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;

fn input_tuple() -> (u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn dfs(i: usize, edges: &Vec<Vec<usize>>, memo: &mut Vec<u64>) -> u64 {
    // println!("{}", i);
    if edges[i].len() == 0 {        
        return 0;
    }
    if memo[i] != 0 {
        return memo[i];
    }
    let mut max = 0;
    for node in &edges[i] {
        let len = dfs(*node, edges, memo) + 1;
        if len > max {
            max = len;
        }
    }
    memo[i] = max;
    return max;
}

fn main() {
    let (n, m) = input_tuple();
    let mut edges: Vec<Vec<usize>> = vec![Vec::new(); (n+1) as usize];
    let mut memo: Vec<u64> = vec![0; (n+1) as usize];
    for i in 1..(n+1) as usize {
        edges[0].push(i);
    }
    for _ in 0..m {
        let (x, y) = input_tuple();
        edges[x as usize].push(y as usize);
    }
    // println!("{:?}", edges);
    println!("{}", dfs(0, &edges, &mut memo) - 1);
}