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>
using namespace std;
#pragma GCC optimize("Ofast") 
#define int long long
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);
#define pb push_back 
#define eb emplace_back
#define fn for(int i =0 ;i <n;i++)
#define fn1 for( int i =1;i<=n;i++)
#define fm for(int j =0 ;j <m;j++)
#define fm1 for(int j =1;j<=m;j++)
#define fi first
#define se second
#define endl '\n'
# define PI  3.14159265358979323846
#define MOD 1000000007
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
const int N = 2e6+5;
const int INF = 1e18L;
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}
int indeg[N];
int dp[N];
int ans;
vector<int>v[N];
void dfs(int s){
	for(auto i : v[s]){
		indeg[i]--;
		dp[i] = max(dp[i] ,1+dp[s]);
		if(indeg[i]==0){
			dfs(i);
		}
	}
}
signed main(){
	// #ifndef ONLINE_JUDGE
	// freopen("input.txt","r",stdin);
	// freopen("output.txt","w",stdout);
	// #endif
	IOS;
	int T=1;
	// cin >> T;
	while(T--){
		int n,m;
		cin >> n >> m;
		fm{
			int x,y;
			cin>>x>>y;
			v[x].pb(y);
			indeg[y]++;
		}
		fn1{
			if(!indeg[i]){
				dfs(i);
			}
		}
		fn1{
			ans= max(ans,dp[i]);
		}
		cout <<ans ;
	
	
	}
	cerr << "Time Taken : " << 1.0 * clock() / CLOCKS_PER_SEC << " sec \n";
	return 0;
}