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: Runtime Error)

require 'tsort'

N, M = gets.split.map(&:to_i)
g = Hash.new

begin
  dp = Array.new(N + 1, 0)
  (1..N).each do |i|
    g[i] = []
  end

  M.times do
    from, to = gets.split.map(&:to_i)
    g[from] << to
  end

  order = []

  each_node = -> (&b) { g.each_key(&b) }
  each_child = -> (n, &b) { g[n].each(&b) }
  order = TSort.tsort(each_node, each_child).reverse

  order.each do |from|
    g[from].each do |to|
      len = dp[from] + 1
      dp[to] = len if dp[to] < len
    end
  end
ensure
  puts dp.max
end