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 <iostream>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <stack>
#include <vector>
using namespace std;

vector <int> graph[100005];
int distance[100005];
bool visited[100005];
int paths[100005];

void dfs (int a) {
    if (!visited[a]){
        visited[a] = true;
        for (int b : graph[a]){
            int pom = max(::distance[b], ::distance[a] + 1);
            ::distance[b] = pom;
            paths[b]--;
            if (paths[b] == 0)
            dfs(b);
        }
    }
}



int main()
{
    int N, K, a, b;
    cin >> N >> K;
    for (int i = 0; i < K; i++){
        cin >> a >> b;
        graph[a].push_back(b);
        paths[b]++;
    }
    
    for (int i = 1; i < N + 1; i++){
        if (!visited[i])
            dfs(i);
    }
    int ans = 0;
    for (int i = 1; i < N + 1; i++){
        ans = max(ans, ::distance[i]);
    }    
    cout << ans;
}