





import functools
from typing import Any
def      _A       (		SCREAMING_SNAKE_CASE     :   str       ,       SCREAMING_SNAKE_CASE     :   list[str]						):





  """simple docstring"""



  if not isinstance(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) or len(SCREAMING_SNAKE_CASE						) == 0:
    raise ValueError("the string should be not empty string"						)

  if not isinstance(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) or not all(
      isinstance(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) and len(SCREAMING_SNAKE_CASE						) > 0 for item in words						):
    raise ValueError("the words should be a list of non-empty strings"						)

  # Build trie
  a__	:					dict[str, Any]										={}
  a__	:					List[Any]										="WORD_KEEPER"

  for word in words:
    a__	:					Union[str, Any]										=trie
    for c in word:
      if c not in trie_node:
        a__	:					Optional[Any]										={}

      a__	:					str										=trie_node[c]

    a__	:					str										=True

  a__	:					Any										=len(SCREAMING_SNAKE_CASE						)

  # Dynamic programming method
  @functools.cache
  def is_breakable(SCREAMING_SNAKE_CASE     :   int						) -> bool:
    if index == len_string:
      return True

    a__	:					Union[str, Any]										=trie
    for i in range(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						):
      a__	:					Union[str, Any]										=trie_node.get(string[i]       ,       SCREAMING_SNAKE_CASE						)

      if trie_node is None:
        return False

      if trie_node.get(SCREAMING_SNAKE_CASE       ,       SCREAMING_SNAKE_CASE						) and is_breakable(i + 1						):
        return True

    return False

  return is_breakable(0						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()













from math import pi
def      _A       (		SCREAMING_SNAKE_CASE     :   int       ,       SCREAMING_SNAKE_CASE     :   int						):





  """simple docstring"""



  return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
     print(arc_length(90, 10))






