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"
class Hash
  include TSort
  alias tsort_each_node each_key
  def tsort_each_child(node, &block)
    fetch(node).each(&block)
  end
end
N,M =gets.split.map &:to_i
@has=Hash.new
for i in 1..N
  @has[i]=Array.new
end
for i in 1..M
  d=gets.split.map &:to_i
  @has[d[0]] << d[1]
end
@idx=@has.tsort
# p @has
# p @idx
@memo=Array.new(N+1,nil)

def dp(n)
  return @memo[n] if !@memo[n].nil?
  if @has[n].empty?
    @memo[n]=0
    return 0
  else
    output=(@has[n].map{|x|dp(x)}.max)+1
    @memo[n]=output
    return output
  end
end
max=0
for i in 1..N
  cnt=dp(@idx.index(i)+1)
  max = max < cnt ? cnt : max
end
puts max