



from __future__ import annotations

from typing import Any




class 							lowerCAmelCase__  :







					def __init__(       self      :     str			,		_A      :     int			,		_A      :     int			,		_A      :     float = 0):
											A__    ,       A__	:							Optional[Any]						    = row, column
											A__	:							Optional[int]						    = [[default_value for c in range(UpperCamelCase_)] for r in range(UpperCamelCase_)]







					def __str__(       self      :     Dict):
											A__	:							Tuple						    = F'Matrix consist of {self.row} rows and {self.column} columns\n'

											# Make string identifier
											A__	:							List[str]						    = 0
											for row_vector in self.array:
																	for obj in row_vector:
																							A__	:							Tuple						    = max(UpperCamelCase_			,		len(str(UpperCamelCase_)))
											A__	:							Any						    = F'%{max_element_length}s'

											# Make string and return
											def single_line(_A      :     list[float]) -> str:
																	nonlocal string_format_identifier
																	A__	:							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      :     int):
											return str(self)







					def  _lowercase			(       self      :     str			,		_A      :     tuple[int, int]):
											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      :     List[str]			,		_A      :     tuple[int, int]):
											assert self.validate_indicies(UpperCamelCase_)
											return self.array[loc[0]][loc[1]]







					def __setitem__(       self      :     Tuple			,		_A      :     tuple[int, int]			,		_A      :     float):
											assert self.validate_indicies(UpperCamelCase_)
											A__	:							List[Any]						    = value







					def __add__(       self      :     Any			,		_A      :     Matrix):
											assert isinstance(UpperCamelCase_			,		UpperCamelCase_)
											assert self.row == another.row and self.column == another.column

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







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







					def __sub__(       self      :     Union[str, Any]			,		_A      :     Matrix):
											return self + (-another)







					def __mul__(       self      :     List[str]			,		_A      :     int | float | Matrix):

											if isinstance(UpperCamelCase_			,		(int, float)):  # Scalar multiplication
																	A__	:							Optional[Any]						    = Matrix(self.row			,		self.column)
																	for r in range(self.row):
																							for c in range(self.column):
																													A__	:							Dict						    = self[r, c] * another
																	return result
											elif isinstance(UpperCamelCase_			,		UpperCamelCase_):  # Matrix multiplication
																	assert self.column == another.row
																	A__	:							str						    = 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:
																	A__	:							Optional[int]						    = F'Unsupported type given for another ({type(UpperCamelCase_)})'
																	raise TypeError(UpperCamelCase_)







					def  _lowercase			(       self      :     str):
											A__	:							int						    = Matrix(self.column			,		self.row)
											for r in range(self.row):
																	for c in range(self.column):
																							A__	:							Any						    = self[r, c]
											return result







					def  _lowercase			(       self      :     str			,		_A      :     Matrix			,		_A      :     Matrix):
											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
											A__	:							str						    = v.transpose()
											A__	:							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__       (					)		->		List[str]:







										"""simple docstring"""

										A__	:							Union[str, Any]						    = Matrix(3							,     3							,     0       )
										for i in range(3       ):
																A__	:							Optional[Any]						    = 1
										print(F'a^(-1) is {ainv}'       )
										# u, v
										A__	:							List[Any]						    = Matrix(3							,     1							,     0       )
										A__    ,       A__    ,       A__	:							int						    = 1, 2, -3
										A__	:							str						    = Matrix(3							,     1							,     0       )
										A__    ,       A__    ,       A__	:							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(A__							,     A__       )}'       )
				def 	snake_case__       (					)		->		Any:







										"""simple docstring"""

										import doctest

										doctest.testmod()




				testa()




def 	snake_case__       (					__lowercase							,     __lowercase							,     __lowercase = 0							,     __lowercase = 0       )		->		int:







						"""simple docstring"""

						A__	:							Tuple						    = right or len(__lowercase       ) - 1
						if left > right:
												return -1
						elif list_data[left] == key:
												return left
						elif list_data[right] == key:
												return right
						else:
												return search(__lowercase							,     __lowercase							,     left + 1							,     right - 1       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()