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>
#define ll long long int
using namespace std;
#define MAX 200005
#define MOD 1000000007
#define max(a,b) (a>b?a:b)
#define min(a,b) (a<b?a:b)
#define vi vector<int>
#define ii pair<int,int>
#define vii vector<ii>
#define si set<int>
#define mp map<ll,ll>
#define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
vi v[100005];
ll vis[100005];
ll pathlenght[10005];
ll ans=0;
void call_dfs(int x)
{
	vis[x]=1;
	for(int i=0;i<v[x].size();i++)
	{
			pathlenght[v[x][i]]=max((pathlenght[x]+1),pathlenght[v[x][i]]);
			ans=max(ans,pathlenght[v[x][i]]);
			call_dfs(v[x][i]);
	}

}
int main()
{ 
	fast 
	ll n,m,i,j,a[MAX];
	cin>>n>>m;
	for(i=0;i<m;i++)
	{
		ll y;
		cin>>a[i]>>y;
		v[a[i]].push_back(y);
	}
	memset(vis,0,sizeof(vis));
	memset(pathlenght,0,sizeof(pathlenght));
	//sort(v1.begin(),v1.end());
	for(i=0;i<m;i++)
	{
		if(vis[a[i]]==0)
		{
			pathlenght[a[i]]=0;
			call_dfs(a[i]);
		}
	}
	cout<<ans;


}