




from __future__ import annotations

import random
from collections.abc import Iterable
class 		UpperCAmelCase       :







      '''simple docstring'''





      def __init__(						self							:					int	,     __lowercase							:					list[str]						):






       """simple docstring"""






       snake_case_		   =					{literal: None for literal in literals}






      def __str__(						self							:					str						):






       """simple docstring"""






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






      def __len__(						self							:					Optional[int]						):






       """simple docstring"""






       return len(self.literals						)






      def 	snake_case__						(						self							:					Dict	,     __lowercase							:					dict[str, bool | None]						):






       """simple docstring"""






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






      def 	snake_case__						(						self							:					List[Any]	,     __lowercase							:					dict[str, bool | None]						):






       """simple docstring"""






       for literal in self.literals:
        snake_case_		   =					literal.rstrip("'"						) if literal.endswith("'"						) else literal + "'"
        if symbol in self.literals:
         return True

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







class 		UpperCAmelCase       :







      '''simple docstring'''





      def __init__(						self							:					Union[str, Any]	,     __lowercase							:					Iterable[Clause]						):






       """simple docstring"""






       snake_case_		   =					list(__lowercase						)






      def __str__(						self							:					Dict						):






       """simple docstring"""






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







def 						lowerCamelCase__   (		):







 '''simple docstring'''





 snake_case_		   =					[]
 snake_case_		   =					random.randint(1					,     5							)
 snake_case_		   =					"A"
 snake_case_		   =					0
 while i < no_of_literals:
  snake_case_		   =					random.randint(1					,     5							)
  snake_case_		   =					base_var + str(_A							)
  snake_case_		   =					random.randint(0					,     1							)
  if var_complement == 1:
   var_name += "'"
  if var_name in literals:
   i -= 1
  else:
   literals.append(_A							)
  i += 1
 return Clause(_A							)


def 						lowerCamelCase__   (		):







 '''simple docstring'''





 snake_case_		   =					set()
 snake_case_		   =					random.randint(1					,     10							)
 while len(_A							) < no_of_clauses:
  clauses.add(generate_clause()							)
 return Formula(_A							)


def 						lowerCamelCase__   (		_A							):







 '''simple docstring'''





 snake_case_		   =					formula.clauses
 snake_case_		   =					[]
 for clause in formula.clauses:
  for literal in clause.literals:
   snake_case_		   =					literal[:2]
   if symbol not in symbols_set:
    symbols_set.append(_A							)
 return clauses, symbols_set


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







 '''simple docstring'''





 snake_case_		   =					[]
 snake_case_		   =					{}
 snake_case_		   =					[]

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

 for s in symbols:
  snake_case_		   =					s + "'"
  if (s in literals and sym not in literals) or (
      s not in literals and sym in literals
  ):
   pure_symbols.append(_A							)
 for p in pure_symbols:
  snake_case_		   =					None
 for s in pure_symbols:
  snake_case_		   =					s + "'"
  if s in literals:
   snake_case_		   =					True
  elif sym in literals:
   snake_case_		   =					False
 return pure_symbols, assignment


def 						lowerCamelCase__   (		_A					,     _A							):







 '''simple docstring'''





 snake_case_		   =					[]
 for clause in clauses:
  if len(_A							) == 1:
   unit_symbols.append(list(clause.literals.keys()							)[0]							)
  else:
   snake_case_   ,				snake_case_		   =					0, 0
   for literal, value in clause.literals.items():
    if value is False:
     f_count += 1
    elif value is None:
     snake_case_		   =					literal
     n_count += 1
   if f_count == len(_A							) - 1 and n_count == 1:
    unit_symbols.append(_A							)
 snake_case_		   =					{}
 for i in unit_symbols:
  snake_case_		   =					i[:2]
  snake_case_		   =					len(_A							) == 2
 snake_case_		   =					[i[:2] for i in unit_symbols]

 return unit_symbols, assignment


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







 '''simple docstring'''





 snake_case_		   =					True
 for clause in clauses:
  snake_case_		   =					clause.evaluate(_A							)
  if clause_check is False:
   return False, None
  elif clause_check is None:
   snake_case_		   =					False
   continue

 if check_clause_all_true:
  return True, model

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

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

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

 return dpll_algorithm(_A					,     _A					,     _A							) or dpll_algorithm(_A					,     _A					,     _A							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  lowercase__    :					Tuple					=						generate_formula()
  print(f'''The formula {formula} is''', end=" ")

  lowercase__    :					str					=						generate_parameters(formula)
  lowercase__    :					List[Any]					=						dpll_algorithm(clauses, symbols, {})

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






def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





	if right <= left:
		return
	snake_case_		   =					snake_case_		   =					left
	snake_case_		   =					right
	snake_case_		   =					sorting[left]
	while i <= b:
		if sorting[i] < pivot:
			snake_case_   ,				snake_case_		   =					sorting[i], sorting[a]
			a += 1
			i += 1
		elif sorting[i] > pivot:
			snake_case_   ,				snake_case_		   =					sorting[i], sorting[b]
			b -= 1
		else:
			i += 1
	quick_sort_apartition(_A					,     _A					,     a - 1							)
	quick_sort_apartition(_A					,     b + 1					,     _A							)


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





	if left < right:
		snake_case_		   =					lomuto_partition(_A					,     _A					,     _A							)
		quick_sort_lomuto_partition(_A					,     _A					,     pivot_index - 1							)
		quick_sort_lomuto_partition(_A					,     pivot_index + 1					,     _A							)


def 						lowerCamelCase__   (		_A					,     _A					,     _A							):







	'''simple docstring'''





	snake_case_		   =					sorting[right]
	snake_case_		   =					left
	for i in range(_A					,     _A							):
		if sorting[i] < pivot:
			snake_case_   ,				snake_case_		   =					sorting[i], sorting[store_index]
			store_index += 1
	snake_case_   ,				snake_case_		   =					sorting[store_index], sorting[right]
	return store_index


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	if len(_A							) <= 1:
		return sorting
	return (
	    three_way_radix_quicksort([i for i in sorting if i < sorting[0]]							)
	    + [i for i in sorting if i == sorting[0]]
	    + three_way_radix_quicksort([i for i in sorting if i > sorting[0]]							)
	)


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)

		lowercase__    :					Tuple					=						input("Enter numbers separated by a comma:\n").strip()
		lowercase__    :					int					=						[int(item) for item in user_input.split(",")]
		quick_sort_apartition(unsorted, 0, len(unsorted) - 1)
		print(unsorted)
