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::*;
use std::str::FromStr;
use std::cmp::*;

fn func(g: &Vec<Vec<usize>>, dp: &mut Vec<i64>, now: usize) -> i64 {
    if dp[now] == -1 {
        let mut cnt: i64 = 0;
        for i in &g[now] {
            cnt = max(cnt, func(&g, dp, *i) + 1);
        }
        dp[now] = cnt;
    }
    dp[now]
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut g: Vec<Vec<usize>> = vec![Vec::new(); n];
    let mut dp: Vec<i64> = vec![-1; n];
    for _ in 0..m {
        let (a, b) = (read::<usize>() - 1, read::<usize>() - 1);
        g[a].push(b);
    }
    let mut ans: i64 = 0;
    for i in 0..n {
        ans = max(ans, func(&g, &mut dp, i));
    }
    println!("{}", ans);
}

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