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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::{input, fastout};
use proconio::marker::Usize1;
use std::collections::{HashMap, HashSet};

macro_rules! echo {
  ($val:expr) => {
    println!("{}", $val);
  }
}

fn dfs(dp: &mut Vec<Option<usize>>, edges: &HashMap<usize, Vec<usize>>, x: usize) -> usize {
  if dp[x].is_some() {
    return dp[x].unwrap();
  }
  if edges[&x].len() == 0 {
    return 0;
  }
  let ch = edges[&x].iter().map(|y| dfs(dp, edges, *y)).max().unwrap() + 1;
  dp[x] = Some(ch);
  return ch;
}

#[fastout]
fn main() {
  input!{
    n: usize,
    m: usize,
    xy: [(Usize1, Usize1); m]
  };

  let mut edges : HashMap<usize, Vec<usize>> = HashMap::new();
  let mut inputs = HashSet::new();
  for i in 0..n {
    edges.insert(i, vec![]);
  }
  for (x, y) in xy {
    edges.get_mut(&x).unwrap().push(y);
    inputs.insert(y);
  }

  let starts : Vec<usize> = (0..n).filter(|x| !inputs.contains(x)).collect();

  let mut dp : Vec<Option<usize>> = vec![None; n];

  let mut ans = Vec::new();
  for start in starts {
    ans.push(dfs(&mut dp, &edges, start));
  }
  let ans = ans.iter().max().unwrap();
  echo!(ans);
}
*/

fn main() {
    let exe = "/tmp/binBCBD6565";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";