



"""simple docstring"""
import functools
from typing import Any





def      __magic_name__				(							lowercase							,			lowercase ):

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

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

   # Build trie
   SCREAMING_SNAKE_CASE_: dict[str, Any]     			={}
   SCREAMING_SNAKE_CASE_: Any     			='WORD_KEEPER'

   for word in words:
      SCREAMING_SNAKE_CASE_: Optional[Any]     			=trie
      for c in word:
         if c not in trie_node:
            SCREAMING_SNAKE_CASE_: Optional[int]     			={}

         SCREAMING_SNAKE_CASE_: str     			=trie_node[c]

      SCREAMING_SNAKE_CASE_: Any     			=True

   SCREAMING_SNAKE_CASE_: List[Any]     			=len(lowerCamelCase_ )

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

      SCREAMING_SNAKE_CASE_: Optional[int]     			=trie
      for i in range(lowerCamelCase_							,			lowerCamelCase_ ):
         SCREAMING_SNAKE_CASE_: Dict     			=trie_node.get(string[i]							,			lowerCamelCase_ )

         if trie_node is None:
            return False

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

      return False

   return is_breakable(0 )


if __name__ == "__main__":
   import doctest

   doctest.testmod()








"""simple docstring"""
from math import pi





def      __magic_name__				(							lowercase							,			lowercase ):
   return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
   print(arc_length(9_0, 1_0))



