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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, m = gets.split.map(&:to_i)
edges = Array.new(m){gets.split.map(&:to_i)}

moves = Hash.new([])
edges.each{|e| moves[e.first] += [e.last]}

ans = 0
starts = (1..n).to_a - edges.map(&:last)
starts.each do |s|
  d = Array.new(n+1, 0)
  queue = []
  queue.push(s)
  until queue.empty?
    u = queue.pop
    moves[u].each do |v|
      d[v] = d[u] + 1
      queue.push(v)
    end
  end
  d_max = d.max
  ans = d_max if d_max > ans
end
puts ans