





from __future__ import annotations

from typing import Any





class 			lowerCAmelCase__:






       '''simple docstring'''


       def __init__(      self    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase = 0							)			->     None:
            _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							row, column
            _SCREAMING_SNAKE_CASE       :	List[Any]						    =							[[default_value for c in range(__A							)] for r in range(__A							)]




       def __str__(      self							)			->     str:
            _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

            # Make string identifier
            _SCREAMING_SNAKE_CASE       :	List[Any]						    =							0
            for row_vector in self.array:
                 for obj in row_vector:
                      _SCREAMING_SNAKE_CASE       :	Optional[int]						    =							max(__A    ,						len(str(__A							)							)							)
            _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							F"""%{max_element_length}s"""

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

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




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




       def     UpperCamelCase_			(      self    ,						__lowerCamelCase							)			->     bool:
            if not (isinstance(__A    ,						(list, tuple)							) and len(__A							) == 2):
                 return False
            elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
                 return False
            else:
                 return True




       def __getitem__(      self    ,						__lowerCamelCase							)			->     Any:
            assert self.validate_indicies(__A							)
            return self.array[loc[0]][loc[1]]




       def __setitem__(      self    ,						__lowerCamelCase    ,						__lowerCamelCase							)			->     None:
            assert self.validate_indicies(__A							)
            _SCREAMING_SNAKE_CASE       :	List[Any]						    =							value




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

            # Add
            _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							Matrix(self.row    ,						self.column							)
            for r in range(self.row							):
                 for c in range(self.column							):
                      _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							self[r, c] + another[r, c]
            return result




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




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




       def __mul__(      self    ,						__lowerCamelCase							)			->     Matrix:

            if isinstance(__A    ,						(int, float)							):  # Scalar multiplication
                 _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							Matrix(self.row    ,						self.column							)
                 for r in range(self.row							):
                      for c in range(self.column							):
                           _SCREAMING_SNAKE_CASE       :	List[Any]						    =							self[r, c] * another
                 return result
            elif isinstance(__A    ,						__A							):  # Matrix multiplication
                 assert self.column == another.row
                 _SCREAMING_SNAKE_CASE       :	List[Any]						    =							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:
                 _SCREAMING_SNAKE_CASE       :	List[Any]						    =							F"""Unsupported type given for another ({type(__A							)})"""
                 raise TypeError(__A							)




       def     UpperCamelCase_			(      self							)			->     Matrix:
            _SCREAMING_SNAKE_CASE       :	Dict						    =							Matrix(self.column    ,						self.row							)
            for r in range(self.row							):
                 for c in range(self.column							):
                      _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							self[r, c]
            return result







       def     UpperCamelCase_			(      self    ,						__lowerCamelCase    ,						__lowerCamelCase							)			->     Any:
            assert isinstance(__A    ,						__A							) and isinstance(__A    ,						__A							)
            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
            _SCREAMING_SNAKE_CASE       :	int						    =							v.transpose()
            _SCREAMING_SNAKE_CASE       :	Dict						    =							(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     lowerCamelCase__			():
            _SCREAMING_SNAKE_CASE       :	Optional[int]						    =							Matrix(3,       3,       0	)
            for i in range(3	):
                 _SCREAMING_SNAKE_CASE       :	Dict						    =							1
            print(f"""a^(-1) is {ainv}"""	)
            # u, v
            _SCREAMING_SNAKE_CASE       :	Dict						    =							Matrix(3,       1,       0	)
            _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							1, 2, -3
            _SCREAMING_SNAKE_CASE       :	Dict						    =							Matrix(3,       1,       0	)
            _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	Tuple						    =							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(_lowercase,       _lowercase	)}"""	)






       def     lowerCamelCase__			():
            import doctest

            doctest.testmod()

       testa()






from PIL import Image






def     lowerCamelCase__			(__lowerCamelCase	):
     _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	List[str]						    =							image.size
     _SCREAMING_SNAKE_CASE       :	Tuple						    =							0
     _SCREAMING_SNAKE_CASE       :	Dict						    =							image.load()
     for i in range(__lowerCamelCase	):
          for j in range(__lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	List[Any]						    =							pixels[j, i]
               mean += pixel
     mean //= width * height

     for j in range(__lowerCamelCase	):
          for i in range(__lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	int						    =							255 if pixels[i, j] > mean else 0
     return image


if __name__ == "__main__":
       UpperCamelCase__      =mean_threshold(Image.open('path_to_image').convert('L'))
       image.save('output_image_path')