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)

// Try Educational DP Contest
// author: Leonardone @ NEETSDKASU

fn main() {
	let mut stdin = String::new();
	std::io::Read::read_to_string(
		&mut std::io::stdin(),
		&mut stdin).unwrap();
	let mut stdin = stdin.split_whitespace();
	let mut get = || stdin.next().unwrap();
	macro_rules! get {
		($t:ty) => (get().parse::<$t>().unwrap());
		() => (get!(usize));
	}
	let n = get!();
	let m = get!();
	
	let mut tree = vec![vec![]; n];
	let mut refs = vec![0_i64; n];
	for _ in 0..m {
		let x = get!()-1;
		let y = get!()-1;
		refs[y] += 1;
		tree[x].push(y);
	}
	let mut ps = vec![];
	for i in 0..refs.len() {
		if refs[i] == 0 {
			ps.push(i);
		}
	}
	let mut dp = vec![0; n];
	while let Some(x) = ps.pop() {
		for &y in tree[x].iter() {
			dp[y] = std::cmp::max(dp[y], dp[x]+1);
			refs[y] -= 1;
			if refs[y] == 0 {
				ps.push(y);
			}
		}
	}
	let ans = dp.iter().max().unwrap();
	println!("{}", ans);
}