




'''simple docstring'''







from __future__ import annotations

import random
from collections.abc import Iterable


class       _a  :
       def __init__(     self						:     Dict       ,    lowercase						:     list[str]    ):



           '''simple docstring'''

           UpperCAmelCase      	=		{literal: None for literal in literals}
       def __str__(     self						:     List[str]    ):



           '''simple docstring'''

           return "{" + " , ".join(self.literals    ) + "}"
       def __len__(     self						:     str    ):



           '''simple docstring'''

           return len(self.literals    )
       def    A				(     self						:     Union[str, Any]       ,    lowercase						:     dict[str, bool | None]    ):



           '''simple docstring'''

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







       def    A				(     self						:     Optional[Any]       ,    lowercase						:     dict[str, bool | None]    ):



           '''simple docstring'''

           for literal in self.literals:
               UpperCAmelCase      	=		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       _a  :
       def __init__(     self						:     Any       ,    lowercase						:     Iterable[Clause]    ):



           '''simple docstring'''

           UpperCAmelCase      	=		list(lowercase    )







       def __str__(     self						:     List[str]    ):



           '''simple docstring'''

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






def 						snake_case_							():
    UpperCAmelCase      	=		[]
    UpperCAmelCase      	=		random.randint(1   ,       5					)
    UpperCAmelCase      	=		'''A'''
    UpperCAmelCase      	=		0
    while i < no_of_literals:
        UpperCAmelCase      	=		random.randint(1   ,       5					)
        UpperCAmelCase      	=		base_var + str(_a					)
        UpperCAmelCase      	=		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 						snake_case_							():
    UpperCAmelCase      	=		set()
    UpperCAmelCase      	=		random.randint(1   ,       1_0					)
    while len(_a					) < no_of_clauses:
        clauses.add(generate_clause()					)
    return Formula(_a					)





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





def 						snake_case_							(_a     :							list[Clause]   ,       _a     :							list[str]   ,       _a     :							dict[str, bool | None]					):
    UpperCAmelCase      	=		[]
    UpperCAmelCase      	=		{}
    UpperCAmelCase      	=		[]

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

    for s in symbols:
        UpperCAmelCase      	=		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:
        UpperCAmelCase      	=		None
    for s in pure_symbols:
        UpperCAmelCase      	=		s + '''\''''
        if s in literals:
            UpperCAmelCase      	=		True
        elif sym in literals:
            UpperCAmelCase      	=		False
    return pure_symbols, assignment





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

    return unit_symbols, assignment





def 						snake_case_							(_a     :							list[Clause]   ,       _a     :							list[str]   ,       _a     :							dict[str, bool | None]					):
    UpperCAmelCase      	=		True
    for clause in clauses:
        UpperCAmelCase      	=		clause.evaluate(_a					)
        if clause_check is False:
            return False, None
        elif clause_check is None:
            UpperCAmelCase      	=		False
            continue

    if check_clause_all_true:
        return True, model

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

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

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

    return dpll_algorithm(_a   ,       _a   ,       _a					) or dpll_algorithm(_a   ,       _a   ,       _a					)


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 						snake_case_							(_a     :							int = 9_9_8_0_0_1					):
    UpperCAmelCase      	=		0
    for i in range(9_9_9   ,       9_9   ,       -1					):  # 3 digit numbers range from 999 down to 100
        for j in range(9_9_9   ,       9_9   ,       -1					):
            UpperCAmelCase      	=		str(i * j					)
            if product_string == product_string[::-1] and i * j < n:
                UpperCAmelCase      	=		max(_a   ,       i * j					)
    return answer


if __name__ == "__main__":
   print(f"""{solution() = }""")




