




"""simple docstring"""


from __future__ import annotations






class    lowercase:







 '''simple docstring'''





 def __init__(							self:						List[Any], a_:						Union[str, Any]						):




   '''simple docstring'''



   _snake_case				:						Optional[Any]								=    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(lowerCamelCase__						) != 0:
     _snake_case				:						Any								=    len(rows[0]						)
     if cols == 0:
       raise error
     for row in rows:
       if len(lowerCamelCase__						) != cols:
         raise error
       for value in row:
         if not isinstance(lowerCamelCase__, (int, float)						):
           raise error
     _snake_case				:						Union[str, Any]								=    rows
   else:
     _snake_case				:						int								=    []


 def 					UpperCamelCase_  (							self:						Dict						):




   '''simple docstring'''



   return [[row[i] for row in self.rows] for i in range(len(self.rows[0]						)						)]


 @property
 def 					UpperCamelCase_  (							self:						List[str]						):




   '''simple docstring'''



   return len(self.rows						)


 @property
 def 					UpperCamelCase_  (							self:						Optional[Any]						):




   '''simple docstring'''



   return len(self.rows[0]						)


 @property
 def 					UpperCamelCase_  (							self:						Dict						):




   '''simple docstring'''



   return (self.num_rows, self.num_columns)


 @property
 def 					UpperCamelCase_  (							self:						Optional[int]						):




   '''simple docstring'''



   return self.order[0] == self.order[1]


 def 					UpperCamelCase_  (							self:						Dict						):




   '''simple docstring'''



   _snake_case				:						Tuple								=    [
       [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(lowerCamelCase__						)


 def 					UpperCamelCase_  (							self:						Dict						):




   '''simple docstring'''



   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 					UpperCamelCase_  (							self:						List[str]						):




   '''simple docstring'''



   return bool(self.determinant()						)


 def 					UpperCamelCase_  (							self:						Any, a_:						List[Any], a_:						Any						):




   '''simple docstring'''



   _snake_case				:						Any								=    [
       [
           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(lowerCamelCase__						).determinant()


 def 					UpperCamelCase_  (							self:						Tuple, a_:						str, a_:						str						):




   '''simple docstring'''



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


 def 					UpperCamelCase_  (							self:						Tuple						):




   '''simple docstring'''



   return Matrix(
       [
           [self.get_minor(lowerCamelCase__, lowerCamelCase__						) for column in range(self.num_columns						)]
           for row in range(self.num_rows						)
       ]						)


 def 					UpperCamelCase_  (							self:						Dict						):




   '''simple docstring'''



   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 					UpperCamelCase_  (							self:						List[str]						):




   '''simple docstring'''



   _snake_case				:						int								=    [
       [self.cofactors().rows[column][row] for column in range(self.num_columns						)]
       for row in range(self.num_rows						)
   ]
   return Matrix(lowerCamelCase__						)


 def 					UpperCamelCase_  (							self:						int						):




   '''simple docstring'''



   _snake_case				:						Optional[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:						int						):




   '''simple docstring'''



   return str(self.rows						)


 def __str__(							self:						Optional[Any]						):




   '''simple docstring'''



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


 def 					UpperCamelCase_  (							self:						Optional[Any], a_:						Tuple, a_:						Dict = None						):




   '''simple docstring'''



   _snake_case				:						Tuple								=    TypeError("""Row must be a list containing all ints and/or floats"""						)
   if not isinstance(lowerCamelCase__, lowerCamelCase__						):
     raise type_error
   for value in row:
     if not isinstance(lowerCamelCase__, (int, float)						):
       raise type_error
   if len(lowerCamelCase__						) != 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(lowerCamelCase__						)
   else:
     _snake_case				:						Any								=    self.rows[0:position] + [row] + self.rows[position:]


 def 					UpperCamelCase_  (							self:						Optional[int], a_:						List[Any], a_:						Dict = None						):




   '''simple docstring'''



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


 def __eq__(							self:						Union[str, Any], a_:						Union[str, Any]						):




   '''simple docstring'''



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


 def __ne__(							self:						List[str], a_:						List[Any]						):




   '''simple docstring'''



   return not self == other


 def __neg__(							self:						List[str]						):




   '''simple docstring'''



   return self * -1


 def __add__(							self:						Tuple, a_:						Optional[Any]						):




   '''simple docstring'''



   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:						Union[str, Any], a_:						List[Any]						):




   '''simple docstring'''



   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], a_:						int						):




   '''simple docstring'''



   if isinstance(lowerCamelCase__, (int, float)						):
     return Matrix(
         [[int(element * other						) for element in row] for row in self.rows]						)
   elif isinstance(lowerCamelCase__, lowerCamelCase__						):
     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(lowerCamelCase__, lowerCamelCase__						) 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:						Dict, a_:						Optional[Any]						):




   '''simple docstring'''



   if not isinstance(lowerCamelCase__, lowerCamelCase__						):
     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"""						)
   _snake_case				:						Optional[Any]								=    self
   for _ in range(other - 1						):
     result *= self
   return result


 @classmethod
 def 					UpperCamelCase_  (							cls:						Tuple, a_:						Optional[Any], a_:						Union[str, Any]						):




   '''simple docstring'''



   return sum(row[i] * column[i] for i in range(len(lowerCamelCase__						)						)						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()








def      lowerCamelCase_						(			UpperCamelCase__							: str )	->			bool:





				"""simple docstring"""


				__lowerCamelCase									=       0
				for ch in input_str:
								__lowerCamelCase									=       ord(UpperCamelCase__ )
								__lowerCamelCase									=       pow(2					,	UpperCamelCase__ )

								# If we already turned on bit for current character's unicode
								if bitmap >> ch_unicode & 1 == 1:
												return False
								bitmap |= ch_bit_index_on
				return True


if __name__ == "__main__":
					import doctest

					doctest.testmod()


