"""simple docstring"""






import functools
from typing import Any



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):

				# 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
				UpperCAmelCase__             =							{}
				UpperCAmelCase__             =							'WORD_KEEPER'

				for word in words:
								UpperCAmelCase__             =							trie
								for c in word:
												if c not in trie_node:
																UpperCAmelCase__             =							{}

												UpperCAmelCase__             =							trie_node[c]

								UpperCAmelCase__             =							True

				UpperCAmelCase__             =							len(lowerCamelCase       )

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

								UpperCAmelCase__             =							trie
								for i in range(lowerCamelCase					,			lowerCamelCase       ):
												UpperCAmelCase__             =							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()






from __future__ import annotations

from typing import Any


class       SCREAMING_SNAKE_CASE__					:





    def __init__(      self						,   a						,   a						,   a = 0):
         lowercase__      , lowercase__    :   Dict      =       row, column
         lowercase__    :   Optional[Any]      =       [[default_value for c in range(a)] for r in range(a)]





    def __str__(      self):
         lowercase__    :   Tuple      =       f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

         # Make string identifier
         lowercase__    :   Optional[int]      =       0
         for row_vector in self.array:
              for obj in row_vector:
                   lowercase__    :   List[str]      =       max(a						,   len(str(a)))
         lowercase__    :   Optional[int]      =       f"""%{max_element_length}s"""

         # Make string and return
         def single_line(a) -> str:
              nonlocal string_format_identifier
              lowercase__    :   Tuple      =       '['
              line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
              line += "]"
              return line

         s += "\n".join(single_line(a) for row_vector in self.array)
         return s





    def __repr__(      self):
         return str(self)





    def       snake_case_				(      self						,   a):
         if not (isinstance(a						,   (list, tuple)) and len(a) == 2):
              return False
         elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
              return False
         else:
              return True





    def __getitem__(      self						,   a):
         assert self.validate_indicies(a)
         return self.array[loc[0]][loc[1]]





    def __setitem__(      self						,   a						,   a):
         assert self.validate_indicies(a)
         lowercase__    :   List[str]      =       value





    def __add__(      self						,   a):
         assert isinstance(a						,   a)
         assert self.row == another.row and self.column == another.column

         # Add
         lowercase__    :   List[str]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   Dict      =       self[r, c] + another[r, c]
         return result





    def __neg__(      self):
         lowercase__    :   List[Any]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   int      =       -self[r, c]
         return result





    def __sub__(      self						,   a):
         return self + (-another)





    def __mul__(      self						,   a):

         if isinstance(a						,   (int, float)):  # Scalar multiplication
              lowercase__    :   Optional[Any]      =       Matrix(self.row						,   self.column)
              for r in range(self.row):
                   for c in range(self.column):
                        lowercase__    :   Union[str, Any]      =       self[r, c] * another
              return result
         elif isinstance(a						,   a):  # Matrix multiplication
              assert self.column == another.row
              lowercase__    :   List[Any]      =       Matrix(self.row						,   another.column)
              for r in range(self.row):
                   for c in range(another.column):
                        for i in range(self.column):
                             result[r, c] += self[r, i] * another[i, c]
              return result
         else:
              lowercase__    :   Optional[Any]      =       f"""Unsupported type given for another ({type(a)})"""
              raise TypeError(a)





    def       snake_case_				(      self):
         lowercase__    :   Optional[int]      =       Matrix(self.column						,   self.row)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   str      =       self[r, c]
         return result





    def       snake_case_				(      self						,   a						,   a):
         assert isinstance(a						,   a) and isinstance(a						,   a)
         assert self.row == self.column == u.row == v.row  # u, v should be column vector
         assert u.column == v.column == 1  # u, v should be column vector

         # Calculate
         lowercase__    :   int      =       v.transpose()
         lowercase__    :   Tuple      =       (v_t * self * u)[0, 0] + 1
         if numerator_factor == 0:
              return None  # It's not invertable
         return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

       def 	snake_case__			(    ):



            '''simple docstring'''





            lowercase__    :   Any      =       Matrix(3	,     3	,     0			)
            for i in range(3			):
                 lowercase__    :   str      =       1
            print(f"""a^(-1) is {ainv}"""			)
            # u, v
            lowercase__    :   Optional[Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   List[Any]      =       1, 2, -3
            lowercase__    :   Union[str, Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   Any      =       4, -2, 5
            print(f"""u is {u}"""			)
            print(f"""v is {v}"""			)
            print(f"""uv^T is {u * v.transpose()}"""			)
            # Sherman Morrison
            print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			)}"""			)

       def 	snake_case__			(    ):



            '''simple docstring'''





            import doctest

            doctest.testmod()

       testa()

