



from __future__ import annotations

from typing import Any



class 						UpperCAmelCase_					:







							def __init__(     self,    __a,    __a,    __a = 0):

														'''simple docstring'''

														_lowerCAmelCase     ,					_lowerCAmelCase  :							Optional[int]				     =					row, column
														_lowerCAmelCase  :							Any				     =					[[default_value for c in range(UpperCamelCase__)] for r in range(UpperCamelCase__)]







							def __str__(     self):

														'''simple docstring'''

														_lowerCAmelCase  :							Tuple				     =					f"Matrix consist of {self.row} rows and {self.column} columns\n"

														# Make string identifier
														_lowerCAmelCase  :							Any				     =					0
														for row_vector in self.array:
																					for obj in row_vector:
																												_lowerCAmelCase  :							Dict				     =					max(UpperCamelCase__,    len(str(UpperCamelCase__)))
														_lowerCAmelCase  :							Union[str, Any]				     =					f"%{max_element_length}s"

														# Make string and return
														def single_line(__a) -> str:
																					nonlocal string_format_identifier
																					_lowerCAmelCase  :							int				     =					"["
																					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):

														'''simple docstring'''

														return str(self)







							def      snake_case__   (     self,    __a):

														'''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,    __a):

														'''simple docstring'''

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







							def __setitem__(     self,    __a,    __a):

														'''simple docstring'''

														assert self.validate_indicies(UpperCamelCase__)
														_lowerCAmelCase  :							str				     =					value







							def __add__(     self,    __a):

														'''simple docstring'''

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

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







							def __neg__(     self):

														'''simple docstring'''

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







							def __sub__(     self,    __a):

														'''simple docstring'''

														return self + (-another)







							def __mul__(     self,    __a):

														'''simple docstring'''

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







							def      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							Tuple				     =					Matrix(self.column,    self.row)
														for r in range(self.row):
																					for c in range(self.column):
																												_lowerCAmelCase  :							Optional[Any]				     =					self[r, c]
														return result







							def      snake_case__   (     self,    __a,    __a):

														'''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
														_lowerCAmelCase  :							Dict				     =					v.transpose()
														_lowerCAmelCase  :							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        A       (      ):





								'''simple docstring'''




								_lowerCAmelCase  :							Optional[int]				     =					Matrix(3       ,				3       ,				0						)
								for i in range(3						):
															_lowerCAmelCase  :							Any				     =					1
								print(F"a^(-1) is {ainv}"						)
								# u, v
								_lowerCAmelCase  :							Union[str, Any]				     =					Matrix(3       ,				1       ,				0						)
								_lowerCAmelCase     ,					_lowerCAmelCase     ,					_lowerCAmelCase  :							int				     =					1, 2, -3
								_lowerCAmelCase  :							int				     =					Matrix(3       ,				1       ,				0						)
								_lowerCAmelCase     ,					_lowerCAmelCase     ,					_lowerCAmelCase  :							int				     =					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(_lowerCamelCase       ,				_lowerCamelCase						)}"						)






	def        A       (      ):





								'''simple docstring'''




								import doctest

								doctest.testmod()



	testa()





import string






def        A       (      _lowerCamelCase						):





							'''simple docstring'''




							for key in range(len(string.ascii_uppercase						)						):
														_lowerCAmelCase  :							str				     =					""
														for symbol in message:
																					if symbol in string.ascii_uppercase:
																												_lowerCAmelCase  :							List[str]				     =					string.ascii_uppercase.find(_lowerCamelCase						)
																												_lowerCAmelCase  :							Dict				     =					num - key
																												if num < 0:
																																			_lowerCAmelCase  :							Dict				     =					num + len(string.ascii_uppercase						)
																												_lowerCAmelCase  :							Optional[Any]				     =					translated + string.ascii_uppercase[num]
																					else:
																												_lowerCAmelCase  :							int				     =					translated + symbol
														print(F"Decryption using Key #{key}: {translated}"						)






def        A       (      ):





							'''simple docstring'''




							_lowerCAmelCase  :							Tuple				     =					input("Encrypted message: "						)
							_lowerCAmelCase  :							Dict				     =					message.upper()
							decrypt(_lowerCamelCase						)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()
