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;

struct graph {
  int n;
  vector<vector<int>> g;
  vector<int> dp;
  int res;

  graph(int _n) {
    n = _n;
    g.resize(n);
    dp.resize(n, -1);
    res = 0;
  };
  void add_edge(int a, int b) { g[a].push_back(b); }

  int rec(int i) {
    if (dp[i] != -1) return dp[i];

    for (auto&& w : g[i]) {
      res = max(res, rec(w) + 1);
    }
    return dp[i] = res;
  }

  int solve() {
    for (int i = 0; i < n; i++) {
      rec(i);
    }
    return res;
  }
};

int main() {
  int n, m;
  cin >> n >> m;
  graph gr(n);
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    gr.add_edge(x, y);
  }
  cout << gr.solve() << endl;
}