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: Accepted)

if !ENV['RUBY_THREAD_VM_STACK_SIZE']
  exec({'RUBY_THREAD_VM_STACK_SIZE'=>'268435456'}, '/usr/bin/ruby', $0)
end

N, M = gets.split.map(&:to_i)
@nodes = Array.new(N + 1) { [] }
M.times.map do
  x, y = gets.split.map(&:to_i)
  @nodes[x] ||= []
  @nodes[x] << y
end

@dp = []

def solve(i)
  return @dp[i] if @dp[i]

  max = 0
  @nodes[i].each do |to|
    solved = solve(to) + 1
    max = solved if solved > max
  end

  @dp[i] = max
  return max
end

ans = 0
1.upto(N) do |i|
  solved = solve(i)
  ans = solved if ans < solved
end

puts ans