from abc import ABC, abstractmethod
from typing import List, Optional







class __snake_case				(						lowerCamelCase_		):




   def __init__(    self			:				Tuple      ):



     """simple docstring"""






     self.test()




   def 	__a						(    self			:				List[Any]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      0
     SCREAMING_SNAKE_CASE__										=      False
     while not completed:
       if counter == 1:
         self.reset()
       SCREAMING_SNAKE_CASE__										=      self.advance()
       if not self.does_advance(_a      ):
         raise Exception(
             """Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true."""      )

       SCREAMING_SNAKE_CASE__										=      self.update(_a      )
       counter += 1

       if counter > 1_00_00:
         raise Exception("""update() does not fulfill the constraint."""      )

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




   @abstractmethod
   def 	__a						(    self			:				Optional[int]      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )




   @abstractmethod
   def 	__a						(    self			:				str       ,	_lowercase			:				str      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )




   @abstractmethod
   def 	__a						(    self			:				str       ,	_lowercase			:				str      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )




   @abstractmethod
   def 	__a						(    self			:				Dict      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )




   @abstractmethod
   def 	__a						(    self			:				int      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )




   @abstractmethod
   def 	__a						(    self			:				Optional[int]       ,	_lowercase			:				Dict=False      ):



     """simple docstring"""






     raise NotImplementedError(
         f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""      )







class __snake_case				(						lowerCamelCase_		):




   def __init__(    self			:				Dict       ,	_lowercase			:				Optional[Any]      ):



     """simple docstring"""






     super(_a       ,	self      ).__init__()

     if not isinstance(_a       ,	_a      ) or len(_a      ) == 0:
       raise ValueError(f"""`token_ids` has to be a non-empty list, but is {token_ids}."""      )
     if any((not isinstance(_a       ,	_a      ) 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}."""      )

     SCREAMING_SNAKE_CASE__										=      token_ids

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




   def 	__a						(    self			:				List[str]      ):



     """simple docstring"""






     if self.completed:
       return None
     return self.token_ids[self.fulfilled_idx + 1]




   def 	__a						(    self			:				List[Any]       ,	_lowercase			:				Union[str, Any]      ):



     """simple docstring"""






     if not isinstance(_a       ,	_a      ):
       raise ValueError(f"""`token_id` has to be an `int`, but is {token_id} of type {type(_a      )}"""      )

     if self.completed:
       return False

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




   def 	__a						(    self			:				Tuple       ,	_lowercase			:				Optional[int]      ):



     """simple docstring"""






     if not isinstance(_a       ,	_a      ):
       raise ValueError(f"""`token_id` has to be an `int`, but is {token_id} of type {type(_a      )}"""      )

     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      False

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




   def 	__a						(    self			:				Optional[Any]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      0




   def 	__a						(    self			:				Dict      ):



     """simple docstring"""






     return self.seqlen - (self.fulfilled_idx + 1)




   def 	__a						(    self			:				Dict       ,	_lowercase			:				int=False      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      PhrasalConstraint(self.token_ids      )

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

     return new_constraint







class __snake_case				:




   def __init__(    self			:				int       ,	_lowercase			:				Any       ,	_lowercase			:				Optional[Any]=True      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      max([len(_a      ) for one in nested_token_ids]      )

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

         SCREAMING_SNAKE_CASE__										=      level[token_id]

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

     SCREAMING_SNAKE_CASE__										=      root




   def 	__a						(    self			:				Dict       ,	_lowercase			:				Union[str, Any]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      self.trie

     for current_token in current_seq:
       SCREAMING_SNAKE_CASE__										=      start[current_token]

     SCREAMING_SNAKE_CASE__										=      list(start.keys()      )

     return next_tokens




   def 	__a						(    self			:				Tuple       ,	_lowercase			:				Tuple      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      self.next_tokens(_a      )

     return len(_a      ) == 0




   def 	__a						(    self			:				List[Any]       ,	_lowercase			:				Dict      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      list(root.values()      )
     if len(_a      ) == 0:
       return 1
     else:
       return sum([self.count_leaves(_a      ) for nn in next_nodes]      )




   def 	__a						(    self			:				Tuple       ,	_lowercase			:				List[Any]       ,	_lowercase			:				List[str]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      self.count_leaves(_a      )
     return len(_a      ) != leaf_count







class __snake_case				(						lowerCamelCase_		):




   def __init__(    self			:				int       ,	_lowercase			:				str      ):



     """simple docstring"""






     super(_a       ,	self      ).__init__()

     if not isinstance(_a       ,	_a      ) or len(_a      ) == 0:
       raise ValueError(f"""`nested_token_ids` has to be a non-empty list, but is {nested_token_ids}."""      )
     if any(not isinstance(_a       ,	_a      ) 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(_a       ,	_a      ) 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}."""      )

     SCREAMING_SNAKE_CASE__										=      DisjunctiveTrie(_a      )
     SCREAMING_SNAKE_CASE__										=      nested_token_ids

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




   def 	__a						(    self			:				str      ):



     """simple docstring"""






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

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




   def 	__a						(    self			:				Dict       ,	_lowercase			:				List[Any]      ):



     """simple docstring"""






     if not isinstance(_a       ,	_a      ):
       raise ValueError(f"""`token_id` is supposed to be type `int`, but is {token_id} of type {type(_a      )}"""      )

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

     return token_id in next_tokens




   def 	__a						(    self			:				List[str]       ,	_lowercase			:				Union[str, Any]      ):



     """simple docstring"""






     if not isinstance(_a       ,	_a      ):
       raise ValueError(f"""`token_id` is supposed to be type `int`, but is {token_id} of type {type(_a      )}"""      )

     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      False

     if self.does_advance(_a      ):
       self.current_seq.append(_a      )
       SCREAMING_SNAKE_CASE__										=      True
     else:
       SCREAMING_SNAKE_CASE__										=      True
       self.reset()

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

     return stepped, completed, reset




   def 	__a						(    self			:				Optional[int]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      False
     SCREAMING_SNAKE_CASE__										=      []




   def 	__a						(    self			:				Dict      ):



     """simple docstring"""






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




   def 	__a						(    self			:				Any       ,	_lowercase			:				List[str]=False      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      DisjunctiveConstraint(self.token_ids      )

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

     return new_constraint







class __snake_case				:




   def __init__(    self			:				List[str]       ,	_lowercase			:				Optional[int]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      constraints

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

     self.init_state()




   def 	__a						(    self			:				Optional[Any]      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      []
     SCREAMING_SNAKE_CASE__										=      None
     SCREAMING_SNAKE_CASE__										=      [constraint.copy(stateful=_a      ) for constraint in self.constraints]




   def 	__a						(    self			:				Any      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      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 	__a						(    self			:				Any      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      []
     if self.inprogress_constraint is None:
       for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
         SCREAMING_SNAKE_CASE__										=      constraint.advance()
         if isinstance(_a       ,	_a      ):
           token_list.append(_a      )
         elif isinstance(_a       ,	_a      ):
           token_list.extend(_a      )
     else:
       SCREAMING_SNAKE_CASE__										=      self.inprogress_constraint.advance()
       if isinstance(_a       ,	_a      ):
         token_list.append(_a      )
       elif isinstance(_a       ,	_a      ):
         token_list.extend(_a      )

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




   def 	__a						(    self			:				Union[str, Any]       ,	_lowercase			:				str      ):



     """simple docstring"""






     self.init_state()

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

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




   def 	__a						(    self			:				Any       ,	_lowercase			:				int      ):



     """simple docstring"""






     if not isinstance(_a       ,	_a      ):
       raise ValueError(f"""`token_id` should be an `int`, but is `{token_id}`."""      )

     SCREAMING_SNAKE_CASE__										=      False, False

     if self.completed:
       SCREAMING_SNAKE_CASE__										=      True
       SCREAMING_SNAKE_CASE__										=      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

       SCREAMING_SNAKE_CASE__										=      self.inprogress_constraint.update(_a      )
       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=_a      )      )
         SCREAMING_SNAKE_CASE__										=      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      )
         SCREAMING_SNAKE_CASE__										=      None

         if len(self.pending_constraints      ) == 0:
           # we're done!
           SCREAMING_SNAKE_CASE__										=      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(_a      ):
           SCREAMING_SNAKE_CASE__										=      pending_constraint.update(_a      )

           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(_a      )
             SCREAMING_SNAKE_CASE__										=      None

           if not complete and stepped:
             SCREAMING_SNAKE_CASE__										=      pending_constraint

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

             SCREAMING_SNAKE_CASE__										=      (
                 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.

               SCREAMING_SNAKE_CASE__										=      True

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

     return complete, stepped




   def 	__a						(    self			:				Tuple       ,	_lowercase			:				List[Any]=True      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      ConstraintListState(self.constraints      )  # we actually never though self.constraints objects
     # throughout this process. So it's at initialization state.

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

     return new_state


from __future__ import annotations





class       _snake_case					:







			def __init__(				self						,   _a		):
				__magic_name__		:		Optional[Any]	   =     data
				__magic_name__		:		Node | None	   =     None
				__magic_name__		:		Node | None	   =     None







def   lowerCAmelCase_						(					_snake_case      :  Node | None   )				->		None:  # In Order traversal of the tree







	'''simple docstring'''


	if tree:
		display(tree.left   )
		print(tree.data   )
		display(tree.right   )






def   lowerCAmelCase_						(					_snake_case      :  Node | None   )				->		int:







	'''simple docstring'''


	return 1 + max(depth_of_tree(tree.left   )      ,   depth_of_tree(tree.right   )   ) if tree else 0






def   lowerCAmelCase_						(					_snake_case      :  Node   )				->		bool:







	'''simple docstring'''


	if not tree:
		return True
	if tree.left and tree.right:
		return is_full_binary_tree(tree.left   ) and is_full_binary_tree(tree.right   )
	else:
		return not tree.left and not tree.right






def   lowerCAmelCase_						(					)				->		None:  # Main function for testing.







	'''simple docstring'''


	__magic_name__		:		int	   =     Node(1   )
	__magic_name__		:		Union[str, Any]	   =     Node(2   )
	__magic_name__		:		Tuple	   =     Node(3   )
	__magic_name__		:		Optional[Any]	   =     Node(4   )
	__magic_name__		:		Union[str, Any]	   =     Node(5   )
	__magic_name__		:		Any	   =     Node(6   )
	__magic_name__		:		int	   =     Node(7   )
	__magic_name__		:		List[str]	   =     Node(8   )
	__magic_name__		:		Union[str, Any]	   =     Node(9   )

	print(is_full_binary_tree(_snake_case   )   )
	print(depth_of_tree(_snake_case   )   )
	print("Tree is: "   )
	display(_snake_case   )


if __name__ == "__main__":
				main()
