


'''simple docstring'''
from abc import ABC, abstractmethod
from typing import List, Optional






class        lowerCAmelCase_  (     UpperCAmelCase	):






       def __init__( self   )->      Any:
            # test for the above condition
            self.test()






       def   UpperCamelCase						( self   )->      List[str]:
            _A				=							0
            _A				=							False
            while not completed:
                 if counter == 1:
                      self.reset()
                 _A				=							self.advance()
                 if not self.does_advance(_UpperCamelCase   ):
                      raise Exception(
                          'Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true.'   )

                 _A		,				_A		,				_A				=							self.update(_UpperCamelCase   )
                 counter += 1

                 if counter > 1_0000:
                      raise Exception('update() does not fulfill the constraint.'   )

            if self.remaining() != 0:
                 raise Exception('Custom Constraint is not defined correctly.'   )






       @abstractmethod
       def   UpperCamelCase						( self   )->      Optional[Any]:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






       @abstractmethod
       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Union[str, Any]:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






       @abstractmethod
       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Optional[int]:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






       @abstractmethod
       def   UpperCamelCase						( self   )->      List[str]:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






       @abstractmethod
       def   UpperCamelCase						( self   )->      Dict:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






       @abstractmethod
       def   UpperCamelCase						( self			,     _UpperCamelCase=False   )->      Union[str, Any]:
            raise NotImplementedError(
                F'{self.__class__} is an abstract class. Only classes inheriting this class can be called.'   )






class        lowerCAmelCase_  (     UpperCAmelCase	):






       def __init__( self			,     _UpperCamelCase   )->      int:
            super(_UpperCamelCase			,     self   ).__init__()

            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ) or len(_UpperCamelCase   ) == 0:
                 raise ValueError(F'`token_ids` has to be a non-empty list, but is {token_ids}.'   )
            if any((not isinstance(_UpperCamelCase			,     _UpperCamelCase   ) or token_id < 0) for token_id in token_ids   ):
                 raise ValueError(F'Each list in `token_ids` has to be a list of positive integers, but is {token_ids}.'   )

            _A				=							token_ids

            _A				=							len(self.token_ids   )
            _A				=							-1  # the index of the currently fulfilled step
            _A				=							False






       def   UpperCamelCase						( self   )->      Optional[int]:
            if self.completed:
                 return None
            return self.token_ids[self.fulfilled_idx + 1]






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      str:
            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(F'`token_id` has to be an `int`, but is {token_id} of type {type(_UpperCamelCase   )}'   )

            if self.completed:
                 return False

            return token_id == self.token_ids[self.fulfilled_idx + 1]






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Any:
            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(F'`token_id` has to be an `int`, but is {token_id} of type {type(_UpperCamelCase   )}'   )

            _A				=							False
            _A				=							False
            _A				=							False

            if self.does_advance(_UpperCamelCase   ):
                 self.fulfilled_idx += 1
                 _A				=							True
                 if self.fulfilled_idx == (self.seqlen - 1):
                      _A				=							True
                 _A				=							completed
            else:
                 # failed to make progress.
                 _A				=							True
                 self.reset()
            return stepped, completed, reset






       def   UpperCamelCase						( self   )->      Dict:
            _A				=							False
            _A				=							0






       def   UpperCamelCase						( self   )->      str:
            return self.seqlen - (self.fulfilled_idx + 1)






       def   UpperCamelCase						( self			,     _UpperCamelCase=False   )->      Any:
            _A				=							PhrasalConstraint(self.token_ids   )

            if stateful:
                 _A				=							self.seqlen
                 _A				=							self.fulfilled_idx
                 _A				=							self.completed

            return new_constraint






class        lowerCAmelCase_  :






       def __init__( self			,     _UpperCamelCase			,     _UpperCamelCase=True   )->      int:
            _A				=							max([len(_UpperCamelCase   ) for one in nested_token_ids]   )

            _A				=							{}
            for token_ids in nested_token_ids:
                 _A				=							root
                 for tidx, token_id in enumerate(_UpperCamelCase   ):
                      if token_id not in level:
                           _A				=							{}

                      _A				=							level[token_id]

            if no_subsets and self.has_subsets(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(
                     'Each list in `nested_token_ids` can\'t be a complete subset of another list, but is'
                     F' {nested_token_ids}.'   )

            _A				=							root






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      str:
            _A				=							self.trie

            for current_token in current_seq:
                 _A				=							start[current_token]

            _A				=							list(start.keys()   )

            return next_tokens






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      str:
            _A				=							self.next_tokens(_UpperCamelCase   )

            return len(_UpperCamelCase   ) == 0






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Any:
            _A				=							list(root.values()   )
            if len(_UpperCamelCase   ) == 0:
                 return 1
            else:
                 return sum([self.count_leaves(_UpperCamelCase   ) for nn in next_nodes]   )






       def   UpperCamelCase						( self			,     _UpperCamelCase			,     _UpperCamelCase   )->      List[str]:
            _A				=							self.count_leaves(_UpperCamelCase   )
            return len(_UpperCamelCase   ) != leaf_count






class        lowerCAmelCase_  (     UpperCAmelCase	):






       def __init__( self			,     _UpperCamelCase   )->      List[Any]:
            super(_UpperCamelCase			,     self   ).__init__()

            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ) or len(_UpperCamelCase   ) == 0:
                 raise ValueError(F'`nested_token_ids` has to be a non-empty list, but is {nested_token_ids}.'   )
            if any(not isinstance(_UpperCamelCase			,     _UpperCamelCase   ) for token_ids in nested_token_ids   ):
                 raise ValueError(F'`nested_token_ids` has to be a list of lists, but is {nested_token_ids}.'   )
            if any(
                any((not isinstance(_UpperCamelCase			,     _UpperCamelCase   ) or token_id < 0) for token_id in token_ids   )
                for token_ids in nested_token_ids   ):
                 raise ValueError(
                     F'Each list in `nested_token_ids` has to be a list of positive integers, but is {nested_token_ids}.'   )

            _A				=							DisjunctiveTrie(_UpperCamelCase   )
            _A				=							nested_token_ids

            _A				=							self.trie.max_height
            _A				=							[]
            _A				=							False






       def   UpperCamelCase						( self   )->      List[Any]:
            _A				=							self.trie.next_tokens(self.current_seq   )

            if len(_UpperCamelCase   ) == 0:
                 return None
            else:
                 return token_list






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Tuple:
            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(F'`token_id` is supposed to be type `int`, but is {token_id} of type {type(_UpperCamelCase   )}'   )

            _A				=							self.trie.next_tokens(self.current_seq   )

            return token_id in next_tokens






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Any:
            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(F'`token_id` is supposed to be type `int`, but is {token_id} of type {type(_UpperCamelCase   )}'   )

            _A				=							False
            _A				=							False
            _A				=							False

            if self.does_advance(_UpperCamelCase   ):
                 self.current_seq.append(_UpperCamelCase   )
                 _A				=							True
            else:
                 _A				=							True
                 self.reset()

            _A				=							self.trie.reached_leaf(self.current_seq   )
            _A				=							completed

            return stepped, completed, reset






       def   UpperCamelCase						( self   )->      int:
            _A				=							False
            _A				=							[]






       def   UpperCamelCase						( self   )->      Dict:
            if self.completed:
                 # since this can be completed without reaching max height
                 return 0
            else:
                 return self.seqlen - len(self.current_seq   )






       def   UpperCamelCase						( self			,     _UpperCamelCase=False   )->      List[str]:
            _A				=							DisjunctiveConstraint(self.token_ids   )

            if stateful:
                 _A				=							self.seqlen
                 _A				=							self.current_seq
                 _A				=							self.completed

            return new_constraint






class        lowerCAmelCase_  :






       def __init__( self			,     _UpperCamelCase   )->      List[Any]:
            _A				=							constraints

            # max # of steps required to fulfill a given constraint
            _A				=							max([c.seqlen for c in constraints]   )
            _A				=							len(_UpperCamelCase   )
            _A				=							False

            self.init_state()






       def   UpperCamelCase						( self   )->      Tuple:
            _A				=							[]
            _A				=							None
            _A				=							[constraint.copy(stateful=_UpperCamelCase   ) for constraint in self.constraints]






       def   UpperCamelCase						( self   )->      Optional[Any]:
            _A				=							0
            if self.inprogress_constraint:
                 # extra points for having a constraint mid-fulfilled
                 add += self.max_seqlen - self.inprogress_constraint.remaining()

            return (len(self.complete_constraints   ) * self.max_seqlen) + add






       def   UpperCamelCase						( self   )->      Union[str, Any]:
            _A				=							[]
            if self.inprogress_constraint is None:
                 for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
                      _A				=							constraint.advance()
                      if isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                           token_list.append(_UpperCamelCase   )
                      elif isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                           token_list.extend(_UpperCamelCase   )
            else:
                 _A				=							self.inprogress_constraint.advance()
                 if isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                      token_list.append(_UpperCamelCase   )
                 elif isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                      token_list.extend(_UpperCamelCase   )

            if len(_UpperCamelCase   ) == 0:
                 return None
            else:
                 return token_list






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      Union[str, Any]:
            self.init_state()

            if token_ids is not None:
                 for token in token_ids:
                      # completes or steps **one** constraint
                      _A		,				_A				=							self.add(_UpperCamelCase   )

                      # the entire list of constraints are fulfilled
                      if self.completed:
                           break






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      List[str]:
            if not isinstance(_UpperCamelCase			,     _UpperCamelCase   ):
                 raise ValueError(F'`token_id` should be an `int`, but is `{token_id}`.'   )

            _A		,				_A				=							False, False

            if self.completed:
                 _A				=							True
                 _A				=							False
                 return complete, stepped

            if self.inprogress_constraint is not None:
                 # In the middle of fulfilling a constraint. If the `token_id` *does* makes an incremental progress to current
                 # job, simply update the state

                 _A		,				_A		,				_A				=							self.inprogress_constraint.update(_UpperCamelCase   )
                 if reset:
                      # 1. If the next token breaks the progress, then we must restart.
                      #     e.g. constraint = "I love pies" and sequence so far is "I love" but `token_id` == "books".

                      #     But that doesn't mean we self.init_state(), since we only reset the state for this particular
                      #     constraint, not the full list of constraints.

                      self.pending_constraints.append(self.inprogress_constraint.copy(stateful=_UpperCamelCase   )   )
                      _A				=							None

                 if complete:
                      # 2. If the next token completes the constraint, move it to completed list, set
                      #     inprogress to None. If there are no pending constraints either, then this full list of constraints
                      #     is complete.

                      self.complete_constraints.append(self.inprogress_constraint   )
                      _A				=							None

                      if len(self.pending_constraints   ) == 0:
                           # we're done!
                           _A				=							True

            else:
                 # Not in the middle of fulfilling a constraint. So does this `token_id` helps us step towards any of our list
                 # of constraints?

                 for cidx, pending_constraint in enumerate(self.pending_constraints   ):
                      if pending_constraint.does_advance(_UpperCamelCase   ):
                           _A		,				_A		,				_A				=							pending_constraint.update(_UpperCamelCase   )

                           if not stepped:
                                raise Exception(
                                    '`constraint.update(token_id)` is not yielding incremental progress, '
                                    'even though `constraint.does_advance(token_id)` is true.'   )

                           if complete:
                                self.complete_constraints.append(_UpperCamelCase   )
                                _A				=							None

                           if not complete and stepped:
                                _A				=							pending_constraint

                           if complete or stepped:
                                # If we made any progress at all, then it's at least not a "pending constraint".

                                _A				=							(
                                    self.pending_constraints[:cidx] + self.pending_constraints[cidx + 1 :]
                                )

                                if len(self.pending_constraints   ) == 0 and self.inprogress_constraint is None:
                                     # If there's no longer any pending after this and no inprogress either, then we must be
                                     # complete.

                                     _A				=							True

                                break  # prevent accidentally stepping through multiple constraints with just one token.

            return complete, stepped






       def   UpperCamelCase						( self			,     _UpperCamelCase=True   )->      List[str]:
            _A				=							ConstraintListState(self.constraints   )  # we actually never though self.constraints objects
            # throughout this process. So it's at initialization state.

            if stateful:
                 _A				=							[
                     constraint.copy(stateful=_UpperCamelCase   ) for constraint in self.complete_constraints
                 ]
                 if self.inprogress_constraint is not None:
                      _A				=							self.inprogress_constraint.copy(stateful=_UpperCamelCase   )
                 _A				=							[constraint.copy() for constraint in self.pending_constraints]

            return new_state









'''simple docstring'''
def 					lowerCamelCase_ ( __UpperCamelCase					:       list							,    __UpperCamelCase					:       int							,    __UpperCamelCase					:       int = 0							,    __UpperCamelCase					:       int = 0		)					->	int:







     """simple docstring"""
     _A				=							right or len(__UpperCamelCase		) - 1
     if left > right:
          return -1
     elif list_data[left] == key:
          return left
     elif list_data[right] == key:
          return right
     else:
          return search(__UpperCamelCase							,    __UpperCamelCase							,    left + 1							,    right - 1		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()





