

'''simple docstring'''






def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				[1]

 __lowercase						,			__lowercase						,			__lowercase													=				0, 0, 0
 __lowercase													=				ugly_nums[ia] * 2
 __lowercase													=				ugly_nums[ia] * 3
 __lowercase													=				ugly_nums[ia] * 5

 for _ in range(1  ,       UpperCamelCase__   ):
  __lowercase													=				min(UpperCamelCase__  ,       UpperCamelCase__  ,       UpperCamelCase__   )
  ugly_nums.append(UpperCamelCase__   )
  if next_num == next_a:
   ia += 1
   __lowercase													=				ugly_nums[ia] * 2
  if next_num == next_a:
   ia += 1
   __lowercase													=				ugly_nums[ia] * 3
  if next_num == next_a:
   ia += 1
   __lowercase													=				ugly_nums[ia] * 5
 return ugly_nums[-1]


if __name__ == "__main__":
 from doctest import testmod

 testmod(verbose=True)
 print(f'{ugly_numbers(200) = }')




'''simple docstring'''






from __future__ import annotations

from typing import Any






class     lowercase_			:




  """simple docstring"""




  def __init__(   self     :  Any      ,lowercase__     :  int      ,lowercase__     :  int      ,lowercase__     :  float = 0    ):
   __lowercase						,			__lowercase													=				row, column
   __lowercase													=				[[default_value for c in range(lowercase__    )] for r in range(lowercase__    )]






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

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

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

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






  def __repr__(   self     :  List[str]    ):
   return str(self    )






  def       SCREAMING_SNAKE_CASE   (   self     :  Any      ,lowercase__     :  tuple[int, int]    ):
   if not (isinstance(lowercase__      ,(list, tuple)    ) and len(lowercase__    ) == 2):
    return False
   elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
    return False
   else:
    return True






  def __getitem__(   self     :  Tuple      ,lowercase__     :  tuple[int, int]    ):
   assert self.validate_indicies(lowercase__    )
   return self.array[loc[0]][loc[1]]






  def __setitem__(   self     :  Tuple      ,lowercase__     :  tuple[int, int]      ,lowercase__     :  float    ):
   assert self.validate_indicies(lowercase__    )
   __lowercase													=				value






  def __add__(   self     :  List[Any]      ,lowercase__     :  Matrix    ):
   assert isinstance(lowercase__      ,lowercase__    )
   assert self.row == another.row and self.column == another.column

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






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






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






  def __mul__(   self     :  Dict      ,lowercase__     :  int | float | Matrix    ):

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






  def       SCREAMING_SNAKE_CASE   (   self     :  Any    ):
   __lowercase													=				Matrix(self.column      ,self.row    )
   for r in range(self.row    ):
    for c in range(self.column    ):
     __lowercase													=				self[r, c]
   return result






  def       SCREAMING_SNAKE_CASE   (   self     :  Any      ,lowercase__     :  Matrix      ,lowercase__     :  Matrix    ):
   assert isinstance(lowercase__      ,lowercase__    ) and isinstance(lowercase__      ,lowercase__    )
   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
   __lowercase													=				v.transpose()
   __lowercase													=				(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  (					):






  """simple docstring"""



  __lowercase													=				Matrix(3  ,       3  ,       0   )
  for i in range(3   ):
   __lowercase													=				1
  print(F"a^(-1) is {ainv}"   )
  # u, v
  __lowercase													=				Matrix(3  ,       1  ,       0   )
  __lowercase						,			__lowercase						,			__lowercase													=				1, 2, -3
  __lowercase													=				Matrix(3  ,       1  ,       0   )
  __lowercase						,			__lowercase						,			__lowercase													=				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(A__  ,       A__   )}"   )


 def 	_A  (					):






  """simple docstring"""



  import doctest

  doctest.testmod()






 testa()

