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)

fn dfs(adjl: &Vec<Vec<usize>>, v: usize, mut memo: &mut Vec<usize>) -> usize {
    if memo[v] != std::usize::MAX {
        memo[v]
    } else {
        let mut res = 0;
        for n in &adjl[v] {
            res = max(res, dfs(&adjl, *n, &mut memo) + 1);
        }
        memo[v] = res;
        res
    }
}

fn main() {
    let (n, m): (usize, usize) = (read::<usize>(), read::<usize>());
    let mut indeg = vec![0; n];
    let mut adjl = vec![vec![]; n];
    let mut leaves = vec![];
    for _ in 0..m {
        let (x, y): (usize, usize) = (read::<usize>() - 1, read::<usize>() - 1);
        adjl[x].push(y);
        indeg[y] += 1;
    }
    for i in 0..n {
        if indeg[i] == 0 {
            leaves.push(i);
        }
    }
    let mut ans = 0;
    for l in leaves {
        let mut memo = vec![std::usize::MAX; n];
        ans = max(dfs(&adjl, l, &mut memo), ans);
    }
    println!("{}", ans);
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: isize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========