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::cmp::{min,max};
#[allow(unused_imports)]
use std::collections::{BTreeMap,BTreeSet};
#[allow(unused_imports)]
use std::ops::*;
#[allow(unused_imports)]
use std::collections::BinaryHeap;

#[allow(unused_macros)]
macro_rules! ite {
    ($c:expr, $t:expr, $f:expr) => {{
        if $c { $t } else { $f }
    }};
}

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

fn dfs(edges: &Vec<Vec<usize>>, i: usize, max_path_len: &mut Vec<Option<i64>>) -> i64 {
    if let Some(res) = max_path_len[i] {
        return res;
    }
    let mut res = 0;
    for &next in &edges[i] {
        let next_max_path_len = dfs(edges, next, max_path_len);
        res = max(res, next_max_path_len + 1)
    }
    max_path_len[i] = Some(res);
    res
}

fn main() {
    input! {
        n: usize,
        m: usize,
        st: [(usize1, usize1); m],
    }
    let mut edges = vec![vec![]; n];
    for &(s,t) in &st {
        edges[s].push(t);
    }
    let mut res = 0;
    let mut max_path_len = vec![None; n];
    for i in 0..n {
        let t = dfs(&edges, i, &mut max_path_len);
        res = max(res, t);
    }
    println!("{}", res);
}

use std::io::BufRead;
use std::io;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R:BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len,complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len-1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T:str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            }
            else {
                self.update_buf();
            }
        }
    }
}

struct Writer {
    s: String,
}

use std::fmt::Display;
impl Writer {
    pub fn new() -> Writer {
        Writer {
            s: String::new(),
        }
    }
    pub fn flush(&mut self) {
        print!("{}", self.s);
        self.s.clear();
    }
    pub fn write<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
    }
    pub fn writeln<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
        self.s.push('\n');
    }
    #[allow(dead_code)]
    pub fn write_vec<T: Display>(&mut self, xs: &Vec<T>) {
        if xs.len() == 0 {
            self.writeln("");
            return;
        }
        self.write(&format!("{}", xs[0]));
        for i in 1..xs.len() {
            self.write(&format!(" {}", xs[i]));
        }
        self.writeln("");
    }
}