




"""simple docstring"""
from __future__ import annotations

import random
from collections.abc import Iterable







class  _SCREAMING_SNAKE_CASE       :



 '''simple docstring'''





 def __init__(self					,     lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	dict[str, bool | None]					      =  {literal: None for literal in literals}






 def __str__(self   ):

  '''simple docstring'''







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






 def __len__(self   ):

  '''simple docstring'''







  return len(self.literals   )






 def lowercase_      (self					,     lowerCAmelCase__   ):

  '''simple docstring'''







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






 def lowercase_      (self					,     lowerCAmelCase__   ):

  '''simple docstring'''







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

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







class  _SCREAMING_SNAKE_CASE       :



 '''simple docstring'''





 def __init__(self					,     lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	str					      =  list(lowerCAmelCase__   )






 def __str__(self   ):

  '''simple docstring'''







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






def 				__lowerCAmelCase					(					)    ->       Clause:
 _UpperCamelCase      :	Any					      =  []
 _UpperCamelCase      :	int					      =  random.randint(1  ,	5						)
 _UpperCamelCase      :	Any					      =  "A"
 _UpperCamelCase      :	int					      =  0
 while i < no_of_literals:
  _UpperCamelCase      :	Optional[int]					      =  random.randint(1  ,	5						)
  _UpperCamelCase      :	str					      =  base_var + str(__lowerCAmelCase						)
  _UpperCamelCase      :	Union[str, Any]					      =  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					(					)    ->       Formula:
 _UpperCamelCase      :	set[Clause]					      =  set()
 _UpperCamelCase      :	List[str]					      =  random.randint(1  ,	10						)
 while len(__lowerCAmelCase						) < no_of_clauses:
  clauses.add(generate_clause()						)
 return Formula(__lowerCAmelCase						)






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






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

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

 for s in symbols:
  _UpperCamelCase      :	Dict					      =  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:
  _UpperCamelCase      :	Tuple					      =  None
 for s in pure_symbols:
  _UpperCamelCase      :	int					      =  s + "'"
  if s in literals:
   _UpperCamelCase      :	Tuple					      =  True
  elif sym in literals:
   _UpperCamelCase      :	str					      =  False
 return pure_symbols, assignment






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

 return unit_symbols, assignment






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

 if check_clause_all_true:
  return True, model

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

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

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

 return dpll_algorithm(__lowerCAmelCase  ,	__lowerCAmelCase  ,	__lowerCAmelCase						) or dpll_algorithm(__lowerCAmelCase  ,	__lowerCAmelCase  ,	__lowerCAmelCase						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    _SCREAMING_SNAKE_CASE						 =     generate_formula()
    print(f'The formula {formula} is', end=""" """)

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

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









"""simple docstring"""
# Lint as: python3

import hashlib
from typing import Union






def 				__lowerCAmelCase					(					__lowerCAmelCase			:		Union[str, int, bytes]						)    ->       bytes:
 if isinstance(__lowerCAmelCase  ,	__lowerCAmelCase						):
  # Data already in bytes, returns as it as
  return hash_data
 elif isinstance(__lowerCAmelCase  ,	__lowerCAmelCase						):
  # We keep the data as it as for it ot be later encoded to UTF-8
  # However replace `\\` with `/` for Windows compatibility
  _UpperCamelCase      :	int					      =  hash_data.replace("\\"  ,	"/"						)
 elif isinstance(__lowerCAmelCase  ,	__lowerCAmelCase						):
  _UpperCamelCase      :	Union[str, Any]					      =  str(__lowerCAmelCase						)
 else:
  # If data is not of the required type, raise error
  raise InvalidKeyError(__lowerCAmelCase						)

 return hash_data.encode("utf-8"						)







class  _SCREAMING_SNAKE_CASE       (     SCREAMING_SNAKE_CASE__				):



 '''simple docstring'''





 def __init__(self					,     lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	int					      =  "\nFAILURE TO GENERATE DATASET: Invalid key type detected"
  _UpperCamelCase      :	Tuple					      =  F"\nFound Key {hash_data} of type {type(lowerCAmelCase__   )}"
  _UpperCamelCase      :	str					      =  "\nKeys should be either str, int or bytes type"
  super().__init__(F"{self.prefix}{self.err_msg}{self.suffix}"   )







class  _SCREAMING_SNAKE_CASE       (     SCREAMING_SNAKE_CASE__				):



 '''simple docstring'''





 def __init__(self					,     lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__=""   ):

  '''simple docstring'''







  _UpperCamelCase      :	Optional[int]					      =  key
  _UpperCamelCase      :	Tuple					      =  duplicate_key_indices
  _UpperCamelCase      :	int					      =  fix_msg
  _UpperCamelCase      :	List[Any]					      =  "Found multiple examples generated with the same key"
  if len(lowerCAmelCase__   ) <= 20:
   _UpperCamelCase      :	Optional[Any]					      =  F"\nThe examples at index {', '.join(lowerCAmelCase__   )} have the key {key}"
  else:
   _UpperCamelCase      :	Union[str, Any]					      =  F"\nThe examples at index {', '.join(duplicate_key_indices[:20]   )}... ({len(lowerCAmelCase__   ) - 20} more) have the key {key}"
  _UpperCamelCase      :	List[Any]					      =  "\n" + fix_msg if fix_msg else ""
  super().__init__(F"{self.prefix}{self.err_msg}{self.suffix}"   )







class  _SCREAMING_SNAKE_CASE       :



 '''simple docstring'''





 def __init__(self					,     lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	Union[str, Any]					      =  hashlib.mda(_as_bytes(lowerCAmelCase__   )   )






 def lowercase_      (self					,     lowerCAmelCase__   ):

  '''simple docstring'''







  _UpperCamelCase      :	Any					      =  self._split_mda.copy()
  _UpperCamelCase      :	List[str]					      =  _as_bytes(lowerCAmelCase__   )
  mda.update(lowerCAmelCase__   )
  # Convert to integer with hexadecimal conversion
  return int(mda.hexdigest()					,     16   )



