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::io;
use std::str;

fn dfs(u: usize, graph: &[Vec<usize>], visited: &mut [bool], toposort: &mut Vec<usize>) {
    visited[u] = true;
    for &v in &graph[u] {
        if !visited[v] {
            dfs(v, graph, visited, toposort);
        }
    }
    toposort.push(u);
}

fn solve<R: io::BufRead, W: io::Write>(scan: &mut Scanner<R>, out: &mut W) {
    let n: usize = scan.token();
    let m: usize = scan.token();
    let mut graph = vec![Vec::new(); n];
    for _ in 0..m {
        let u = scan.token::<usize>() - 1;
        let v = scan.token::<usize>() - 1;
        graph[u].push(v);
    }
    let mut visited = vec![false; n];
    let mut toposort = Vec::new();
    for u in 0..n {
        if !visited[u] {
            dfs(u, &mut graph, &mut visited, &mut toposort);
        }
    }

    let mut dp = vec![0; n];
    for &u in toposort.iter().rev() {
        for &v in &graph[u] {
            dp[v] = dp[v].max(1 + dp[u]);
        }
    }

    let mut ans = 0;
    for u in 0..n {
        ans = ans.max(dp[u]);
    }
    writeln!(out, "{}", ans).ok();
}

fn main() {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut scan = Scanner::new(stdin.lock());
    let mut out = io::BufWriter::new(stdout.lock());
    solve(&mut scan, &mut out);
}

pub struct Scanner<R> {
    reader: R,
    buffer: Vec<String>,
}

impl<R: io::BufRead> Scanner<R> {
    pub fn new(reader: R) -> Self {
        Self {
            reader,
            buffer: vec![],
        }
    }

    pub fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buffer.pop() {
                return token.parse().ok().expect("Failed parse");
            }
            let mut input = String::new();
            self.reader.read_line(&mut input).expect("Failed read");
            self.buffer = input.split_whitespace().rev().map(String::from).collect();
        }
    }

    pub fn tokens<T: str::FromStr>(&mut self) -> Vec<T> {
        assert!(self.buffer.is_empty());
        let mut input = String::new();
        self.reader.read_line(&mut input).expect("Failed read");
        input
            .split_whitespace()
            .map(|x| x.parse().ok().expect("Failed parse"))
            .collect()
    }
}