



'''simple docstring'''





class     UpperCAmelCase_       :
    """simple docstring"""







    def __init__(    self					:     int ,     snake_case_					:     int						):
          snake_case__  :    Tuple    						=      n
          snake_case__  :    int    						=      [None] * self.n
          snake_case__  :    Optional[int]    						=      0  # index of the first element
          snake_case__  :    List[Any]    						=      0
          snake_case__  :    str    						=      0




    def __len__(    self					:     Optional[Any]						):
          return self.size




    def lowerCamelCase       (    self					:     Dict						):
          return self.size == 0




    def lowerCamelCase       (    self					:     Optional[int]						):
          return False if self.is_empty() else self.array[self.front]




    def lowerCamelCase       (    self					:     Optional[int] ,     snake_case_					:     str						):
          if self.size >= self.n:
                raise Exception("""QUEUE IS FULL"""						)

          snake_case__  :    Optional[int]    						=      data
          snake_case__  :    Optional[int]    						=      (self.rear + 1) % self.n
          self.size += 1
          return self




    def lowerCamelCase       (    self					:     List[Any]						):
          if self.size == 0:
                raise Exception("""UNDERFLOW"""						)

          snake_case__  :    List[str]    						=      self.array[self.front]
          snake_case__  :    str    						=      None
          snake_case__  :    Any    						=      (self.front + 1) % self.n
          self.size -= 1
          return temp




'''simple docstring'''




from __future__ import annotations

from typing import Any

class 		UpperCAmelCase_      :





     def __init__( self       :      Optional[int]    ,      UpperCAmelCase__       :      int    ,      UpperCAmelCase__       :      int    ,      UpperCAmelCase__       :      float = 0    )				->  None:
        lowerCAmelCase     ,  lowerCAmelCase     =			row, column
        lowerCAmelCase     =			[[default_value for c in range(UpperCAmelCase__    )] for r in range(UpperCAmelCase__    )]





     def __str__( self       :      List[str]    )				->  str:
        lowerCAmelCase     =			F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

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

        # Make string and return
        def single_line(UpperCAmelCase__       :      list[float]    ) -> str:
           nonlocal string_format_identifier
           lowerCAmelCase     =			'['
           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       :      List[str]    )				->  str:
        return str(self    )





     def 							__UpperCAmelCase      ( self       :      Optional[int]    ,      UpperCAmelCase__       :      tuple[int, int]    )				->  bool:
        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       :      Any    ,      UpperCAmelCase__       :      tuple[int, int]    )				->  Any:
        assert self.validate_indicies(UpperCAmelCase__    )
        return self.array[loc[0]][loc[1]]





     def __setitem__( self       :      Dict    ,      UpperCAmelCase__       :      tuple[int, int]    ,      UpperCAmelCase__       :      float    )				->  None:
        assert self.validate_indicies(UpperCAmelCase__    )
        lowerCAmelCase     =			value





     def __add__( self       :      Any    ,      UpperCAmelCase__       :      Matrix    )				->  Matrix:
        assert isinstance(UpperCAmelCase__    ,      UpperCAmelCase__    )
        assert self.row == another.row and self.column == another.column

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





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





     def __sub__( self       :      str    ,      UpperCAmelCase__       :      Matrix    )				->  Matrix:
        return self + (-another)





     def __mul__( self       :      str    ,      UpperCAmelCase__       :      int | float | Matrix    )				->  Matrix:

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





     def 							__UpperCAmelCase      ( self       :      Optional[Any]    )				->  Matrix:
        lowerCAmelCase     =			Matrix(self.column    ,      self.row    )
        for r in range(self.row    ):
           for c in range(self.column    ):
              lowerCAmelCase     =			self[r, c]
        return result





     def 							__UpperCAmelCase      ( self       :      List[str]    ,      UpperCAmelCase__       :      Matrix    ,      UpperCAmelCase__       :      Matrix    )				->  Any:
        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     =			v.transpose()
        lowerCAmelCase     =			(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_					( ):
          # a^(-1)
          lowerCAmelCase     =			Matrix(3	, 3	, 0				)
          for i in range(3				):
             lowerCAmelCase     =			1
          print(f'''a^(-1) is {ainv}'''				)
          # u, v
          lowerCAmelCase     =			Matrix(3	, 1	, 0				)
          lowerCAmelCase     ,  lowerCAmelCase     ,  lowerCAmelCase     =			1, 2, -3
          lowerCAmelCase     =			Matrix(3	, 1	, 0				)
          lowerCAmelCase     ,  lowerCAmelCase     ,  lowerCAmelCase     =			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_					( ):
          import doctest

          doctest.testmod()




       testa()





