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 itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

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

    let mut graph = vec![Vec::new(); n];
    let mut indegree = vec![0; n];
    for (u, v) in edges {
        graph[u].push(v);
        indegree[v] += 1;
    }
    let mut que = VecDeque::new();
    for i in 0..n {
        if indegree[i] == 0 {
            que.push_back(i);
        }
    }
    let mut dp = vec![0; n];
    while let Some(u) = que.pop_front() {
        for &v in &graph[u] {
            indegree[v] -= 1;
            if indegree[v] == 0 {
                dp[v] = dp[u] + 1;
                que.push_back(v);
            }
        }
    }
    let res = dp.into_iter().max().unwrap();
    println!("{}", res);
}