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)

use std::collections::VecDeque;

fn main() {
    proconio::input! {
        n: usize,
        m: usize,
        edge: [(usize, usize); m]
    };
    let mut dp= vec![0; n];
    let mut cnt = vec![0; n];
    let mut g = vec![Vec::new(); n];
    for &e in &edge {
        cnt[e.0-1] += 1;
        g[e.1-1].push(e.0-1);
    }
    let mut qu = VecDeque::new();
    for i in 0..n {
        if cnt[i] == 0 { qu.push_back(i); }
    }
    while !qu.is_empty() {
        let p = qu.pop_front().unwrap();
        for &next in &g[p] {
            dp[next] = dp[next].max(dp[p]+1);
            cnt[next] -= 1;
            if cnt[next] == 0 { qu.push_back(next); }
        }
    }
    println!("{}", dp.iter().max().unwrap());
}