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 (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::io::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque };

#[allow(unused_macros)]
macro_rules! trace {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    };
    ($($args:expr),*) => { trace!(($($args),*)) }
}

#[allow(unused_macros)]
macro_rules! put {
    ($var:expr) => {
        let _ = writeln!(&mut std::io::stdout(), "{}", $var);
    };
    ($var:expr, $($args:expr),*) => {
        let _ = write!(&mut std::io::stdout(), "{} ", $var);
        put!($($args),*);
    };
}

#[derive(Debug)]
struct Topological(Vec<usize>);

impl Topological {

    fn visit(u: usize, mut used: &mut Vec<bool>, rd: &Vec<Vec<usize>>, mut ord: &mut Vec<usize>) {
        if used[u] { return }
        used[u] = true;
        for &v in rd[u].iter() {
            Self::visit(v, &mut used, &rd, &mut ord);
        }
        ord.push(u);
    }

    fn new(neigh: &Vec<Vec<usize>>) -> Self {
        let n = neigh.len();
        let mut rd = vec![vec![]; n];
        for u in 0..n {
            for &v in neigh[u].iter() {
                rd[v].push(u);
            }
        }
        // sort
        let mut used = vec![false; n];
        let mut ord = vec![];
        for u in 0..n { Self::visit(u, &mut used, &rd, &mut ord); }
        Topological(ord)
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();
    let mut g = vec![vec![]; n];
    let mut h = vec![vec![]; n];
    for _ in 0..m {
        let x: usize = sc.cin();
        let y: usize = sc.cin();
        g[x-1].push(y-1);
        h[y-1].push(x-1);
    }

    let Topological(ord) = Topological::new(&g);

    let mut d = vec![0; n];
    for &u in ord.iter() {
        d[u] =
            if let Some(m) = h[u].iter().map(|&i| d[i]).max() {
                m + 1
            } else {
                0
            };
    }

    // trace!(&d);
    let ans = d.iter().max().unwrap();
    put!(ans);

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
}