





'''simple docstring'''



from __future__ import annotations




def       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     dict[str, str] ):
			__lowercase  ,						__lowercase  ,						__lowercase   =							'''''', '''''', ''''''
			__lowercase   =							[]

			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       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     dict[str, str] ):
			__lowercase  ,						__lowercase   =							'''''', ''''''
			__lowercase   =							[]

			for character in message_part:
						this_part += character_to_number[character]

			for digit in this_part:
						tmp += digit
						if len(lowerCamelCase_ ) == len(lowerCamelCase_ ):
									result.append(lowerCamelCase_ )
									__lowercase   =							''''''

			return result[0], result[1], result[2]




def       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     str ):
			# Validate message and alphabet, set to upper and remove spaces
			__lowercase   =							alphabet.replace(''' '''						,				'''''' ).upper()
			__lowercase   =							message.replace(''' '''						,				'''''' ).upper()

			# Check length and characters
			if len(lowerCamelCase_ ) != 2_7:
						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
			__lowercase   =							(
			    '''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''',
			)
			__lowercase   =							{}
			__lowercase   =							{}
			for letter, number in zip(lowerCamelCase_						,				lowerCamelCase_ ):
						__lowercase   =							number
						__lowercase   =							letter

			return message, alphabet, character_to_number, number_to_character




def       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."						,				lowerCamelCase_	:     int = 5 ):
			__lowercase  ,						__lowercase  ,						__lowercase  ,						__lowercase   =							__prepare(
			    lowerCamelCase_						,				lowerCamelCase_ )
			__lowercase  ,						__lowercase   =							'''''', ''''''

			for i in range(0						,				len(lowerCamelCase_ ) + 1						,				lowerCamelCase_ ):
						encrypted_numeric += __encrypt_part(
						    message[i : i + period]						,				lowerCamelCase_ )

			for i in range(0						,				len(lowerCamelCase_ )						,				3 ):
						encrypted += number_to_character[encrypted_numeric[i : i + 3]]

			return encrypted




def       _lowerCAmelCase  ( lowerCamelCase_	:     str						,				lowerCamelCase_	:     str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."						,				lowerCamelCase_	:     int = 5 ):
			__lowercase  ,						__lowercase  ,						__lowercase  ,						__lowercase   =							__prepare(
			    lowerCamelCase_						,				lowerCamelCase_ )
			__lowercase   =							[]
			__lowercase   =							''''''

			for i in range(0						,				len(lowerCamelCase_ ) + 1						,				lowerCamelCase_ ):
						__lowercase  ,						__lowercase  ,						__lowercase   =							__decrypt_part(message[i : i + period]						,				lowerCamelCase_ )

						for j in range(0						,				len(lowerCamelCase_ ) ):
									decrypted_numeric.append(a[j] + b[j] + c[j] )

			for each in decrypted_numeric:
						decrypted += number_to_character[each]

			return decrypted


if __name__ == "__main__":
	_SCREAMING_SNAKE_CASE    =			'''DEFEND THE EAST WALL OF THE CASTLE.'''
	_SCREAMING_SNAKE_CASE    =			encrypt_message(msg, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
	_SCREAMING_SNAKE_CASE    =			decrypt_message(encrypted, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
	print(f'''Encrypted: {encrypted}\nDecrypted: {decrypted}''')








def    UpperCamelCase(					lowercase_							)	->				str:





  '''simple docstring'''





  if len(lowercase_							) == 0 or not all(len(lowercase_							) == 2 for pair in coordinates							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  if len({tuple(lowercase_							) for pair in coordinates}							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      {x for x, _ in coordinates}
  if len(lowercase_							) == 1:
    return f'''x={coordinates[0][0]}'''

  if len(lowercase_							) != len(lowercase_							):
    raise ValueError("""The program cannot work out a fitting polynomial."""							)

  snake_case_       						=      len(lowercase_							)

  snake_case_       						=      0
  snake_case_       						=      []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    snake_case_       						=      0
    snake_case_       						=      coordinates[count_of_line][0]
    snake_case_       						=      []
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))							)
      count_in_line += 1
    matrix.append(lowercase_							)
    count_of_line += 1

  snake_case_       						=      0
  # put the y values into a vector
  snake_case_       						=      []
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]							)
    count_of_line += 1

  snake_case_       						=      0

  while count < x:
    snake_case_       						=      0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      snake_case_       						=      matrix[zahlen][count] / matrix[count][count]
      for counting_columns, item in enumerate(matrix[count]							):
        # manipulating all the values in the matrix
        matrix[zahlen][counting_columns] -= item * bruch
      # manipulating the values in the vector
      vector[zahlen] -= vector[count] * bruch
      zahlen += 1
    count += 1

  snake_case_       						=      0
  # make solutions
  snake_case_       						=      []
  while count < x:
    solution.append(str(vector[count] / matrix[count][count]							)							)
    count += 1

  snake_case_       						=      0
  snake_case_       						=      """f(x)="""

  while count < x:
    snake_case_       						=      solution[count].split("""E"""							)
    if len(lowercase_							) > 1:
      snake_case_       						=      f'''{remove_e[0]}*10^{remove_e[1]}'''
    solved += f'''x^{x - (count + 1)}*{solution[count]}'''
    if count + 1 != x:
      solved += "+"
    count += 1

  return solved


if __name__ == "__main__":
    print(points_to_polynomial([]))
    print(points_to_polynomial([[]]))
    print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
    print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
    print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
    print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
    print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
    print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
    print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))