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)

fn main() {
    proconio::input! {
        n: usize,
        m: usize,
        e: [(usize, usize); m],
    }
    let mut g = vec![vec![]; n + 1];
    let mut deg = vec![0; n + 1];
    for i in 1..=n {
        g[0].push(i);
        deg[i] += 1;
    }
    for (x, y) in e {
        g[x].push(y);
        deg[y] += 1;
    }
    let mut q = vec![];
    let mut stack = vec![0];
    while let Some(v) = stack.pop() {
        q.push(v);
        for &u in g[v].iter() {
            deg[u] -= 1;
            if deg[u] == 0 {
                stack.push(u);
            }
        }
    }
    let mut dp = vec![0; n + 1];
    for &v in q.iter().rev() {
        let mut d = 0;
        for &u in g[v].iter() {
            d = std::cmp::max(d, dp[u] + 1);
        }
        dp[v] = d;
    }
    let ans = dp[0] - 1;
    println!("{}", ans);
}