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 proconio::{input, fastout};
use proconio::marker::Usize1;

macro_rules! chmin {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_min = min!($($cmps),+);
        if $base > cmp_min {
            $base = cmp_min;
            true
        } else {
            false
        }
    }};
}

macro_rules! chmax {
    ($base:expr, $($cmps:expr),+ $(,)*) => {{
        let cmp_max = max!($($cmps),+);
        if $base < cmp_max {
            $base = cmp_max;
            true
        } else {
            false
        }
    }};
}

macro_rules! min {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::min($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::min($a, min!($($rest),+))
    }};
}

macro_rules! max {
    ($a:expr $(,)*) => {{
        $a
    }};
    ($a:expr, $b:expr $(,)*) => {{
        std::cmp::max($a, $b)
    }};
    ($a:expr, $($rest:expr),+ $(,)*) => {{
        std::cmp::max($a, max!($($rest),+))
    }};
}

fn dfs(g: &Vec<Vec<usize>>,
        dp: &mut Vec<usize>,
        used: &mut Vec<bool>,
        i: usize,
        cnt: &mut usize)
-> usize {
    *cnt += 1;
    if used[i] {
        return dp[i];
    }

    used[i] = true;
    let mut res: usize = 0;
    for j in &g[i] {
        chmax!(res, dfs(g, dp, used, *j, cnt) + 1);
    }
    dp[i] = res;
    dp[i]
}

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

    let mut g: Vec<Vec<usize>> = vec![vec![]; n];
    let mut dp: Vec<usize> = vec![0; n];
    let mut used: Vec<bool> = vec![false; n];

    for item in xy {
        g[item.0].push(item.1);
    }

    let mut cnt: usize = 0;
    let mut ans = 0;
    for i in 0..n {
        chmax!(ans, dfs(&g, &mut dp, &mut used, i, &mut cnt));
    }
    println!("{}", ans);

}