





"""simple docstring"""




import dataclasses
import enum
import functools
import math
import re

# The following script is adapted from the script of TaPas.
# Original: https://github.com/google-research/tapas/master/wikisql_utils.py
from typing import Any, List, Text


lowerCamelCase_	:		Optional[int]         =   'none'
lowerCamelCase_	:		List[str]         =   'none'





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			List[Any]									=    value.split(_UpperCAmelCase   )
  return len(_UpperCAmelCase   ) > 1 and any((len(_UpperCAmelCase   ) == 3 for x in split)   )





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  if isinstance(_UpperCAmelCase					,   _UpperCAmelCase   ):
    return value
  if isinstance(_UpperCAmelCase					,   _UpperCAmelCase   ):
    return float(_UpperCAmelCase   )
  if not isinstance(_UpperCAmelCase					,   _UpperCAmelCase   ):
    raise ValueError('Argument value is not a string. Can\'t parse it as float'   )
  A_    :			Any									=    value

  try:
    # Example: 1,000.7
    if "." in sanitized and "," in sanitized:
      return float(sanitized.replace(','					,   ''   )   )
    # 1,000
    if "," in sanitized and _split_thousands(','					,   _UpperCAmelCase   ):
      return float(sanitized.replace(','					,   ''   )   )
    # 5,5556
    if "," in sanitized and sanitized.count(','   ) == 1 and not _split_thousands(','					,   _UpperCAmelCase   ):
      return float(sanitized.replace(','					,   '.'   )   )
    # 0.0.0.1
    if sanitized.count('.'   ) > 1:
      return float(sanitized.replace('.'					,   ''   )   )
    # 0,0,0,1
    if sanitized.count(','   ) > 1:
      return float(sanitized.replace(','					,   ''   )   )
    return float(_UpperCAmelCase   )
  except ValueError:
    # Avoid adding the sanitized value in the error message.
    raise ValueError('Unable to convert value to float'   )





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  if answer is None:
    return None
  try:
    A_    :			List[str]									=    convert_to_float(_UpperCAmelCase   )
    if isinstance(_UpperCAmelCase					,   _UpperCAmelCase   ) and math.isnan(_UpperCAmelCase   ):
      return None
    return value
  except ValueError:
    return answer.lower()


lowerCamelCase_	:		Dict         =   {
    'text': lambda x: x,
    'real': convert_to_float,
}

class 					_UpperCAmelCase    (  enum.Enum						):



      '''simple docstring'''
      lowercase_ :					Union[str, Any]             =  0
      lowercase_ :					Union[str, Any]             =  1
      lowercase_ :					int             =  2
      lowercase_ :					Union[str, Any]             =  3
      lowercase_ :					Tuple             =  4
      lowercase_ :					Optional[int]             =  5


class 					_UpperCAmelCase    (  enum.Enum						):



      '''simple docstring'''
      lowercase_ :					str             =  0
      lowercase_ :					str             =  1
      lowercase_ :					Any             =  2


@dataclasses.dataclass
class 					_UpperCAmelCase    :



      '''simple docstring'''
      lowercase_ :					Text
      lowercase_ :					_Operator
      lowercase_ :					Any


lowerCamelCase_	:		Optional[Any]         =   re.compile(r'\w+|[^\w\s]+', re.UNICODE | re.MULTILINE | re.DOTALL)





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  return list(_TOKENIZER.findall(x.lower()   )   )





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  if operator == _Operator.EQUALS:
    return src == tgt
  elif operator == _Operator.GREATER:
    return src > tgt
  elif operator == _Operator.LESSER:
    return src < tgt
  raise ValueError(f"""Unknown operator: {operator}"""   )





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Any									=    table['types']
  return _TYPE_CONVERTER[types[column]](_UpperCAmelCase   )





def 		UpperCAmelCase__						(	_UpperCAmelCase   ):






  """simple docstring"""





  return isinstance(_UpperCAmelCase					,   _UpperCAmelCase   )





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  for cond in conditions:
    A_    :			Tuple									=    row[cond.column]

    A_    :			int									=    _parse_value(_UpperCAmelCase					,   cond.column					,   cond.cmp_value   )

    if _is_string(_UpperCAmelCase   ) and _is_string(_UpperCAmelCase   ):
      A_    :			Optional[Any]									=    _normalize_for_match(_UpperCAmelCase   )
      A_    :			Union[str, Any]									=    _normalize_for_match(_UpperCAmelCase   )

    if not isinstance(_UpperCAmelCase					,   type(_UpperCAmelCase   )   ):
      raise ValueError('Type difference {} != {}'.format(type(_UpperCAmelCase   )					,   type(_UpperCAmelCase   )   )   )

    if not _compare(cond.operator					,   _UpperCAmelCase					,   _UpperCAmelCase   ):
      return False
  return True





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  if not answer_coordinates:
    if aggregation_op == _Aggregation.COUNT:
      return 0.0
    else:
      return EMPTY_ANSWER_AGG

    # Count can support non numeric answers.
  if aggregation_op == _Aggregation.COUNT:
    return float(len(_UpperCAmelCase   )   )

  # If we have just one answer, if float returns it or try a conversion.
  A_    :			Dict									=    [table['rows'][i][j] for (i, j) in answer_coordinates]
  if len(_UpperCAmelCase   ) == 1:
    try:
      return convert_to_float(values[0]   )
    except ValueError as e:
      if aggregation_op != _Aggregation.NONE:
        raise e

  if aggregation_op == _Aggregation.NONE:
    return None

  # Other aggregation only support numeric values. Bail out if we have strings.
  if not all((isinstance(_UpperCAmelCase					,   (int, float)   ) for v in values)   ):
    return None

  if aggregation_op == _Aggregation.SUM:
    return float(sum(_UpperCAmelCase   )   )
  elif aggregation_op == _Aggregation.AVERAGE:
    return sum(_UpperCAmelCase   ) / len(_UpperCAmelCase   )
  else:
    raise ValueError(f"""Unknown aggregation: {aggregation_op}"""   )





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_    :			Optional[Any]									=    sql_query['agg']
  if aggregation_op_index >= 3:
    A_    :			Tuple									=    _Aggregation(_UpperCAmelCase   )
  else:
    A_    :			str									=    _Aggregation.NONE

  A_    :			List[Any]									=    sql_query['sel']
  A_    :			List[str]									=    [
      _Condition(_UpperCAmelCase					,   _Operator(_UpperCAmelCase   )					,   _UpperCAmelCase   )
      for column, operator, cmp_value in zip(
          sql_query['conds']['column_index']					,   sql_query['conds']['operator_index']					,   sql_query['conds']['condition']   )
  ]

  A_    :			Tuple									=    []
  for row in range(len(table['rows']   )   ):
    if _respect_conditions(_UpperCAmelCase					,   table['rows'][row]					,   _UpperCAmelCase   ):
      indices.append((row, target_column)   )

  if not indices:
    return [], aggregation_op

  if len(_UpperCAmelCase   ) == 1:
    return indices, aggregation_op

  # Parsing of MIN/MAX.
  if aggregation_op_index in (1, 2):
    A_    :			int									=    {2: min, 1: max}
    A_    :			int									=    [(table['rows'][i][j], index) for index, (i, j) in enumerate(_UpperCAmelCase   )]
    A_    :			str									=    functools.reduce(operators[sql_query['agg']]					,   _UpperCAmelCase   )

    A_    :			Optional[int]									=    [indices[reduced[1]]]
    return ret, _Aggregation.NONE

  return indices, aggregation_op





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  if float_answer is not None:
    return [str(_UpperCAmelCase   )]
  return [str(table['real_rows'][r][c]   ) for r, c in answer_coordinates]





def 		UpperCAmelCase__						(	_UpperCAmelCase					,   _UpperCAmelCase   ):






  """simple docstring"""





  A_		,			A_    :			Dict									=    _get_answer_coordinates(_UpperCAmelCase					,   _UpperCAmelCase   )
  A_    :			Union[str, Any]									=    _get_float_answer(_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   )
  A_    :			List[str]									=    _get_answer_text(_UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase   )
  # keep the original data the same with TaPas
  if len(_UpperCAmelCase   ) == 0:
    A_    :			Union[str, Any]									=    [EMPTY_ANSWER]
  return answer_text




from __future__ import annotations

import random
from collections.abc import Iterable


class    _lowercase :
				'''simple docstring'''







				def __init__(			self  ,			snake_case__     ):

									'''simple docstring'''


									UpperCamelCase_			= {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    _lowerCamelCase       (			self  ,			snake_case__     ):

									'''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    _lowerCamelCase       (			self  ,			snake_case__     ):

									'''simple docstring'''


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

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




class    _lowercase :
				'''simple docstring'''







				def __init__(			self  ,			snake_case__     ):

									'''simple docstring'''


									UpperCamelCase_			= list(snake_case__     )

				def __str__(			self     ):

									'''simple docstring'''


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




def  _lowerCAmelCase     ():
					UpperCamelCase_			= []
					UpperCamelCase_			= random.randint(1 ,						5)
					UpperCamelCase_			= "A"
					UpperCamelCase_			= 0
					while i < no_of_literals:
										UpperCamelCase_			= random.randint(1 ,						5)
										UpperCamelCase_			= base_var + str(_lowerCAmelCase)
										UpperCamelCase_			= 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     ():
					UpperCamelCase_			= set()
					UpperCamelCase_			= random.randint(1 ,						10)
					while len(_lowerCAmelCase) < no_of_clauses:
										clauses.add(generate_clause())
					return Formula(_lowerCAmelCase)



def  _lowerCAmelCase     (_lowerCAmelCase):
					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(_lowerCAmelCase)
					return clauses, symbols_set



def  _lowerCAmelCase     (_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase):
					UpperCamelCase_			= []
					UpperCamelCase_			= {}
					UpperCamelCase_			= []

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

					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(_lowerCAmelCase)
					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  _lowerCAmelCase     (_lowerCAmelCase ,						_lowerCAmelCase):
					UpperCamelCase_			= []
					for clause in clauses:
										if len(_lowerCAmelCase) == 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(_lowerCAmelCase) - 1 and n_count == 1:
																				unit_symbols.append(_lowerCAmelCase)
					UpperCamelCase_			= {}
					for i in unit_symbols:
										UpperCamelCase_			= i[:2]
										UpperCamelCase_			= len(_lowerCAmelCase) == 2
					UpperCamelCase_			= [i[:2] for i in unit_symbols]

					return unit_symbols, assignment



def  _lowerCAmelCase     (_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase):
					UpperCamelCase_			= True
					for clause in clauses:
										UpperCamelCase_			= clause.evaluate(_lowerCAmelCase)
										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(_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase)
					except RecursionError:
										print("raises a RecursionError and is")
										return None, {}
					UpperCamelCase_			= None
					if len(_lowerCAmelCase) > 0:
										UpperCamelCase_	,     UpperCamelCase_			= pure_symbols[0], assignment[pure_symbols[0]]

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

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

					return dpll_algorithm(_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase) or dpll_algorithm(_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	UpperCAmelCase :				List[Any]							=generate_formula()
	print(F"The formula {formula} is", end=""" """)

	UpperCAmelCase			,			UpperCAmelCase :				Any							=generate_parameters(formula)
	UpperCAmelCase			,			UpperCAmelCase :				str							=dpll_algorithm(clauses, symbols, {})

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