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 Rust (1.42.0) (judge verdict: Accepted)

use std::cmp;
use std::option::Option;

type Graph = Vec<(Vec<usize>, Option<usize>)>;

fn computeLengthFrom(mut graph: &mut Graph, from: usize) -> usize {
  if let Some(len) = graph[from].1 {
    return len;
  };
  let mut max = 0;
  for j in 0..graph[from].0.len() {
    let k = graph[from].0[j];
    let size = computeLengthFrom(&mut graph, k);
    max = cmp::max(max, size + 1);
  };
  graph[from].1 = Some(max);
  max
}

fn main() {
  
  let nm = read::<usize>();
  let n = nm[0];
  let m = nm[1];
  let mut graph: Vec<(Vec<usize>, Option<usize>)> = vec![(vec![], None); n];
  for _ in 0..m {
    let xy = read::<usize>();
    graph[xy[0]-1].0.push(xy[1]-1);
  }
  
  let mut max = 0;
  for i in 0..n {
    let size = computeLengthFrom(&mut graph, i);
    max = cmp::max(max, size);
  }
  
  println!("{}", max);
}

fn read<T: std::str::FromStr>() -> Vec<T> {
  gets().split_whitespace().filter_map(|s|s.parse().ok()).collect()
}

fn gets() -> String {
  let mut line = String::new();
  std::io::stdin().read_line(&mut line).ok();
  line.trim().to_string()
}