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;

using ll = long long;

const int INF = 1e9 + 5;

template<typename T>
void min_self(T& a, T b)
{
    a = min(a,b);
}

template<typename T>
void max_self(T& a, T b)
{
    a = max(a,b);
}

const int Nax=1e5 + 5;

vector<int> edges[Nax];
bool visited[Nax];
int dist[Nax];
int in[Nax];

void dfs(int a)
{
    //visited[a] = true;
    
    for(int b: edges[a])
    {
        dist[b] = max(dist[b],1+dist[a]);
        
        if(--in[b] == 0)
        {
            dfs(b);
        }
    }
}

int main() {
    
    ios::sync_with_stdio(0);
    cin.tie(0);

    int N, M;
    cin >> N >> M;
    
    int a, b;

    while(M--)
    {
        cin >> a >> b;
        edges[a].push_back(b);
        
        ++in[b];
    }
    
    for(int i=1; i<=N; ++i)
    {
        if(/*!visited[i] && */in[i] == 0)
        {
            dfs(i);
        }
    }
    
    cout << *max_element(dist+1,dist+N+1);
    
}