code: 
  import numpy as np
  from numpy import floataa
  from numpy.typing import NDArray
  
  
  def       a			(   a		,	a  )    ->NDArray[floataa]:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   np.shape(a  )
  
  			SCREAMING_SNAKE_CASE    	=   np.zeros((rows, 1)		,	dtype=a  )
  			for row in reversed(range(a  )  ):
  						SCREAMING_SNAKE_CASE    	=   0
  						for col in range(row + 1		,	a  ):
  									total += coefficients[row, col] * x[col]
  
  						SCREAMING_SNAKE_CASE    	=   (vector[row] - total) / coefficients[row, row]
  
  			return x
  
  
  def       a			(   a		,	a  )    ->NDArray[floataa]:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   np.shape(a  )
  			if rows != columns:
  						return np.array(()		,	dtype=a  )
  
  			# augmented matrix
  			SCREAMING_SNAKE_CASE    	=   np.concatenate((coefficients, vector)		,	axis=1  )
  			SCREAMING_SNAKE_CASE    	=   augmented_mat.astype('''float64'''  )
  
  			# scale the matrix leaving it triangular
  			for row in range(rows - 1  ):
  						SCREAMING_SNAKE_CASE    	=   augmented_mat[row, row]
  						for col in range(row + 1		,	a  ):
  									SCREAMING_SNAKE_CASE    	=   augmented_mat[col, row] / pivot
  									augmented_mat[col, :] -= factor * augmented_mat[row, :]
  
  			SCREAMING_SNAKE_CASE    	=   retroactive_resolution(
  			    augmented_mat[:, 0:columns]		,	augmented_mat[:, columns : columns + 1]  )
  
  			return x
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()
style_context: 
  from __future__ import annotations
  
  
  def       a			(   a		,	a  )    ->str:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   '''''', '''''', ''''''
  			SCREAMING_SNAKE_CASE    	=   []
  
  			for character in message_part:
  						tmp.append(character_to_number[character]  )
  
  			for each in tmp:
  						one += each[0]
  						two += each[1]
  						three += each[2]
  
  			return one + two + three
  
  
  def       a			(   a		,	a  )    ->tuple[str, str, str]:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   '''''', ''''''
  			SCREAMING_SNAKE_CASE    	=   []
  
  			for character in message_part:
  						this_part += character_to_number[character]
  
  			for digit in this_part:
  						tmp += digit
  						if len(a  ) == len(a  ):
  									result.append(a  )
  									SCREAMING_SNAKE_CASE    	=   ''''''
  
  			return result[0], result[1], result[2]
  
  
  def       a			(   a		,	a  )    ->tuple[str, str, dict[str, str], dict[str, str]]:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE    	=   alphabet.replace(''' '''		,	''''''  ).upper()
  			SCREAMING_SNAKE_CASE    	=   message.replace(''' '''		,	''''''  ).upper()
  
  			# Check length and characters
  			if len(a  ) != 27:
  						raise KeyError('''Length of alphabet has to be 27.'''  )
  			for each in message:
  						if each not in alphabet:
  									raise ValueError('''Each message character has to be included in alphabet!'''  )
  
      # Generate dictionares
  			SCREAMING_SNAKE_CASE    	=   (
  			    '''111''',
  			    '''112''',
  			    '''113''',
  			    '''121''',
  			    '''122''',
  			    '''123''',
  			    '''131''',
  			    '''132''',
  			    '''133''',
  			    '''211''',
  			    '''212''',
  			    '''213''',
  			    '''221''',
  			    '''222''',
  			    '''223''',
  			    '''231''',
  			    '''232''',
  			    '''233''',
  			    '''311''',
  			    '''312''',
  			    '''313''',
  			    '''321''',
  			    '''322''',
  			    '''323''',
  			    '''331''',
  			    '''332''',
  			    '''333''',
  			)
  			SCREAMING_SNAKE_CASE    	=   {}
  			SCREAMING_SNAKE_CASE    	=   {}
  			for letter, number in zip(a		,	a  ):
  						SCREAMING_SNAKE_CASE    	=   number
  						SCREAMING_SNAKE_CASE    	=   letter
  
  			return message, alphabet, character_to_number, number_to_character
  
  
  def       a			(   a		,	a = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."		,	a = 5  )    ->str:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   __prepare(
  			    a		,	a  )
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   '''''', ''''''
  
  			for i in range(0		,	len(a  ) + 1		,	a  ):
  						encrypted_numeric += __encrypt_part(
  						    message[i : i + period]		,	a  )
  
  			for i in range(0		,	len(a  )		,	3  ):
  						encrypted += number_to_character[encrypted_numeric[i : i + 3]]
  
  			return encrypted
  
  
  def       a			(   a		,	a = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."		,	a = 5  )    ->str:
  
  
  
  
  			'''simple docstring'''
  
  
  			SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   __prepare(
  			    a		,	a  )
  			SCREAMING_SNAKE_CASE    	=   []
  			SCREAMING_SNAKE_CASE    	=   ''''''
  
  			for i in range(0		,	len(a  ) + 1		,	a  ):
  						SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE	,       SCREAMING_SNAKE_CASE    	=   __decrypt_part(message[i : i + period]		,	a  )
  
  						for j in range(0		,	len(a  )  ):
  									decrypted_numeric.append(a[j] + b[j] + c[j]  )
  
  			for each in decrypted_numeric:
  						decrypted += number_to_character[each]
  
  			return decrypted
  
  
  if __name__ == "__main__":
  							__lowerCAmelCase				      =					'DEFEND THE EAST WALL OF THE CASTLE.'
  							__lowerCAmelCase				      =					encrypt_message(msg, 'EPSDUCVWYM.ZLKXNBTFGORIJHAQ')
  							__lowerCAmelCase				      =					decrypt_message(encrypted, 'EPSDUCVWYM.ZLKXNBTFGORIJHAQ')
  							print(F'''Encrypted: {encrypted}\nDecrypted: {decrypted}''')