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(dead_code, unused_variables)]
use proconio::{fastout, input};
use proconio::marker::Usize1;
use std::collections::VecDeque;
use std::cmp::max;

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        edges: [(Usize1, Usize1); m],
    }
    let mut graph = vec![vec![];n];
    let mut indeg = vec![0;n];
    let mut dp = vec![0;n];

    edges.into_iter().for_each(|(x,y)|{
        graph[x].push(y);
        indeg[y] += 1;
    });

    let mut q = VecDeque::new();
    for i in 0..n{
        if indeg[i] == 0{
            q.push_back(i);
        }
    }

    while !q.is_empty(){
        let v = q.pop_front().unwrap();
        for e in &graph[v]{
            let nv = *e;
            indeg[nv] -= 1;
            if indeg[nv] == 0{
                q.push_back(nv);
            }
            dp[nv] = max(dp[nv],dp[v] + 1);
        }
    }
    let ans = dp.into_iter().max().unwrap();
    println!("{}",ans);

}