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;
void util(vector<int> adj[],int s,int& c,int& max_c,vector<bool>&vis)
{
    vis[s]=true;
    c++;
    max_c=max(max_c,c);
    for(auto x:adj[s])
    {
        if(!vis[x])
        {
            util(adj,x,c,max_c,vis);
            vis[x]=false;
            c--;
        }
    }
    vis[s]=false;
    c--;
    return;
}
int main() {
	// your code goes here
	int n,m;
	cin>>n>>m;
	vector<int> adj[n];
	int a,b;
	for(int i=0;i<m;i++)
	{
	    cin>>a>>b;
	    adj[a-1].push_back(b-1);
	}
	vector<bool> vis(n,0);
	int max_c=0;
	int c=0;
	for(int i=0;i<n;i++)
	{
	    if(!vis[i])
	    {
	        util(adj,i,c,max_c,vis);
	    }
	}
	cout<<max_c<<endl;
	return 0;
}