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)

use std::cmp::*;
use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    let v: Vec<usize> = read_vec();
    let (n, m) = (v[0], v[1]);
    let mut edges = Vec::new();
    for _ in 0..m {
        let a = read_vec::<usize>();
        edges.push((a[0], a[1]));
    }

    let mut outs = HashMap::new();
    let mut ins = HashMap::new();

    for (v1, v2) in edges.clone() {
        (*outs.entry(v1).or_insert(Vec::new())).push(v2);
        *ins.entry(v2).or_insert(0) += 1;
    }

    let mut q = VecDeque::new();
    for v in 0..n + 1 {
        if !ins.contains_key(&v) || ins[&v] == 0 {
            q.push_back(v);
        }
    }

    let mut sorted_vertexes = Vec::new();
    while let Some(v1) = q.pop_front() {
        sorted_vertexes.push(v1);
        if !outs.contains_key(&v1) {
            continue;
        }
        for v2 in outs[&v1].iter() {
            *ins.get_mut(v2).unwrap() -= 1;
            if !ins.contains_key(&v2) || ins[v2] == 0 {
                q.push_back(*v2);
            }
        }
    }

    // println!("{:?}", sorted_vertexes);

    let mut ins = HashMap::new();
    for (v1, v2) in edges {
        (*ins.entry(v2).or_insert(Vec::new())).push(v1);
    }

    let mut dp = vec![0; n + 1];
    for i in 0..n + 1 {
        let i = sorted_vertexes[i];
        if !ins.contains_key(&i) {
            continue;
        }
        for j in ins[&i].iter() {
            dp[i] = max(dp[i], dp[*j] + 1);
        }
    }

    let mut ans = 0;
    for i in 0..n + 1 {
        ans = std::cmp::max(ans, dp[i]);
    }
    println!("{:?}", ans);
}