
'''simple docstring'''




import functools
from typing import Any







def 		lowerCAmelCase_				(   snake_case__		,				snake_case__						):




    '''simple docstring'''



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

    if not isinstance(snake_case__		,				snake_case__						) or not all(
        isinstance(snake_case__		,				snake_case__						) and len(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       :   Union[str, Any]					=						'''WORD_KEEPER'''

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

            A       :   Tuple					=						trie_node[c]

        A       :   int					=						True

    A       :   str					=						len(snake_case__						)

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

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

            if trie_node is None:
                return False

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

        return False

    return is_breakable(0						)


if __name__ == "__main__":
      import doctest

      doctest.testmod()








def 				UpperCamelCase_(      lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )    ->						float:
    _lowercase       :							Tuple      		=		(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
    # formula for sum of series
    return total



def 				UpperCamelCase_(      )    ->						Optional[int]:
    print(sum_of_series(1							, 1							, 10 ) )


if __name__ == "__main__":
 import doctest

 doctest.testmod()


