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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::Reverse;

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Chars, Usize1},
};

#[allow(unused_imports)]
use itertools::Itertools;

fn rec(node: usize, dp: &mut [usize], graph: &[Vec<usize>]) -> usize {
    if dp[node] != std::usize::MAX {
        return dp[node];
    }

    let mut result = 0;
    graph[node].iter().for_each(|v| {
        result = result.max(rec(*v, dp, graph) + 1);
    });
    dp[node] = result;
    result
}

#[fastout]
pub fn main() {
    input! {
        n: usize,
        m: usize,
        edges: [(Usize1, Usize1); m],
    }

    let mut graph = vec![Vec::new(); n];
    edges.into_iter().for_each(|(x, y)| {
        graph[x].push(y);
    });
    let mut dp = vec![std::usize::MAX; n];

    println!(
        "{}",
        (0..n)
            .into_iter()
            .map(|i| rec(i, &mut dp, &graph))
            .max()
            .unwrap()
    );
}