from __future__ import annotations

import random
from collections.abc import Iterable


class 						a__							:



			def __init__(						self      ,						UpperCAmelCase    ) ->    None:
								__a							=   {literal: None for literal in literals}



			def __str__(						self    ) ->    str:
								return "{" + " , ".join(self.literals    ) + "}"



			def __len__(						self    ) ->    int:
								return len(self.literals    )



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







			def __SCREAMING_SNAKE_CASE							(						self      ,						UpperCAmelCase    ) ->    bool | None:
								for literal in self.literals:
													__a							=   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 						a__							:



			def __init__(						self      ,						UpperCAmelCase    ) ->    None:
								__a							=   list(UpperCAmelCase    )







			def __str__(						self    ) ->    str:
								return "{" + " , ".join(str(UpperCAmelCase    ) for clause in self.clauses    ) + "}"






def 							lowerCAmelCase(	):
					__a							=   []
					__a							=   random.randint(1      ,				5						)
					__a							=   'A'
					__a							=   0
					while i < no_of_literals:
										__a							=   random.randint(1      ,				5						)
										__a							=   base_var + str(__lowerCamelCase						)
										__a							=   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(	):
					__a							=   set()
					__a							=   random.randint(1      ,				10						)
					while len(__lowerCamelCase						) < no_of_clauses:
										clauses.add(generate_clause()						)
					return Formula(__lowerCamelCase						)
def 							lowerCAmelCase(	__lowerCamelCase						):
					__a							=   formula.clauses
					__a							=   []
					for clause in formula.clauses:
										for literal in clause.literals:
															__a							=   literal[:2]
															if symbol not in symbols_set:
																				symbols_set.append(__lowerCamelCase						)
					return clauses, symbols_set
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   []
					__a							=   {}
					__a							=   []

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

					for s in symbols:
										__a							=   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:
										__a							=   None
					for s in pure_symbols:
										__a							=   s + '\''
										if s in literals:
															__a							=   True
										elif sym in literals:
															__a							=   False
					return pure_symbols, assignment
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   []
					for clause in clauses:
										if len(__lowerCamelCase						) == 1:
															unit_symbols.append(list(clause.literals.keys()						)[0]						)
										else:
															__a					,      __a							=   0, 0
															for literal, value in clause.literals.items():
																				if value is False:
																									f_count += 1
																				elif value is None:
																									__a							=   literal
																									n_count += 1
															if f_count == len(__lowerCamelCase						) - 1 and n_count == 1:
																				unit_symbols.append(__lowerCamelCase						)
					__a							=   {}
					for i in unit_symbols:
										__a							=   i[:2]
										__a							=   len(__lowerCamelCase						) == 2
					__a							=   [i[:2] for i in unit_symbols]

					return unit_symbols, assignment
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   True
					for clause in clauses:
										__a							=   clause.evaluate(__lowerCamelCase						)
										if clause_check is False:
															return False, None
										elif clause_check is None:
															__a							=   False
															continue

					if check_clause_all_true:
										return True, model

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

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

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

					return dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						) or dpll_algorithm(__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	lowerCamelCase_				:		Any       						=       generate_formula()
	print(F'''The formula {formula} is''', end=""" """)

	lowerCamelCase_						,  lowerCamelCase_				:		Dict       						=       generate_parameters(formula)
	lowerCamelCase_						,  lowerCamelCase_				:		Tuple       						=       dpll_algorithm(clauses, symbols, {})

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











from collections import OrderedDict
from typing import Any, List, Mapping, Optional

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast, PatchingSpec
from ...utils import logging


UpperCAmelCase__  :	str     =logging.get_logger(__name__)

UpperCAmelCase__  :	Optional[int]     ={
    '''gpt2''': '''https://huggingface.co/gpt2/resolve/main/config.json''',
    '''gpt2-medium''': '''https://huggingface.co/gpt2-medium/resolve/main/config.json''',
    '''gpt2-large''': '''https://huggingface.co/gpt2-large/resolve/main/config.json''',
    '''gpt2-xl''': '''https://huggingface.co/gpt2-xl/resolve/main/config.json''',
    '''distilgpt2''': '''https://huggingface.co/distilgpt2/resolve/main/config.json''',
}

class 					__A   (  a			):
				__A            = """gpt2"""
				__A            = ["""past_key_values"""]
				__A            = {
				    """hidden_size""": """n_embd""",
				    """max_position_embeddings""": """n_positions""",
				    """num_attention_heads""": """n_head""",
				    """num_hidden_layers""": """n_layer""",
				}


				def __init__(						self      ,       UpperCAmelCase_=50257      ,       UpperCAmelCase_=1024      ,       UpperCAmelCase_=768      ,       UpperCAmelCase_=12      ,       UpperCAmelCase_=12      ,       UpperCAmelCase_=None      ,       UpperCAmelCase_="gelu_new"      ,       UpperCAmelCase_=0.1      ,       UpperCAmelCase_=0.1      ,       UpperCAmelCase_=0.1      ,       UpperCAmelCase_=1E-5      ,       UpperCAmelCase_=0.0_2      ,       UpperCAmelCase_="cls_index"      ,       UpperCAmelCase_=True      ,       UpperCAmelCase_=None      ,       UpperCAmelCase_=True      ,       UpperCAmelCase_=0.1      ,       UpperCAmelCase_=True      ,       UpperCAmelCase_=True      ,       UpperCAmelCase_=50256      ,       UpperCAmelCase_=50256      ,       UpperCAmelCase_=False      ,       UpperCAmelCase_=False      ,       **UpperCAmelCase_      ,       ):
								lowerCamelCase		       =vocab_size
								lowerCamelCase		       =n_positions
								lowerCamelCase		       =n_embd
								lowerCamelCase		       =n_layer
								lowerCamelCase		       =n_head
								lowerCamelCase		       =n_inner
								lowerCamelCase		       =activation_function
								lowerCamelCase		       =resid_pdrop
								lowerCamelCase		       =embd_pdrop
								lowerCamelCase		       =attn_pdrop
								lowerCamelCase		       =layer_norm_epsilon
								lowerCamelCase		       =initializer_range
								lowerCamelCase		       =summary_type
								lowerCamelCase		       =summary_use_proj
								lowerCamelCase		       =summary_activation
								lowerCamelCase		       =summary_first_dropout
								lowerCamelCase		       =summary_proj_to_labels
								lowerCamelCase		       =scale_attn_weights
								lowerCamelCase		       =use_cache
								lowerCamelCase		       =scale_attn_by_inverse_layer_idx
								lowerCamelCase		       =reorder_and_upcast_attn

								lowerCamelCase		       =bos_token_id
								lowerCamelCase		       =eos_token_id

								super().__init__(bos_token_id=UpperCAmelCase_      ,       eos_token_id=UpperCAmelCase_      ,       **UpperCAmelCase_							)




class 					__A   (  a			):


				def __init__(						self      ,       UpperCAmelCase_      ,       UpperCAmelCase_ = "default"      ,       UpperCAmelCase_ = None      ,       UpperCAmelCase_ = False      ,       ):
								super().__init__(UpperCAmelCase_      ,       task=UpperCAmelCase_      ,       patching_specs=UpperCAmelCase_      ,       use_past=UpperCAmelCase_							)
								if not getattr(self._config      ,       """pad_token_id"""      ,       UpperCAmelCase_							):
												# TODO: how to do that better?
												lowerCamelCase		       =0


				@property
				def _snake_case				(						self							):
								lowerCamelCase		       =OrderedDict({"""input_ids""": {0: """batch""", 1: """sequence"""}}							)
								if self.use_past:
												self.fill_with_past_key_values_(UpperCAmelCase_      ,       direction="""inputs"""							)
												lowerCamelCase		       ={0: """batch""", 1: """past_sequence + sequence"""}
								else:
												lowerCamelCase		       ={0: """batch""", 1: """sequence"""}

								return common_inputs


				@property
				def _snake_case				(						self							):
								return self._config.n_layer


				@property
				def _snake_case				(						self							):
								return self._config.n_head


				def _snake_case				(						self      ,       UpperCAmelCase_      ,       UpperCAmelCase_ = -1      ,       UpperCAmelCase_ = -1      ,       UpperCAmelCase_ = False      ,       UpperCAmelCase_ = None      ,       ):
								lowerCamelCase		       =super(UpperCAmelCase_      ,       self							).generate_dummy_inputs(
								    UpperCAmelCase_      ,       batch_size=UpperCAmelCase_      ,       seq_length=UpperCAmelCase_      ,       is_pair=UpperCAmelCase_      ,       framework=UpperCAmelCase_							)

								# We need to order the input in the way they appears in the forward()
								lowerCamelCase		       =OrderedDict({"""input_ids""": common_inputs["""input_ids"""]}							)

								# Need to add the past_keys
								if self.use_past:
												if not is_torch_available():
																raise ValueError("""Cannot generate dummy past_keys inputs without PyTorch installed."""							)
												else:
																import torch

																lowerCamelCase       ,     lowerCamelCase		       =common_inputs["""input_ids"""].shape
																# Not using the same length for past_key_values
																lowerCamelCase		       =seqlen + 2
																lowerCamelCase		       =(
																    batch,
																    self.num_attention_heads,
																    past_key_values_length,
																    self._config.hidden_size // self.num_attention_heads,
																)
																lowerCamelCase		       =[
																    (torch.zeros(UpperCAmelCase_							), torch.zeros(UpperCAmelCase_							)) for _ in range(self.num_layers							)
																]

								lowerCamelCase		       =common_inputs["""attention_mask"""]
								if self.use_past:
												lowerCamelCase		       =ordered_inputs["""attention_mask"""].dtype
												lowerCamelCase		       =torch.cat(
												    [ordered_inputs["""attention_mask"""], torch.ones(UpperCAmelCase_      ,       UpperCAmelCase_      ,       dtype=UpperCAmelCase_							)]      ,       dim=1							)

								return ordered_inputs


				@property
				def _snake_case				(						self							):
								return 13





