a,val,sizeof(a))
	#define eb emplace_back
	#define f first
	#define s second
	using namespace std;
	ll n,m;
	vector<ll> adj[100005];
	bool vis[100005]={false};
	ll len[100005]={0};
	ll dfs(ll s)
	{
		vis[s]=true;
		if(adj[s].size()==0)
			len[s]=1;
		for(ll j:adj[s])
		{
			if(vis[j]==false)
				len[s]=max(len[s],dfs(j)+1);
			else
				len[s]=len[j]+1;
		}
		return len[s];
	}
	int main()
	{
		std::ios::sync_with_stdio(false);
		// cin.ignore(); must be there when using getline(cin, s)
		cin>>n>>m;
		ll u,v;
		while(m--)
		{
			cin>>u>>v;
			//cout<<u<<" "<<v<<endl;
			adj[u].push_back(v);
		}
		// for(ll i=1;i<=n;i++)
		// {
		// 	for(ll j:adj[i])
		// 		cout<<adj[i][j]<<" ";
		// 	cout<<endl;
		// }
		for(ll i=1;i<=n;i++){
			//cout<<i<<" ";
			if(!vis[i])
				dfs(i);

		}
		ll ml=0;
		for(ll i=1;i<n;i++)
			ml=max(ml,len[i]);
		cout<<ml;
		return 0;
	}