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: Wrong Answer)

#include<bits/stdc++.h>
#define fast ios_base::sync_with_stdio(false),cin.tie(NULL)
#define frr(i,s,n) for(int i=s;i<=n;i++)
#define fr(i,s,n) for(int i=s;i<n;i++)
#define lli long long int
#define llu unsigned long long int
#define vi vector <int>
#define vii vector <long long int>
#define pb push_back
#define eb emplace_back
#define pi pair<int,int>
#define mk make_pair
#define mpp map<int,int>
#define ff first
#define ss second
#define mod 1000000007

using namespace std;

vector <int> v[100001];
vector<int> vis(100001);
int cnt = 0;

void dfs(int node)
{
	vis[node] = 1;
	for(auto child : v[node])
	{
		if(!vis[child])
		{
			dfs(child);
			cnt++;
		}
	} 
}
void loop()
{
	int n,m;
	cin>>n>>m;
	for(int i=1;i<=m;i++)
	{
		int a,b;
		cin>>a>>b;
		v[a].pb(b);
	}
	int mx = 0;
	for(int i=1;i<=n;i++)
	{
		dfs(i);
		//cout<<cnt<<"\n";
		mx = max(mx,cnt);
		cnt = 0;
		vis.clear();
	}
	cout<<mx<<"\n";
}
int main()
{
	// #ifndef ONLINE_JUDGE
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	// #endif
	fast;
    int t=1;
    //cin>>t;
    while(t--)
    	loop();
}