




import functools







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_						)       ->	int:



       """simple docstring"""

       A__							=   len(lowercase_						)
       A__							=   len(lowercase_						)

       @functools.cache
       def min_distance(lowercase_			,    lowercase_						) -> int:
              # if first word index is overflow - delete all from the second word
              if indexa >= len_worda:
                     return len_worda - indexa
              # if second word index is overflow - delete all from the first word
              if indexa >= len_worda:
                     return len_worda - indexa
              A__							=   int(worda[indexa] != worda[indexa]						)  # current letters not identical
              return min(
                  1 + min_distance(indexa + 1			,    lowercase_						)			,    1 + min_distance(lowercase_			,    indexa + 1						)			,    diff + min_distance(indexa + 1			,    indexa + 1						)			,    )

       return min_distance(0			,    0						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()








from __future__ import annotations

from typing import Any


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     str ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     float = 0)						->None:





           '''simple docstring'''

           A__			,							A__							=   row, column
           A__							=   [[default_value for c in range(UpperCAmelCase__)] for r in range(UpperCAmelCase__)]


    def __str__(      self				:     List[str])						->str:





           '''simple docstring'''

           A__							=   f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

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

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





           '''simple docstring'''

           return str(self)


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str] ,			UpperCAmelCase__				:     tuple[int, int])						->bool:





           '''simple docstring'''

           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				:     List[Any] ,			UpperCAmelCase__				:     tuple[int, int])						->Any:





           '''simple docstring'''

           assert self.validate_indicies(UpperCAmelCase__)
           return self.array[loc[0]][loc[1]]


    def __setitem__(      self				:     List[Any] ,			UpperCAmelCase__				:     tuple[int, int] ,			UpperCAmelCase__				:     float)						->None:





           '''simple docstring'''

           assert self.validate_indicies(UpperCAmelCase__)
           A__							=   value


    def __add__(      self				:     Optional[int] ,			UpperCAmelCase__				:     Matrix)						->Matrix:





           '''simple docstring'''

           assert isinstance(UpperCAmelCase__ ,			UpperCAmelCase__)
           assert self.row == another.row and self.column == another.column

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


    def __neg__(      self				:     str)						->Matrix:





           '''simple docstring'''

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


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





           '''simple docstring'''

           return self + (-another)


    def __mul__(      self				:     Union[str, Any] ,			UpperCAmelCase__				:     int | float | Matrix)						->Matrix:





           '''simple docstring'''

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


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str])						->Matrix:





           '''simple docstring'''

           A__							=   Matrix(self.column ,			self.row)
           for r in range(self.row):
                  for c in range(self.column):
                         A__							=   self[r, c]
           return result





    def 	SCREAMING_SNAKE_CASE							(      self				:     Tuple ,			UpperCAmelCase__				:     Matrix ,			UpperCAmelCase__				:     Matrix)						->Any:





           '''simple docstring'''

           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
           A__							=   v.transpose()
           A__							=   (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 SCREAMING_SNAKE_CASE    (	)       ->	None:



         """simple docstring"""

         A__							=   Matrix(3			,    3			,    0						)
         for i in range(3						):
                A__							=   1
         print(f"""a^(-1) is {ainv}"""						)
         # u, v
         A__							=   Matrix(3			,    1			,    0						)
         A__			,							A__			,							A__							=   1, 2, -3
         A__							=   Matrix(3			,    1			,    0						)
         A__			,							A__			,							A__							=   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 SCREAMING_SNAKE_CASE    (	)       ->	None:



         """simple docstring"""

         import doctest

         doctest.testmod()
  testa()


