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_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use text_io::*;

fn main() {
    const U_INF: usize = 1 << 50;
    const I_INF: isize = 1 << 50;

    let n: usize = read!();
    let m: usize = read!();
    let mut vertexes = vec![vec![]; n];
    for _ in 0..m {
        let x: usize = read!();
        let y: usize = read!();
        vertexes[y - 1].push(x - 1);
    }

    let mut dp = vec![None; n];

    println!("{}", (0..n).map(|i| memo(i, &vertexes, &mut dp)).max().unwrap() - 1);
}

fn memo(i: usize, vertexes: &Vec<Vec<usize>>, dp: &mut Vec<Option<usize>>) -> usize {
    match dp[i] {
        Some(n) => n,
        None => {
            let bs = vertexes[i].iter().map(|&j| memo(j, vertexes, dp));
            let ans = bs.max().unwrap_or(0) + 1;
            dp[i] = Some(ans);
            ans
        }
    }
}