




from __future__ import annotations

from typing import Any







class a			:
						"""simple docstring"""

						def __init__(			self			:  List[str]					,				lowerCamelCase__			:  int					,				lowerCamelCase__			:  Dict					,				lowerCamelCase__			:  Optional[int] = 0					)     ->    None:
													"""simple docstring"""


													__lowercase  ,  __lowercase			  =     row, column
													__lowercase			  =     [[default_value for c in range(UpperCAmelCase_					)] for r in range(UpperCAmelCase_					)]






						def __str__(			self			:  int					)     ->    str:
													"""simple docstring"""


													__lowercase			  =     f'Matrix consist of {self.row} rows and {self.column} columns\n'

													# Make string identifier
													__lowercase			  =     0
													for row_vector in self.array:
																				for obj in row_vector:
																											__lowercase			  =     max(UpperCAmelCase_					,				len(str(UpperCAmelCase_					)					)					)
													__lowercase			  =     f'%{max_element_length}s'

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

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






						def __repr__(			self			:  Dict					)     ->    str:
													"""simple docstring"""


													return str(self					)






						def      UpperCAmelCase_   (			self			:  List[str]					,				lowerCamelCase__			:  List[Any]					)     ->    bool:
													"""simple docstring"""


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






						def __getitem__(			self			:  int					,				lowerCamelCase__			:  Optional[int]					)     ->    Any:
													"""simple docstring"""


													assert self.validate_indicies(UpperCAmelCase_					)
													return self.array[loc[0]][loc[1]]






						def __setitem__(			self			:  Optional[Any]					,				lowerCamelCase__			:  Dict					,				lowerCamelCase__			:  Tuple					)     ->    None:
													"""simple docstring"""


													assert self.validate_indicies(UpperCAmelCase_					)
													__lowercase			  =     value






						def __add__(			self			:  Any					,				lowerCamelCase__			:  Optional[Any]					)     ->    Matrix:
													"""simple docstring"""


													assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_					)
													assert self.row == another.row and self.column == another.column

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






						def __neg__(			self			:  Tuple					)     ->    Matrix:
													"""simple docstring"""


													__lowercase			  =     Matrix(self.row					,				self.column					)
													for r in range(self.row					):
																				for c in range(self.column					):
																											__lowercase			  =     -self[r, c]
													return result






						def __sub__(			self			:  Optional[Any]					,				lowerCamelCase__			:  Any					)     ->    Matrix:
													"""simple docstring"""


													return self + (-another)






						def __mul__(			self			:  List[str]					,				lowerCamelCase__			:  Any					)     ->    Matrix:
													"""simple docstring"""


													if isinstance(UpperCAmelCase_					,				(int, float)					):  # Scalar multiplication
																				__lowercase			  =     Matrix(self.row					,				self.column					)
																				for r in range(self.row					):
																											for c in range(self.column					):
																																		__lowercase			  =     self[r, c] * another
																				return result
													elif isinstance(UpperCAmelCase_					,				UpperCAmelCase_					):  # Matrix multiplication
																				assert self.column == another.row
																				__lowercase			  =     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			  =     f'Unsupported type given for another ({type(UpperCAmelCase_					)})'
																				raise TypeError(UpperCAmelCase_					)






						def      UpperCAmelCase_   (			self			:  Union[str, Any]					)     ->    Matrix:
													"""simple docstring"""


													__lowercase			  =     Matrix(self.column					,				self.row					)
													for r in range(self.row					):
																				for c in range(self.column					):
																											__lowercase			  =     self[r, c]
													return result






						def      UpperCAmelCase_   (			self			:  Union[str, Any]					,				lowerCamelCase__			:  List[Any]					,				lowerCamelCase__			:  Optional[int]					)     ->    Any:
													"""simple docstring"""


													assert isinstance(UpperCAmelCase_					,				UpperCAmelCase_					) and isinstance(UpperCAmelCase_					,				UpperCAmelCase_					)
													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			  =     v.transpose()
													__lowercase			  =     (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 		_A(							)     ->			Any:
										'''simple docstring'''


										__lowercase			  =     Matrix(3					,							3					,							0					)
										for i in range(3					):
																	__lowercase			  =     1
										print(F'a^(-1) is {ainv}'					)
										# u, v
										__lowercase			  =     Matrix(3					,							1					,							0					)
										__lowercase  ,  __lowercase  ,  __lowercase			  =     1, 2, -3
										__lowercase			  =     Matrix(3					,							1					,							0					)
										__lowercase  ,  __lowercase  ,  __lowercase			  =     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(_snake_case					,							_snake_case					)}'					)







			def 		_A(							)     ->			Tuple:
										'''simple docstring'''


										import doctest

										doctest.testmod()



			testa()











'''simple docstring'''





def 							lowerCamelCase	(					_snake_case	:    str							):





    '''simple docstring'''


    return " ".join(
        "".join(word[::-1]							) if len(_snake_case							) > 4 else word for word in sentence.split()							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(reverse_long_words("Hey wollef sroirraw"))




