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::io::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let m: usize = input();
    let xy: Vec<(usize, usize)> = (0..m).map(|_| (input(), input())).collect();

    let mut e = vec![vec![]; n];
    for &(x, y) in &xy {
        e[x - 1].push(y - 1);
    }

    let mut m = vec![-1; n];
    let mut ans = 0;
    for i in 0..n {
        ans = std::cmp::max(ans, dfs(i, &e, &mut m));
    }

    println!("{}", ans);
}

fn dfs(cur: usize, edge: &Vec<Vec<usize>>, m: &mut Vec<i64>) -> i64 {
    if m[cur] >= 0 {
        m[cur]
    } else {
        let mut mx = 0;
        for &next in &edge[cur] {
            mx = std::cmp::max(mx, 1 + dfs(next, edge, m));
        }

        m[cur] = mx;
        m[cur]
    }
}