code: 
  '''simple docstring'''
  from __future__ import annotations
  
  import random
  import string
  
  
  
  
  
  
  class   snake_case__					:
  
  
  
  
  
  
  
  		"""simple docstring"""
  
  		def __init__(			self							: str     ,  UpperCamelCase__							: List[str] = None			)	-> int:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					Union[str, Any]     =	passcode or self.__passcode_creator()
  				snake_case     :					Union[str, Any]     =	self.__make_key_list()
  				snake_case     :					int     =	self.__make_shift_key()
  
  
  
  		def __str__(			self							: str			)	-> List[Any]:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				return "".join(self.__passcode			)
  
  
  
  		def 			lowerCAmelCase							(			self							: Union[str, Any]     ,  UpperCamelCase__							: str			)	-> int:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				for i in range(1     ,  len(_lowerCamelCase			)     ,  2			):
  						iterlist[i] *= -1
  				return iterlist
  
  
  
  		def 			lowerCAmelCase							(			self							: int			)	-> List[str]:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					int     =	string.ascii_letters + string.digits
  				snake_case     :					str     =	[random.choice(_lowerCamelCase			) for _ in range(random.randint(10     ,  20			)			)]
  				return password
  
  
  
  		def 			lowerCAmelCase							(			self							: str			)	-> Union[str, Any]:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					str     =	(
  				    string.ascii_letters + string.digits + string.punctuation + """ \t\n"""
  				)
  
  				snake_case     :					Union[str, Any]     =	[]
  
  				# creates points known as breakpoints to break the key_list_options at those
  				# points and pivot each substring
  				snake_case     :					Dict     =	sorted(set(self.__passcode			)			)
  				snake_case     :					list[str]     =	[]
  
  				# algorithm for creating a new shuffled list, keys_l, out of key_list_options
  				for i in key_list_options:
  						temp_list.extend(_lowerCamelCase			)
  
  						# checking breakpoints at which to pivot temporary sublist and add it into
  						# keys_l
  						if i in breakpoints or i == key_list_options[-1]:
  								keys_l.extend(temp_list[::-1]			)
  								temp_list.clear()
  
          # returning a shuffled keys_l to prevent brute force guessing of shift key
  				return keys_l
  
  
  
  		def 			lowerCAmelCase							(			self							: Optional[Any]			)	-> Union[str, Any]:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					Dict     =	sum(self.__neg_pos([ord(_lowerCamelCase			) for x in self.__passcode]			)			)
  				return num if num > 0 else len(self.__passcode			)
  
  
  
  		def 			lowerCAmelCase							(			self							: Optional[int]     ,  UpperCamelCase__							: Tuple			)	-> Optional[Any]:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					List[str]     =	""""""
  
  				# decoding shift like Caesar cipher algorithm implementing negative shift or
  				# reverse shift or left shift
  				for i in encoded_message:
  						snake_case     :					Optional[int]     =	self.__key_list.index(_lowerCamelCase			)
  						decoded_message += self.__key_list[
  						    (position - self.__shift_key) % -len(self.__key_list			)
  						]
  
  				return decoded_message
  
  
  
  		def 			lowerCAmelCase							(			self							: Optional[int]     ,  UpperCamelCase__							: Union[str, Any]			)	-> int:
  
  
  
  
  
  
  				"""simple docstring"""
  
  
  
  
  
  
  
  				snake_case     :					str     =	""""""
  
  				# encoding shift like Caesar cipher algorithm implementing positive shift or
  				# forward shift or right shift
  				for i in plaintext:
  						snake_case     :					Optional[int]     =	self.__key_list.index(_lowerCamelCase			)
  						encoded_message += self.__key_list[
  						    (position + self.__shift_key) % len(self.__key_list			)
  						]
  
  				return encoded_message
  
  
  
  
  
  
  
  def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ = "Hello, this is a modified Caesar cipher" )     ->       str:
  
  
  		'''simple docstring'''
  
  
  		snake_case     :					List[Any]     =	ShuffledShiftCipher()
  		return cipa.decrypt(cipa.encrypt(SCREAMING_SNAKE_CASE__ ) )
  
  
  if __name__ == "__main__":
  						import doctest
  
  						doctest.testmod()
  
  
  
style_context: 
  '''simple docstring'''
  import numpy as np
  
  
  
  
  def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ )     ->       Optional[Any]:
  
  
  		'''simple docstring'''
  
  
  		snake_case ,snake_case     :					str     =	a.shape
  		snake_case     :					Union[str, Any]     =	min(SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__ )
  		snake_case     :					List[Any]     =	np.eye(SCREAMING_SNAKE_CASE__ )
  		snake_case     :					Union[str, Any]     =	a.copy()
  
  		for k in range(t - 1 ):
  				# select a column of modified matrix A':
  				snake_case     :					Union[str, Any]     =	r[k:, [k]]
  				# construct first basis vector
  				snake_case     :					str     =	np.zeros_like(SCREAMING_SNAKE_CASE__ )
  				snake_case     :					List[str]     =	1.0
  				# determine scaling factor
  				snake_case     :					int     =	np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  				# construct vector v for Householder reflection
  				snake_case     :					Optional[int]     =	x + np.sign(x[0] ) * alpha * ea
  				v /= np.linalg.norm(SCREAMING_SNAKE_CASE__ )
  
  				# construct the Householder matrix
  				snake_case     :					Tuple     =	np.eye(m - k ) - 2.0 * v @ v.T
  				# pad with ones and zeros as necessary
  				snake_case     :					int     =	np.block([[np.eye(SCREAMING_SNAKE_CASE__ ), np.zeros((k, m - k) )], [np.zeros((m - k, k) ), q_k]] )
  
  				snake_case     :					int     =	q @ q_k.T
  				snake_case     :					Dict     =	q_k @ r
  
  		return q, r
  
  
  if __name__ == "__main__":
  						import doctest
  
  						doctest.testmod()
  
  
  