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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <vector>
#include <cmath>
#include <climits>
using namespace std;

vector<vector<int>> adj;
vector<int> dp;

int dfs(int p) {
  if (dp[p] != -1) return dp[p];
  dp[p] = 0;
  for (auto to: adj[p]) {
    dp[p] = max(dp[p], dfs(to) + 1);
  }
  return dp[p];
}

int main() {

  int n, m;
  cin >> n >> m;
  adj.resize(n + 1);
  int u, v;
  for (int i = 0; i < m; ++i) {
    cin >> u >> v;
    adj[u].push_back(v);
  }

  dp = vector<int>(n + 1, -1);
  int ans = 0;
  for (int i = 1; i <= n; ++i) {
    if (dp[i] == -1) {
      ans = max(ans, dfs(i));
    }
  }
  cout << ans << '\n';

  return 0;
}