




from __future__ import annotations





class 					snake_case_   :



				'''simple docstring'''





				def __init__(      self							:   Optional[int]      ,							__magic_name__							:   list[list[int]]							)							->			str:
											lowerCamelCase_			:    str   						=      TypeError(
											    "Matrices must be formed from a list of zero or more lists containing at "
											    "least one and the same number of values, each of which must be of type "
											    "int or float."							)
											if len(__magic_name__							) != 0:
																		lowerCamelCase_			:    List[str]   						=      len(rows[0]							)
																		if cols == 0:
																									raise error
																		for row in rows:
																									if len(__magic_name__							) != cols:
																																raise error
																									for value in row:
																																if not isinstance(__magic_name__      ,							(int, float)							):
																																							raise error
																		lowerCamelCase_			:    Any   						=      rows
											else:
																		lowerCamelCase_			:    List[Any]   						=      []





				def    __SCREAMING_SNAKE_CASE     (      self							:   int							)							->			list[list[int]]:
											return [[row[i] for row in self.rows] for i in range(len(self.rows[0]							)							)]





				@property
				def    __SCREAMING_SNAKE_CASE     (      self							:   Union[str, Any]							)							->			int:
											return len(self.rows							)





				@property
				def    __SCREAMING_SNAKE_CASE     (      self							:   Any							)							->			int:
											return len(self.rows[0]							)





				@property
				def    __SCREAMING_SNAKE_CASE     (      self							:   str							)							->			tuple[int, int]:
											return (self.num_rows, self.num_columns)





				@property
				def    __SCREAMING_SNAKE_CASE     (      self							:   Optional[int]							)							->			bool:
											return self.order[0] == self.order[1]





				def    __SCREAMING_SNAKE_CASE     (      self							:   List[str]							)							->			Matrix:
											lowerCamelCase_			:    List[str]   						=      [
											    [0 if column_num != row_num else 1 for column_num in range(self.num_rows							)]
											    for row_num in range(self.num_rows							)
											]
											return Matrix(__magic_name__							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   str							)							->			int:

											if not self.is_square:
																		return 0
											if self.order == (0, 0):
																		return 1
											if self.order == (1, 1):
																		return int(self.rows[0][0]							)
											if self.order == (2, 2):
																		return int(
																		    (self.rows[0][0] * self.rows[1][1])
																		    - (self.rows[0][1] * self.rows[1][0])							)
											else:
																		return sum(
																		    self.rows[0][column] * self.cofactors().rows[0][column]
																		    for column in range(self.num_columns							)							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   Any							)							->			bool:
											return bool(self.determinant()							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   str      ,							__magic_name__							:   int      ,							__magic_name__							:   int							)							->			int:
											lowerCamelCase_			:    Optional[int]   						=      [
											    [
											        self.rows[other_row][other_column]
											        for other_column in range(self.num_columns							)
											        if other_column != column
											    ]
											    for other_row in range(self.num_rows							)
											    if other_row != row
											]
											return Matrix(__magic_name__							).determinant()





				def    __SCREAMING_SNAKE_CASE     (      self							:   Optional[int]      ,							__magic_name__							:   int      ,							__magic_name__							:   int							)							->			int:

											if (row + column) % 2 == 0:
																		return self.get_minor(__magic_name__      ,							__magic_name__							)
											return -1 * self.get_minor(__magic_name__      ,							__magic_name__							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   int							)							->			Matrix:
											return Matrix(
											    [
											        [self.get_minor(__magic_name__      ,							__magic_name__							) for column in range(self.num_columns							)]
											        for row in range(self.num_rows							)
											    ]							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   str							)							->			Matrix:
											return Matrix(
											    [
											        [
											            self.minors().rows[row][column]
											            if (row + column) % 2 == 0
											            else self.minors().rows[row][column] * -1
											            for column in range(self.minors().num_columns							)
											        ]
											        for row in range(self.minors().num_rows							)
											    ]							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   List[str]							)							->			Matrix:
											lowerCamelCase_			:    List[str]   						=      [
											    [self.cofactors().rows[column][row] for column in range(self.num_columns							)]
											    for row in range(self.num_rows							)
											]
											return Matrix(__magic_name__							)





				def    __SCREAMING_SNAKE_CASE     (      self							:   Any							)							->			Matrix:
											lowerCamelCase_			:    List[Any]   						=      self.determinant()
											if not determinant:
																		raise TypeError("Only matrices with a non-zero determinant have an inverse"							)
											return self.adjugate() * (1 / determinant)





				def __repr__(      self							:   Optional[int]							)							->			str:
											return str(self.rows							)





				def __str__(      self							:   Optional[Any]							)							->			str:

											if self.num_rows == 0:
																		return "[]"
											if self.num_rows == 1:
																		return "[[" + ". ".join(str(self.rows[0]							)							) + "]]"
											return (
											    "["
											    + "\n ".join(
											        [
											            "[" + ". ".join([str(__magic_name__							) for value in row]							) + ".]"
											            for row in self.rows
											        ]							)
											    + "]"
											)





				def    __SCREAMING_SNAKE_CASE     (      self							:   Union[str, Any]      ,							__magic_name__							:   list[int]      ,							__magic_name__							:   int | None = None							)							->			None:
											lowerCamelCase_			:    Tuple   						=      TypeError("Row must be a list containing all ints and/or floats"							)
											if not isinstance(__magic_name__      ,							__magic_name__							):
																		raise type_error
											for value in row:
																		if not isinstance(__magic_name__      ,							(int, float)							):
																									raise type_error
											if len(__magic_name__							) != self.num_columns:
																		raise ValueError(
																		    "Row must be equal in length to the other rows in the matrix"							)
											if position is None:
																		self.rows.append(__magic_name__							)
											else:
																		lowerCamelCase_			:    Optional[Any]   						=      self.rows[0:position] + [row] + self.rows[position:]





				def    __SCREAMING_SNAKE_CASE     (      self							:   List[Any]      ,							__magic_name__							:   list[int]      ,							__magic_name__							:   int | None = None							)							->			None:
											lowerCamelCase_			:    Tuple   						=      TypeError(
											    "Column must be a list containing all ints and/or floats"							)
											if not isinstance(__magic_name__      ,							__magic_name__							):
																		raise type_error
											for value in column:
																		if not isinstance(__magic_name__      ,							(int, float)							):
																									raise type_error
											if len(__magic_name__							) != self.num_rows:
																		raise ValueError(
																		    "Column must be equal in length to the other columns in the matrix"							)
											if position is None:
																		lowerCamelCase_			:    str   						=      [self.rows[i] + [column[i]] for i in range(self.num_rows							)]
											else:
																		lowerCamelCase_			:    List[Any]   						=      [
																		    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
																		    for i in range(self.num_rows							)
																		]





				def __eq__(      self							:   Tuple      ,							__magic_name__							:   object							)							->			bool:

											if not isinstance(__magic_name__      ,							__magic_name__							):
																		return NotImplemented
											return self.rows == other.rows





				def __ne__(      self							:   List[Any]      ,							__magic_name__							:   object							)							->			bool:
											return not self == other





				def __neg__(      self							:   Dict							)							->			Matrix:
											return self * -1





				def __add__(      self							:   List[Any]      ,							__magic_name__							:   Matrix							)							->			Matrix:

											if self.order != other.order:
																		raise ValueError("Addition requires matrices of the same order"							)
											return Matrix(
											    [
											        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns							)]
											        for i in range(self.num_rows							)
											    ]							)





				def __sub__(      self							:   Optional[Any]      ,							__magic_name__							:   Matrix							)							->			Matrix:

											if self.order != other.order:
																		raise ValueError("Subtraction requires matrices of the same order"							)
											return Matrix(
											    [
											        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns							)]
											        for i in range(self.num_rows							)
											    ]							)





				def __mul__(      self							:   Union[str, Any]      ,							__magic_name__							:   Matrix | int | float							)							->			Matrix:

											if isinstance(__magic_name__      ,							(int, float)							):
																		return Matrix(
																		    [[int(element * other							) for element in row] for row in self.rows]							)
											elif isinstance(__magic_name__      ,							__magic_name__							):
																		if self.num_columns != other.num_rows:
																									raise ValueError(
																									    "The number of columns in the first matrix must "
																									    "be equal to the number of rows in the second"							)
																		return Matrix(
																		    [
																		        [Matrix.dot_product(__magic_name__      ,							__magic_name__							) for column in other.columns()]
																		        for row in self.rows
																		    ]							)
											else:
																		raise TypeError(
																		    "A Matrix can only be multiplied by an int, float, or another matrix"							)





				def __pow__(      self							:   Tuple      ,							__magic_name__							:   int							)							->			Matrix:

											if not isinstance(__magic_name__      ,							__magic_name__							):
																		raise TypeError("A Matrix can only be raised to the power of an int"							)
											if not self.is_square:
																		raise ValueError("Only square matrices can be raised to a power"							)
											if other == 0:
																		return self.identity()
											if other < 0:
																		if self.is_invertable():
																									return self.inverse() ** (-other)
																		raise ValueError(
																		    "Only invertable matrices can be raised to a negative power"							)
											lowerCamelCase_			:    int   						=      self
											for _ in range(other - 1							):
																		result *= self
											return result





				@classmethod
				def    __SCREAMING_SNAKE_CASE     (      cls							:   Dict      ,							__magic_name__							:   list[int]      ,							__magic_name__							:   list[int]							)							->			int:
											return sum(row[i] * column[i] for i in range(len(__magic_name__							)							)							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()








'''simple docstring'''






def 					_a						(       _lowerCamelCase ) ->				int:



			"""simple docstring"""


			if not isinstance(_lowerCamelCase    ,	_lowerCamelCase ):
						raise TypeError("""only integers accepted as input""" )
			else:
						__snake_case					:      List[Any]							      =     str(abs(_lowerCamelCase ) )
						__snake_case					:      Union[str, Any]							      =     [list(_lowerCamelCase ) for char in range(len(_lowerCamelCase ) )]
						for index in range(len(_lowerCamelCase ) ):
									num_transpositions[index].pop(_lowerCamelCase )
						return max(
						    int("""""".join(list(_lowerCamelCase ) ) ) for transposition in num_transpositions )


if __name__ == "__main__":
	__import__("doctest").testmod()


