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)

use std::cmp::*;
use std::io::*;

fn dfs(v: usize, p: usize, memo: &mut Vec<usize>, graph: &Vec<Vec<usize>>) -> usize {
    if memo[v] != 0 {
        return memo[v];
    }
    let mut res = 0;
    for &nv in graph[v].iter() {
        if nv != p {
            res = max(res, dfs(nv, v, memo, &graph) + 1);
        }
    }

    memo[v] = res;
    res
}

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let m: usize = itr.next().unwrap().parse().unwrap();
    let xy: Vec<(usize, usize)> = (0..m)
        .map(|_| {
            (
                itr.next().unwrap().parse::<usize>().unwrap() - 1,
                itr.next().unwrap().parse::<usize>().unwrap() - 1,
            )
        })
        .collect();

    let mut starts = Vec::new();
    let mut degree: Vec<usize> = vec![0; n];
    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); n];
    for i in 0..m {
        graph[xy[i].0].push(xy[i].1);
        degree[xy[i].1] += 1;
    }

    for i in 0..n {
        if degree[i] == 0 {
            starts.push(i);
        }
    }

    let mut ans = 0;
    let memo: Vec<usize> = vec![0; n];
    for start in starts {
        ans = max(ans, dfs(start, 0, &mut memo.clone(), &graph));
    }
    println!("{}", ans);
}