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: Time Limit Exceeded)

use proconio::{fastout, input};

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

    let mut graph: Vec<Vec<usize>> = vec![vec![]; n];
    let mut dp: Vec<usize> = vec![std::usize::MAX; n];

    for _ in 0..m {
        input! {
            x: usize,
            y: usize
        }
        graph[x - 1].push(y - 1);
    }

    let mut ans = 0;
    for i in 0..n {
        ans = std::cmp::max(ans, f(i, &graph, &mut dp));
    }

    println!("{}", ans);
}

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

    let mut res = 0;

    for &next in graph[node].iter() {
        res = std::cmp::max(res, f(next, graph, dp) + 1);
    }

    res
}