

"""simple docstring"""





from __future__ import annotations

import random
from collections.abc import Iterable




class    _lowerCAmelCase    :







 """simple docstring"""







 def __init__(     self				:     str,   UpperCAmelCase__				:     list[str]      ):
    __lowercase								=		{literal: None for literal in literals}


 def __str__(     self				:     List[str]      ):
    return "{" + " , ".join(self.literals      ) + "}"


 def __len__(     self				:     Union[str, Any]      ):
    return len(self.literals      )


 def    _lowercase					(     self				:     Tuple,   UpperCAmelCase__				:     dict[str, bool | None]      ):
    for literal in self.literals:
       __lowercase								=		literal[:2]
       if symbol in model:
          __lowercase								=		model[symbol]
       else:
          continue
       if value is not None:
          # Complement assignment if literal is in complemented form
          if literal.endswith("'"      ):
             __lowercase								=		not value
       __lowercase								=		value



 def    _lowercase					(     self				:     Optional[int],   UpperCAmelCase__				:     dict[str, bool | None]      ):
    for literal in self.literals:
       __lowercase								=		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    _lowerCAmelCase    :







 """simple docstring"""







 def __init__(     self				:     List[str],   UpperCAmelCase__				:     Iterable[Clause]      ):
    __lowercase								=		list(UpperCAmelCase__      )



 def __str__(     self				:     Any      ):
    return "{" + " , ".join(str(UpperCAmelCase__      ) for clause in self.clauses      ) + "}"







def     _A    (    )      ->		Clause:
   '''simple docstring'''


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




def     _A    (    )      ->		Formula:
   '''simple docstring'''


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




def     _A    (    UpperCamelCase_	:			Formula)      ->		tuple[list[Clause], list[str]]:
   '''simple docstring'''


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




def     _A    (    UpperCamelCase_	:			list[Clause],     UpperCamelCase_	:			list[str],     UpperCamelCase_	:			dict[str, bool | None])      ->		tuple[list[str], dict[str, bool | None]]:
   '''simple docstring'''


   __lowercase								=		[]
   __lowercase								=		{}
   __lowercase								=		[]

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

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




def     _A    (    UpperCamelCase_	:			list[Clause],     UpperCamelCase_	:			dict[str, bool | None])      ->		tuple[list[str], dict[str, bool | None]]:
   '''simple docstring'''


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

   return unit_symbols, assignment




def     _A    (    UpperCamelCase_	:			list[Clause],     UpperCamelCase_	:			list[str],     UpperCamelCase_	:			dict[str, bool | None])      ->		tuple[bool | None, dict[str, bool | None] | None]:
   '''simple docstring'''


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

   if check_clause_all_true:
      return True, model

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

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

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

   return dpll_algorithm(UpperCamelCase_,     UpperCamelCase_,     UpperCamelCase_) or dpll_algorithm(UpperCamelCase_,     UpperCamelCase_,     UpperCamelCase_)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

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

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

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







"""simple docstring"""





def     _A    (    UpperCamelCase_	:			list)      ->		list:
   '''simple docstring'''


   for i, _ in enumerate(UpperCamelCase_):
      if (i % 2 == 1) == (nums[i - 1] > nums[i]):
         __lowercase						,__lowercase								=		nums[i], nums[i - 1]

   return nums


if __name__ == "__main__":
   print('Enter the array elements:')
   _a					 =				list(map(int, input().split()))
   print('The unsorted array is:')
   print(array)
   print('Array after Wiggle sort:')
   print(wiggle_sort(array))




