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(unused_macros)]
macro_rules! input {
    ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } };
    ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } };
}
#[allow(unused_macros)]
macro_rules! input_inner {
    ( $ next : expr ) => { };
    ( $ next : expr , ) => { };
    ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } };
}
#[allow(unused_macros)]
macro_rules! read_value {
    ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) };
    ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) };
    ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) };
    ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 };
    ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) };
}

#[allow(unused_macros)]
macro_rules! chmax {
    ( $ x : expr , $ y : expr ) => { if $ x < $ y { $ x = $ y ; true } else { false } };
}

fn main() {
    input! {
        n: usize, m: usize,
        xy: [(usize1, usize1); m]
    }

    let mut g = vec![vec![];n];
    for i in 0..m {
        g[xy[i].0].push(xy[i].1);
    }
    let mut dp = vec![None;n];
    let mut ret = 0u64;
    for i in 0..n {
        chmax!(ret, rec(&g, &mut dp, i));
    }
    println!("{}", ret);
}

fn rec(g: &[Vec<usize>], dp: &mut [Option<u64>], c: usize) -> u64 {
    if let Some(src) = dp[c] {
        return src;
    }

    let mut ret = 0u64;
    for &v in &g[c] {
        chmax!(ret, rec(g,dp,v) + 1);
    }
    dp[c] = Some(ret);
    ret
}