from __future__ import annotations

import random
from collections.abc import Iterable


class 						a__							:



			def __init__(						self      ,						UpperCAmelCase    ) ->    None:
								__a							=   {literal: None for literal in literals}



			def __str__(						self    ) ->    str:
								return "{" + " , ".join(self.literals    ) + "}"



			def __len__(						self    ) ->    int:
								return len(self.literals    )



			def __SCREAMING_SNAKE_CASE							(						self      ,						UpperCAmelCase    ) ->    None:
								for literal in self.literals:
													__a							=   literal[:2]
													if symbol in model:
																		__a							=   model[symbol]
													else:
																		continue
													if value is not None:
																		# Complement assignment if literal is in complemented form
																		if literal.endswith('\''    ):
																							__a							=   not value
													__a							=   value







			def __SCREAMING_SNAKE_CASE							(						self      ,						UpperCAmelCase    ) ->    bool | None:
								for literal in self.literals:
													__a							=   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 						a__							:



			def __init__(						self      ,						UpperCAmelCase    ) ->    None:
								__a							=   list(UpperCAmelCase    )







			def __str__(						self    ) ->    str:
								return "{" + " , ".join(str(UpperCAmelCase    ) for clause in self.clauses    ) + "}"






def 							lowerCAmelCase(	):
					__a							=   []
					__a							=   random.randint(1      ,				5						)
					__a							=   'A'
					__a							=   0
					while i < no_of_literals:
										__a							=   random.randint(1      ,				5						)
										__a							=   base_var + str(__lowerCamelCase						)
										__a							=   random.randint(0      ,				1						)
										if var_complement == 1:
															var_name += "'"
										if var_name in literals:
															i -= 1
										else:
															literals.append(__lowerCamelCase						)
										i += 1
					return Clause(__lowerCamelCase						)
def 							lowerCAmelCase(	):
					__a							=   set()
					__a							=   random.randint(1      ,				10						)
					while len(__lowerCamelCase						) < no_of_clauses:
										clauses.add(generate_clause()						)
					return Formula(__lowerCamelCase						)
def 							lowerCAmelCase(	__lowerCamelCase						):
					__a							=   formula.clauses
					__a							=   []
					for clause in formula.clauses:
										for literal in clause.literals:
															__a							=   literal[:2]
															if symbol not in symbols_set:
																				symbols_set.append(__lowerCamelCase						)
					return clauses, symbols_set
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   []
					__a							=   {}
					__a							=   []

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

					for s in symbols:
										__a							=   s + '\''
										if (s in literals and sym not in literals) or (
										    s not in literals and sym in literals
										):
															pure_symbols.append(__lowerCamelCase						)
					for p in pure_symbols:
										__a							=   None
					for s in pure_symbols:
										__a							=   s + '\''
										if s in literals:
															__a							=   True
										elif sym in literals:
															__a							=   False
					return pure_symbols, assignment
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   []
					for clause in clauses:
										if len(__lowerCamelCase						) == 1:
															unit_symbols.append(list(clause.literals.keys()						)[0]						)
										else:
															__a					,      __a							=   0, 0
															for literal, value in clause.literals.items():
																				if value is False:
																									f_count += 1
																				elif value is None:
																									__a							=   literal
																									n_count += 1
															if f_count == len(__lowerCamelCase						) - 1 and n_count == 1:
																				unit_symbols.append(__lowerCamelCase						)
					__a							=   {}
					for i in unit_symbols:
										__a							=   i[:2]
										__a							=   len(__lowerCamelCase						) == 2
					__a							=   [i[:2] for i in unit_symbols]

					return unit_symbols, assignment
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   True
					for clause in clauses:
										__a							=   clause.evaluate(__lowerCamelCase						)
										if clause_check is False:
															return False, None
										elif clause_check is None:
															__a							=   False
															continue

					if check_clause_all_true:
										return True, model

					try:
										__a					,      __a							=   find_pure_symbols(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						)
					except RecursionError:
										print('raises a RecursionError and is'						)
										return None, {}
					__a							=   None
					if len(__lowerCamelCase						) > 0:
										__a					,      __a							=   pure_symbols[0], assignment[pure_symbols[0]]

					if p:
										__a							=   model
										__a							=   value
										__a							=   list(__lowerCamelCase						)
										if p in tmp_symbols:
															tmp_symbols.remove(__lowerCamelCase						)
										return dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						)

					__a					,      __a							=   find_unit_clauses(__lowerCamelCase      ,				__lowerCamelCase						)
					__a							=   None
					if len(__lowerCamelCase						) > 0:
										__a					,      __a							=   unit_symbols[0], assignment[unit_symbols[0]]
					if p:
										__a							=   model
										__a							=   value
										__a							=   list(__lowerCamelCase						)
										if p in tmp_symbols:
															tmp_symbols.remove(__lowerCamelCase						)
										return dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						)
					__a							=   symbols[0]
					__a							=   symbols[1:]
					__a					,      __a							=   model, model
					__a					,      __a							=   True, False

					return dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						) or dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	lowerCamelCase_				:		Any       						=       generate_formula()
	print(F'''The formula {formula} is''', end=""" """)

	lowerCamelCase_						,  lowerCamelCase_				:		Dict       						=       generate_parameters(formula)
	lowerCamelCase_						,  lowerCamelCase_				:		Tuple       						=       dpll_algorithm(clauses, symbols, {})

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







from math import sqrt





def 	snake_case_      (__A     :						int     )			->	list[int]:
   __lowerCAmelCase  :			List[str]					    =						[1]
   for i in range(2					,   int(sqrt(__A     )     ) + 1					,   1     ):
      if number % i == 0:
         values.append(__A     )
         if int(number // i     ) != i:
            values.append(int(number // i     )     )
   return sorted(__A     )





def 	snake_case_      (__A     :						int     )			->	bool:
   return sum(factors(__A     )     ) > n





def 	snake_case_      (__A     :						int     )			->	bool:
   __lowerCAmelCase  :			Any					    =						factors(__A     )
   __lowerCAmelCase  :			Union[str, Any]					    =						len(__A     )
   __lowerCAmelCase  :			str					    =						[[0 for i in range(number + 1     )] for j in range(r + 1     )]
   for i in range(r + 1     ):
      __lowerCAmelCase  :			Tuple					    =						True

   for i in range(1					,   number + 1     ):
      __lowerCAmelCase  :			List[str]					    =						False

   for i in range(1					,   r + 1     ):
      for j in range(1					,   number + 1     ):
         if j < values[i - 1]:
            __lowerCAmelCase  :			Dict					    =						subset[i - 1][j]
         else:
            __lowerCAmelCase  :			Dict					    =						subset[i - 1][j] or subset[i - 1][j - values[i - 1]]

   return subset[r][number] != 0





def 	snake_case_      (__A     :						int     )			->	bool:
   return abundant(__A     ) and not semi_perfect(__A     )


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)
   for number in (69, 70, 71):
      print(F'{number} is {"" if weird(number) else "not "}weird.')


