

"""simple docstring"""


from __future__ import annotations

import random
from collections.abc import Iterable





class 					snake_case			:

				def __init__(			self							:       str  ,						UpperCamelCase__							:       Optional[int])->     None:



						'''simple docstring'''


						__lowerCAmelCase: Union[str, Any]					   =    {literal: None for literal in literals}

				def __str__(			self							:       str)->     str:



						'''simple docstring'''


						return "{" + " , ".join(self.literals) + "}"

				def __len__(			self							:       Optional[int])->     int:



						'''simple docstring'''


						return len(self.literals)

				def 							lowercase_  (			self							:       List[Any]  ,						UpperCamelCase__							:       Dict)->     None:



						'''simple docstring'''


						for literal in self.literals:
								__lowerCAmelCase: str					   =    literal[:2]
								if symbol in model:
										__lowerCAmelCase: Optional[Any]					   =    model[symbol]
								else:
										continue
								if value is not None:
										# Complement assignment if literal is in complemented form
										if literal.endswith("\'"):
												__lowerCAmelCase: str					   =    not value
								__lowerCAmelCase: Optional[Any]					   =    value




				def 							lowercase_  (			self							:       Union[str, Any]  ,						UpperCamelCase__							:       Tuple)->     bool | None:



						'''simple docstring'''


						for literal in self.literals:
								__lowerCAmelCase: Optional[int]					   =    literal.rstrip("\'") if literal.endswith("\'") else literal + "\'"
								if symbol in self.literals:
										return True

						self.assign(UpperCamelCase__)
						for value in self.literals.values():
								if value in (True, None):
										return value
						return any(self.literals.values())





class 					snake_case			:

				def __init__(			self							:       int  ,						UpperCamelCase__							:       Union[str, Any])->     None:



						'''simple docstring'''


						__lowerCAmelCase: Tuple					   =    list(UpperCamelCase__)




				def __str__(			self							:       Tuple)->     str:



						'''simple docstring'''


						return "{" + " , ".join(str(UpperCamelCase__) for clause in self.clauses) + "}"






def 					a__					(					)			->			Clause:
		__lowerCAmelCase: Tuple					   =    []
		__lowerCAmelCase: Tuple					   =    random.randint(1      ,				5				)
		__lowerCAmelCase: Dict					   =    "A"
		__lowerCAmelCase: Dict					   =    0
		while i < no_of_literals:
				__lowerCAmelCase: Optional[int]					   =    random.randint(1      ,				5				)
				__lowerCAmelCase: Optional[Any]					   =    base_var + str(__SCREAMING_SNAKE_CASE				)
				__lowerCAmelCase: List[str]					   =    random.randint(0      ,				1				)
				if var_complement == 1:
						var_name += "'"
				if var_name in literals:
						i -= 1
				else:
						literals.append(__SCREAMING_SNAKE_CASE				)
				i += 1
		return Clause(__SCREAMING_SNAKE_CASE				)






def 					a__					(					)			->			Formula:
		__lowerCAmelCase: List[str]					   =    set()
		__lowerCAmelCase: List[str]					   =    random.randint(1      ,				1_0				)
		while len(__SCREAMING_SNAKE_CASE				) < no_of_clauses:
				clauses.add(generate_clause()				)
		return Formula(__SCREAMING_SNAKE_CASE				)






def 					a__					(					__SCREAMING_SNAKE_CASE				)			->			tuple[list[Clause], list[str]]:
		__lowerCAmelCase: Any					   =    formula.clauses
		__lowerCAmelCase: Optional[int]					   =    []
		for clause in formula.clauses:
				for literal in clause.literals:
						__lowerCAmelCase: Union[str, Any]					   =    literal[:2]
						if symbol not in symbols_set:
								symbols_set.append(__SCREAMING_SNAKE_CASE				)
		return clauses, symbols_set






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			tuple[list[str], dict[str, bool | None]]:
		__lowerCAmelCase: str					   =    []
		__lowerCAmelCase: str					   =    {}
		__lowerCAmelCase: List[Any]					   =    []

		for clause in clauses:
				if clause.evaluate(__SCREAMING_SNAKE_CASE				):
						continue
				for literal in clause.literals:
						literals.append(__SCREAMING_SNAKE_CASE				)

		for s in symbols:
				__lowerCAmelCase: Dict					   =    s + "\'"
				if (s in literals and sym not in literals) or (
				    s not in literals and sym in literals
				):
						pure_symbols.append(__SCREAMING_SNAKE_CASE				)
		for p in pure_symbols:
				__lowerCAmelCase: int					   =    None
		for s in pure_symbols:
				__lowerCAmelCase: Union[str, Any]					   =    s + "\'"
				if s in literals:
						__lowerCAmelCase: List[Any]					   =    True
				elif sym in literals:
						__lowerCAmelCase: str					   =    False
		return pure_symbols, assignment






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			tuple[list[str], dict[str, bool | None]]:
		__lowerCAmelCase: Optional[int]					   =    []
		for clause in clauses:
				if len(__SCREAMING_SNAKE_CASE				) == 1:
						unit_symbols.append(list(clause.literals.keys()				)[0]				)
				else:
						__lowerCAmelCase   ,				__lowerCAmelCase: Optional[Any]					   =    0, 0
						for literal, value in clause.literals.items():
								if value is False:
										f_count += 1
								elif value is None:
										__lowerCAmelCase: Optional[int]					   =    literal
										n_count += 1
						if f_count == len(__SCREAMING_SNAKE_CASE				) - 1 and n_count == 1:
								unit_symbols.append(__SCREAMING_SNAKE_CASE				)
		__lowerCAmelCase: List[str]					   =    {}
		for i in unit_symbols:
				__lowerCAmelCase: int					   =    i[:2]
				__lowerCAmelCase: List[Any]					   =    len(__SCREAMING_SNAKE_CASE				) == 2
		__lowerCAmelCase: Any					   =    [i[:2] for i in unit_symbols]

		return unit_symbols, assignment






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			tuple[bool | None, dict[str, bool | None] | None]:
		__lowerCAmelCase: Union[str, Any]					   =    True
		for clause in clauses:
				__lowerCAmelCase: Tuple					   =    clause.evaluate(__SCREAMING_SNAKE_CASE				)
				if clause_check is False:
						return False, None
				elif clause_check is None:
						__lowerCAmelCase: Optional[int]					   =    False
						continue

		if check_clause_all_true:
				return True, model

		try:
				__lowerCAmelCase   ,				__lowerCAmelCase: int					   =    find_pure_symbols(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)
		except RecursionError:
				print("raises a RecursionError and is"				)
				return None, {}
		__lowerCAmelCase: Optional[Any]					   =    None
		if len(__SCREAMING_SNAKE_CASE				) > 0:
				__lowerCAmelCase   ,				__lowerCAmelCase: Dict					   =    pure_symbols[0], assignment[pure_symbols[0]]

		if p:
				__lowerCAmelCase: List[Any]					   =    model
				__lowerCAmelCase: List[str]					   =    value
				__lowerCAmelCase: int					   =    list(__SCREAMING_SNAKE_CASE				)
				if p in tmp_symbols:
						tmp_symbols.remove(__SCREAMING_SNAKE_CASE				)
				return dpll_algorithm(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)

		__lowerCAmelCase   ,				__lowerCAmelCase: Union[str, Any]					   =    find_unit_clauses(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)
		__lowerCAmelCase: Tuple					   =    None
		if len(__SCREAMING_SNAKE_CASE				) > 0:
				__lowerCAmelCase   ,				__lowerCAmelCase: Dict					   =    unit_symbols[0], assignment[unit_symbols[0]]
		if p:
				__lowerCAmelCase: List[Any]					   =    model
				__lowerCAmelCase: Any					   =    value
				__lowerCAmelCase: Dict					   =    list(__SCREAMING_SNAKE_CASE				)
				if p in tmp_symbols:
						tmp_symbols.remove(__SCREAMING_SNAKE_CASE				)
				return dpll_algorithm(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)
		__lowerCAmelCase: Any					   =    symbols[0]
		__lowerCAmelCase: List[Any]					   =    symbols[1:]
		__lowerCAmelCase   ,				__lowerCAmelCase: int					   =    model, model
		__lowerCAmelCase   ,				__lowerCAmelCase: int					   =    True, False

		return dpll_algorithm(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				) or dpll_algorithm(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	__A		     =    generate_formula()
	print(F'''The formula {formula} is''', end=" ")

	__A		     =    generate_parameters(formula)
	__A		     =    dpll_algorithm(clauses, symbols, {})

	if solution:
		print(F'''satisfiable with the assignment {model}.''')
	else:
		print("not satisfiable.")





"""simple docstring"""


from __future__ import annotations






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			str:
		__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase: Any					   =    "", "", ""
		__lowerCAmelCase: Any					   =    []

		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__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			tuple[str, str, str]:
		__lowerCAmelCase   ,				__lowerCAmelCase: Union[str, Any]					   =    "", ""
		__lowerCAmelCase: int					   =    []

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

		for digit in this_part:
				tmp += digit
				if len(__SCREAMING_SNAKE_CASE				) == len(__SCREAMING_SNAKE_CASE				):
						result.append(__SCREAMING_SNAKE_CASE				)
						__lowerCAmelCase: Union[str, Any]					   =    ""

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






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)			->			tuple[str, str, dict[str, str], dict[str, str]]:
		# Validate message and alphabet, set to upper and remove spaces
		__lowerCAmelCase: int					   =    alphabet.replace(" "      ,				""				).upper()
		__lowerCAmelCase: int					   =    message.replace(" "      ,				""				).upper()

		# Check length and characters
		if len(__SCREAMING_SNAKE_CASE				) != 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
		__lowerCAmelCase: Optional[int]					   =    (
		    "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",
		)
		__lowerCAmelCase: Tuple					   =    {}
		__lowerCAmelCase: Optional[int]					   =    {}
		for letter, number in zip(__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				):
				__lowerCAmelCase: List[Any]					   =    number
				__lowerCAmelCase: Any					   =    letter

		return message, alphabet, character_to_number, number_to_character






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."      ,				__SCREAMING_SNAKE_CASE = 5				)			->			str:
		__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase: Optional[int]					   =    __prepare(
		    __SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)
		__lowerCAmelCase   ,				__lowerCAmelCase: str					   =    "", ""

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

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

		return encrypted






def 					a__					(					__SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."      ,				__SCREAMING_SNAKE_CASE = 5				)			->			str:
		__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase: Dict					   =    __prepare(
		    __SCREAMING_SNAKE_CASE      ,				__SCREAMING_SNAKE_CASE				)
		__lowerCAmelCase: List[str]					   =    []
		__lowerCAmelCase: Optional[int]					   =    ""

		for i in range(0      ,				len(__SCREAMING_SNAKE_CASE				) + 1      ,				__SCREAMING_SNAKE_CASE				):
				__lowerCAmelCase   ,				__lowerCAmelCase   ,				__lowerCAmelCase: List[Any]					   =    __decrypt_part(message[i : i + period]      ,				__SCREAMING_SNAKE_CASE				)

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

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

		return decrypted


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


