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)

//       In the name of         ****                      God                     ****

/*

Copyright (C)          JadedBeast

                                   Morocco

created : 19/3/2019

*/

#include <bits/stdc++.h>

using namespace std;

inline void JadedBeast() {
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
}
const int MAX=1e5+1;
int n,m,x,y;
vector <int> v[MAX];
bool used[MAX];
int d[MAX];
int connected[MAX];
int ans=0;
void addEdge(int x , int y){
	v[x].push_back(y);
}
void dfs(int s){
    if(used[s])return;
    used[s] = true;
    for(int x: v[s]){
        d[x] = max(d[x],d[s]+1);
        connected[x]--;
        if(connected[x]==0)
            dfs(x);
        
    }
}
int main() {
	JadedBeast();
	memset(used,false,sizeof(used));
	memset(d,0,sizeof(d));
	memset(connected,0,sizeof(connected));
	cin >> n >> m;
	for(int i=0 ; i<m ;i++){
		cin >>x >> y;
		addEdge(x,y);
		connected[y]++;
	}

	for(int i=1 ; i<=n ; i++)
		if(!used[i])
			dfs(i);
	for(int x:d)
        ans = max(ans,x);
    
	cout << ans <<endl;

    return 0;
}