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: Time Limit Exceeded)

#![allow(unused_imports)]

#[macro_use]
mod _input {
    use std::fmt;
    use std::io::{self, Read};
    use std::str::{self, FromStr};

    macro_rules! input {
        ($($name:ident : $t:tt),*,) => {
            input!($($name: $t),*)
        };
        ($($name:ident : $t:tt),*) => {
            let mut _scanned = ::_input::Scanned::new(::std::io::stdin(), 1024);
            $(
                let $name = _read_value!(_scanned, $t);
            )*
        };
    }

    macro_rules! _read_value {
        ($scanned:expr, ($($t:tt),*)) => {
            ($(_read_value!($scanned, $t)),*)
        };
        ($scanned:expr, [$t:tt; $n:expr]) => {
            (0..$n).map(|_| _read_value!($scanned, $t)).collect::<Vec<_>>()
        };
        ($scanned:expr, _bytes) => {
            _read_value!($scanned, String).into_bytes()
        };
        ($scanned:expr, _1based) => {
            _read_value!($scanned, usize) - 1
        };
        ($scanned:expr, $t:ty) => {
            $scanned.next::<$t>()
        };
    }

    #[derive(Default)]
    pub struct Scanned {
        buf: Vec<u8>,
        pos: usize,
    }

    impl Scanned {
        pub fn new<R: Read>(mut input: R, estimated: usize) -> Self {
            let mut buf_ = Vec::with_capacity(estimated);
            let _ = io::copy(&mut input, &mut buf_).unwrap();
            if buf_.last() != Some(&b'\n') {
                buf_.push(b'\n'); // input may not end with '\n'
            }
            debug_assert!(str::from_utf8(&buf_).is_ok());
            debug_assert!(buf_.iter().all(|&c| u32::from(c) <= 0x7F));
            Scanned { buf: buf_, pos: 0 }
        }

        #[inline]
        pub fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: fmt::Debug,
        {
            let mut start = None;
            loop {
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
        }
    }
}

#[allow(dead_code)]
mod output {
    use std::io::{self, BufWriter, StdoutLock, Write as _Write};

    pub fn with_stdout<F: FnMut(&mut BufWriter<StdoutLock>)>(mut f: F) {
        let stdout = io::stdout();
        let mut stdout = BufWriter::new(stdout.lock());
        f(&mut stdout);
        stdout.flush().unwrap();
    }
}

use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::Write;
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
};
use std::str::{self, FromStr};
use std::{char, cmp, f32, f64, fmt, i16, i32, i64, i8, mem, thread, u16, u32, u64, u8};

fn main() {
    input! {
        n: usize,
        m: usize,
        xys: [(_1based, _1based); m],
    }
    let (g_rev, ends) = {
        let mut g_rev = vec![vec![]; n];
        let mut is_end = vec![true; n];
        for (x, y) in xys {
            g_rev[y].push(x);
            is_end[x] = false;
        }
        let ends = (0..n).filter(|&x| is_end[x]).collect::<Vec<_>>();
        (g_rev, ends)
    };
    let mut dp = vec![0; n];
    let mut current = ends.into_iter().collect::<BTreeSet<_>>();
    while !current.is_empty() {
        let mut next = BTreeSet::new();
        for &y in &current {
            for &x in &g_rev[y] {
                dp[x] = cmp::max(dp[x], dp[y] + 1);
                next.insert(x);
            }
        }
        current = next;
    }
    let r = dp.into_iter().max().unwrap();
    println!("{}", r);
}