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 main() {
    let (n, m) = read_tuple();
    let mut g: Vec<Vec<usize>> = Vec::new();
    for _ in 0..n+1 {
       g.push(Vec::new());
    }
    for _ in 0..m {
        let (x, y) = read_tuple();
        g[x].push(y);
    }

    let mut res: i32 = 0;
    let mut dp = vec![-1; n+1];
    for i in 1..n+1 {
        chmax(&mut res, dfs(&g, i, &mut dp));
    }

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

fn dfs(g: &Vec<Vec<usize>>, i: usize, dp: &mut Vec<i32>) -> i32 {
    if dp[i] != -1 {
        return dp[i]
    }

    let mut res = 0;
    for n in g[i].clone() {
        chmax(&mut res, dfs(g, n, dp) + 1);
    }

    res
}

fn chmax(a: &mut i32, b: i32) {
    if *a < b {
        *a = b;
    }
}

fn read_tuple() -> (usize, usize) {
    let v = read_vec::<usize>();
    (v[0], v[1])
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}