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: Runtime Error)

#include<bits/stdc++.h>
#include <string> 
using namespace std;
#include <string> 
#define fast ios_base::sync_with_stdio(false);	cin.tie(NULL);
typedef long long ll;
#define MAX 1000000000
const int maxn=10000;
string ma="";
int dis[maxn];
int vis[maxn];
vector<int> v[maxn];
void reset(){
    for(int i=0;i<maxn;i++)
    {
        dis[i]=0;
        vis[i]=-1;
    }
}
void DFS(int s)
{
    //vis[s]=1;
    for(int x:v[s])
    {   
        if(dis[x]<dis[s]+1)
            dis[x]=dis[s]+1;
        DFS(x);

    }
}
int main()
{
	fast;
    int n,m,i,x,y;
    cin>>n>>m;
    for(i=0;i<m;i++)
    {    cin>>x>>y;
        v[x].push_back(y);
    }
    reset();
    for(i=1;i<=n;i++)
    {   
        if(vis[i]==-1){
            DFS(i);
            vis[i]=1;
        }
    }
    int z=0;
    for(i=1;i<=n;i++){
        //cout<<dis[i];
        z=max(z,dis[i]);
    }
    cout<<z;
    return 0;
}