





'''simple docstring'''




from __future__ import annotations

from typing import Any







class     A_      :




 def __init__(   self			:       int      ,     snake_case_			:       Optional[int]      ,     snake_case_			:       Any      ,     snake_case_			:       Any = 0       ):
      _UpperCAmelCase				,    _UpperCAmelCase					=  row, column
      _UpperCAmelCase					=  [[default_value for c in range(snake_case_       )] for r in range(snake_case_       )]




 def __str__(   self			:       Optional[int]       ):
      _UpperCAmelCase					=  f'Matrix consist of {self.row} rows and {self.column} columns\n'

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

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

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




 def __repr__(   self			:       str       ):
      return str(self       )




 def 	lowercase      (   self			:       Tuple      ,     snake_case_			:       Dict       ):
      if not (isinstance(snake_case_      ,     (list, tuple)       ) and len(snake_case_       ) == 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]      ,     snake_case_			:       List[str]       ):
      assert self.validate_indicies(snake_case_       )
      return self.array[loc[0]][loc[1]]




 def __setitem__(   self			:       Union[str, Any]      ,     snake_case_			:       Optional[int]      ,     snake_case_			:       Any       ):
      assert self.validate_indicies(snake_case_       )
      _UpperCAmelCase					=  value




 def __add__(   self			:       Optional[Any]      ,     snake_case_			:       Dict       ):
      assert isinstance(snake_case_      ,     snake_case_       )
      assert self.row == another.row and self.column == another.column

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




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




 def __sub__(   self			:       Optional[int]      ,     snake_case_			:       Union[str, Any]       ):
      return self + (-another)




 def __mul__(   self			:       Optional[int]      ,     snake_case_			:       str       ):

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




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




 def 	lowercase      (   self			:       Optional[Any]      ,     snake_case_			:       Union[str, Any]      ,     snake_case_			:       Union[str, Any]       ):
      assert isinstance(snake_case_      ,     snake_case_       ) and isinstance(snake_case_      ,     snake_case_       )
      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
      _UpperCAmelCase					=  v.transpose()
      _UpperCAmelCase					=  (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       UpperCAmelCase_				(   )						->			int:


       '''simple docstring'''



       _UpperCAmelCase					=  Matrix(3     ,	3     ,	0			)
       for i in range(3			):
            _UpperCAmelCase					=  1
       print(f'a^(-1) is {ainv}'			)
       # u, v
       _UpperCAmelCase					=  Matrix(3     ,	1     ,	0			)
       _UpperCAmelCase				,    _UpperCAmelCase				,    _UpperCAmelCase					=  1, 2, -3
       _UpperCAmelCase					=  Matrix(3     ,	1     ,	0			)
       _UpperCAmelCase				,    _UpperCAmelCase				,    _UpperCAmelCase					=  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(__UpperCAmelCase     ,	__UpperCAmelCase			)}'			)
  def       UpperCAmelCase_				(   )						->			List[str]:


       '''simple docstring'''



       import doctest

       doctest.testmod()






  testa()









a_      :      str    =     6_55_21






def     __a					(		__UpperCAmelCase       ):
 a__												= 1
 a__												= 0
 for plain_chr in plain_text:
  a__												= (a + ord(__UpperCAmelCase       )) % MOD_ADLER
  a__												= (b + a) % MOD_ADLER
 return (b << 16) | a





