
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()

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}''')