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)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::cmp::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    }
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
macro_rules! chmax {
    ($x:expr, $e:expr) => {
        $x = max($x, $e);
    };
}
macro_rules! chmin {
    ($x:expr, $e:expr) => {
        $x = min($x, $e);
    };
}

const INF: i64 = 1 << 60;

fn main() {
    input!{
        N: usize,
        M: usize,
        xy: [(usize, usize); M],
    }
    let mut graph = vec![Vec::new(); N + 10];
    let mut deg = vec![0; N + 10];
    for i in 0..M {
        let (x, y) = xy[i];
        graph[x].push(y);
        deg[y] += 1;
    }
    let mut stack = Vec::new();
    for i in 1..(N+1) {
        if deg[i] == 0 {
            stack.push(i);
        }
    }
    let mut sorted_nodes = Vec::new();
    while let Some(i) = stack.pop() {
        sorted_nodes.push(i);
        for &j in &graph[i] {
            deg[j] -= 1;
            if deg[j] == 0 {
                stack.push(j);
            }
        }
    }
    let mut dp = vec![0; N+10];
    for &i in &sorted_nodes {
        for &ni in &graph[i] {
            chmax!(dp[ni], dp[i] + 1);
        }
    }
    let mut ans = 0;
    for i in 1..(N+1) {
        chmax!(ans, dp[i]);
    }
    println!("{}", ans);
}