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: Accepted)


use std::collections::*;
// use std::io::prelude;
use std::io;
use std::io::Read;
use std::cmp::*;

fn main(){
    let t_cases = 1;
    for _ in 0..t_cases{
        solve();
    }
}

fn solve(){
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    let a = buf
                .trim()
                .split_whitespace()
                .map(|x| x.parse::<usize>().unwrap())
                .collect::<Vec<usize>>();
    let (n,m) = (a[0],a[1]);
    let mut g = vec![vec![];n+1];
    for i in 0..m{
        let mut buf = String::new();
        io::stdin().read_line(&mut buf).unwrap();
        let a = buf
                    .trim()
                    .split_whitespace()
                    .map(|x| x.parse::<usize>().unwrap())
                    .collect::<Vec<usize>>();
        g[a[0]].push(a[1]);
    }
    let mut dp = vec![-1i32;n+1];
    fn dfs(g:& Vec<Vec<usize>>, x:usize,dp:&mut Vec<i32>)->i32{
        if dp[x] != -1{return dp[x];}
        dp[x] = 0;
        for &item in &g[x]{
            dp[x] = max(dfs(g, item, dp)+1,dp[x]);
        }
        return dp[x];
    }
    let mut res = 0;
    for i in 1..(n+1){
        res = max(res, dfs(&g,i,&mut dp));
    }
    println!("{}",res);
}