





from itertools import count


def _A       (   __magic_name__ = 50	):
   lowercase__			       =  [1] * min_block_length

   for n in count(__magic_name__	):
      fill_count_functions.append(1	)

      for block_length in range(__magic_name__  , n + 1	):
         for block_start in range(n - block_length	):
            fill_count_functions[n] += fill_count_functions[
                n - block_start - block_length - 1
            ]

         fill_count_functions[n] += 1

      if fill_count_functions[n] > 100_0000:
         break

   return n


if __name__ == "__main__":
  print(F"""{solution() = }""")













from __future__ import annotations

from collections import deque





class  lowerCAmelCase							:







  def __init__(      self  :List[Any]   ,							_lowercase  :list[str] ):






     '''simple docstring'''





     lowercase__			       =  []
     self.adlist.append(
         {"value": "", "next_states": [], "fail_state": 0, "output": []} )

     for keyword in keywords:
        self.add_keyword(_lowercase )
     self.set_fail_transitions()







  def   UpperCAmelCase					(      self  :str   ,							_lowercase  :int   ,							_lowercase  :str ):






     '''simple docstring'''





     for state in self.adlist[current_state]["next_states"]:
        if char == self.adlist[state]["value"]:
           return state
     return None







  def   UpperCAmelCase					(      self  :List[str]   ,							_lowercase  :str ):






     '''simple docstring'''





     lowercase__			       =  0
     for character in keyword:
        lowercase__			       =  self.find_next_state(_lowercase   ,							_lowercase )
        if next_state is None:
           self.adlist.append(
               {
                   "value": character,
                   "next_states": [],
                   "fail_state": 0,
                   "output": [],
               } )
           self.adlist[current_state]["next_states"].append(len(self.adlist ) - 1 )
           lowercase__			       =  len(self.adlist ) - 1
        else:
           lowercase__			       =  next_state
     self.adlist[current_state]["output"].append(_lowercase )







  def   UpperCAmelCase					(      self  :int ):






     '''simple docstring'''





     lowercase__			       =  deque()
     for node in self.adlist[0]["next_states"]:
        q.append(_lowercase )
        lowercase__			       =  0
     while q:
        lowercase__			       =  q.popleft()
        for child in self.adlist[r]["next_states"]:
           q.append(_lowercase )
           lowercase__			       =  self.adlist[r]["fail_state"]
           while (
               self.find_next_state(_lowercase   ,							self.adlist[child]["value"] ) is None
               and state != 0
           ):
              lowercase__			       =  self.adlist[state]["fail_state"]
           lowercase__			       =  self.find_next_state(
               _lowercase   ,							self.adlist[child]["value"] )
           if self.adlist[child]["fail_state"] is None:
              lowercase__			       =  0
           lowercase__			       =  (
               self.adlist[child]["output"]
               + self.adlist[self.adlist[child]["fail_state"]]["output"]
           )







  def   UpperCAmelCase					(      self  :Optional[Any]   ,							_lowercase  :str ):






     '''simple docstring'''





     lowercase__			       =  {}  # returns a dict with keywords and list of its occurrences
     lowercase__			       =  0
     for i in range(len(_lowercase ) ):
        while (
            self.find_next_state(_lowercase   ,							string[i] ) is None
            and current_state != 0
        ):
           lowercase__			       =  self.adlist[current_state]["fail_state"]
        lowercase__			       =  self.find_next_state(_lowercase   ,							string[i] )
        if next_state is None:
           lowercase__			       =  0
        else:
           lowercase__			       =  next_state
           for key in self.adlist[current_state]["output"]:
              if key not in result:
                 lowercase__			       =  []
              result[key].append(i - len(_lowercase ) + 1 )
     return result


if __name__ == "__main__":
  import doctest

  doctest.testmod()






