


"""simple docstring"""





from __future__ import annotations

from typing import Any



class 		snake_case_:






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






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

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

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






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






     def __setitem__(	self  :					Any					,				UpperCamelCase_  :					tuple[int, int]					,				UpperCamelCase_  :					float				):
           assert self.validate_indicies(UpperCamelCase_				)
           lowerCAmelCase					:	Optional[int]       =   value






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

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






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






     def __sub__(	self  :					Dict					,				UpperCamelCase_  :					Matrix				):
           return self + (-another)






     def __mul__(	self  :					str					,				UpperCamelCase_  :					int | float | Matrix				):

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






     def      lowerCamelCase__     (	self  :					Optional[Any]				):
           lowerCAmelCase					:	Optional[int]       =   Matrix(self.column					,				self.row				)
           for r in range(self.row				):
                 for c in range(self.column				):
                       lowerCAmelCase					:	List[str]       =   self[r, c]
           return result






     def      lowerCamelCase__     (	self  :					Optional[int]					,				UpperCamelCase_  :					Matrix					,				UpperCamelCase_  :					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
           lowerCAmelCase					:	Optional[int]       =   v.transpose()
           lowerCAmelCase					:	Any       =   (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						(						):
       # a^(-1)
       lowerCAmelCase					:	List[str]       =   Matrix(3 ,   3 ,   0			)
       for i in range(3			):
             lowerCAmelCase					:	Union[str, Any]       =   1
       print(f'''a^(-1) is {ainv}'''			)
       # u, v
       lowerCAmelCase					:	Dict       =   Matrix(3 ,   1 ,   0			)
       lowerCAmelCase,      lowerCAmelCase,      lowerCAmelCase					:	Tuple       =   1, 2, -3
       lowerCAmelCase					:	List[str]       =   Matrix(3 ,   1 ,   0			)
       lowerCAmelCase,      lowerCAmelCase,      lowerCAmelCase					:	Any       =   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(_snake_case ,   _snake_case			)}'''			)


 def      _snake_case						(						):
       import doctest

       doctest.testmod()






 testa()






"""simple docstring"""





from __future__ import annotations


def      _snake_case						(						_snake_case				:			list[int] ,   _snake_case				:			int			):
      if len(_snake_case			) == 0:
            return False
      lowerCAmelCase					:	List[Any]       =   len(_snake_case			) // 2
      if a_list[midpoint] == item:
            return True
      if item < a_list[midpoint]:
            return binary_search(a_list[:midpoint] ,   _snake_case			)
      else:
            return binary_search(a_list[midpoint + 1 :] ,   _snake_case			)


if __name__ == "__main__":
 snake_case__		:     List[str]    				=				input('''Enter numbers separated by comma:\n''').strip()
 snake_case__		:     Optional[int]    				=				[int(item.strip()) for item in user_input.split(''',''')]
 snake_case__		:     Dict    				=				int(input('''Enter the number to be found in the list:\n''').strip())
 snake_case__		:     str    				=				'''''' if binary_search(sequence, target) else '''not '''
 print(f"""{target} was {not_str}found in {sequence}""")


