


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



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		def __init__(self					):





			'''simple docstring'''

			self.test()



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						List[str]						=				0
			__snake_case	:						Tuple						=				False
			while not completed:
				if counter == 1:
					self.reset()
				__snake_case	:						Dict						=				self.advance()
				if not self.does_advance(a_					):
					raise Exception(
					    '''Custom Constraint is not defined correctly. self.does_advance(self.advance()) must be true.'''					)

				__snake_case	,							__snake_case	,							__snake_case	:						Tuple						=				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 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

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



		@abstractmethod
		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

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



		@abstractmethod
		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

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



		@abstractmethod
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

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



		@abstractmethod
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

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



		@abstractmethod
		def 				SCREAMING_SNAKE_CASE  (self				,       a_=False					):





			'''simple docstring'''

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



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''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}."""					)

			__snake_case	:						str						=				token_ids

			__snake_case	:						Optional[Any]						=				len(self.token_ids					)
			__snake_case	:						Dict						=				-1  # the index of the currently fulfilled step
			__snake_case	:						List[str]						=				False



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

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



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''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 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''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_					)}"""					)

			__snake_case	:						Optional[Any]						=				False
			__snake_case	:						Tuple						=				False
			__snake_case	:						Optional[Any]						=				False

			if self.does_advance(a_					):
				self.fulfilled_idx += 1
				__snake_case	:						Optional[Any]						=				True
				if self.fulfilled_idx == (self.seqlen - 1):
					__snake_case	:						List[str]						=				True
				__snake_case	:						Tuple						=				completed
			else:
				# failed to make progress.
				__snake_case	:						Union[str, Any]						=				True
				self.reset()
			return stepped, completed, reset



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				False
			__snake_case	:						Optional[int]						=				0



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

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



		def 				SCREAMING_SNAKE_CASE  (self				,       a_=False					):





			'''simple docstring'''

			__snake_case	:						Union[str, Any]						=				PhrasalConstraint(self.token_ids					)

			if stateful:
				__snake_case	:						List[Any]						=				self.seqlen
				__snake_case	:						str						=				self.fulfilled_idx
				__snake_case	:						Union[str, Any]						=				self.completed

			return new_constraint



class 			_UpperCAmelCase :






		'''simple docstring'''

		def __init__(self				,       a_				,       a_=True					):





			'''simple docstring'''

			__snake_case	:						List[str]						=				max([len(a_					) for one in nested_token_ids]					)

			__snake_case	:						str						=				{}
			for token_ids in nested_token_ids:
				__snake_case	:						Optional[Any]						=				root
				for tidx, token_id in enumerate(a_					):
					if token_id not in level:
						__snake_case	:						Optional[Any]						=				{}

					__snake_case	:						List[Any]						=				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}."""					)

			__snake_case	:						Any						=				root



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			__snake_case	:						int						=				self.trie

			for current_token in current_seq:
				__snake_case	:						str						=				start[current_token]

			__snake_case	:						Tuple						=				list(start.keys()					)

			return next_tokens



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			__snake_case	:						int						=				self.next_tokens(a_					)

			return len(a_					) == 0



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

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



		def 				SCREAMING_SNAKE_CASE  (self				,       a_				,       a_					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				self.count_leaves(a_					)
			return len(a_					) != leaf_count



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''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}."""					)

			__snake_case	:						Union[str, Any]						=				DisjunctiveTrie(a_					)
			__snake_case	:						int						=				nested_token_ids

			__snake_case	:						List[Any]						=				self.trie.max_height
			__snake_case	:						Optional[Any]						=				[]
			__snake_case	:						List[Any]						=				False



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Optional[Any]						=				self.trie.next_tokens(self.current_seq					)

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



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''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_					)}"""					)

			__snake_case	:						List[Any]						=				self.trie.next_tokens(self.current_seq					)

			return token_id in next_tokens



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''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_					)}"""					)

			__snake_case	:						Any						=				False
			__snake_case	:						int						=				False
			__snake_case	:						Optional[Any]						=				False

			if self.does_advance(a_					):
				self.current_seq.append(a_					)
				__snake_case	:						List[Any]						=				True
			else:
				__snake_case	:						Optional[Any]						=				True
				self.reset()

			__snake_case	:						Union[str, Any]						=				self.trie.reached_leaf(self.current_seq					)
			__snake_case	:						List[Any]						=				completed

			return stepped, completed, reset



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				False
			__snake_case	:						List[str]						=				[]



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''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 				SCREAMING_SNAKE_CASE  (self				,       a_=False					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				DisjunctiveConstraint(self.token_ids					)

			if stateful:
				__snake_case	:						List[str]						=				self.seqlen
				__snake_case	:						Optional[Any]						=				self.current_seq
				__snake_case	:						Optional[int]						=				self.completed

			return new_constraint



class 			_UpperCAmelCase :






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''simple docstring'''

			__snake_case	:						int						=				constraints

			# max # of steps required to fulfill a given constraint
			__snake_case	:						List[str]						=				max([c.seqlen for c in constraints]					)
			__snake_case	:						List[str]						=				len(a_					)
			__snake_case	:						Optional[Any]						=				False

			self.init_state()



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Dict						=				[]
			__snake_case	:						List[str]						=				None
			__snake_case	:						Dict						=				[constraint.copy(stateful=a_					) for constraint in self.constraints]



		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				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 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				[]
			if self.inprogress_constraint is None:
				for constraint in self.pending_constraints:  # "pending" == "unfulfilled yet"
					__snake_case	:						List[Any]						=				constraint.advance()
					if isinstance(a_				,       a_					):
						token_list.append(a_					)
					elif isinstance(a_				,       a_					):
						token_list.extend(a_					)
			else:
				__snake_case	:						Dict						=				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 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			self.init_state()

			if token_ids is not None:
				for token in token_ids:
					# completes or steps **one** constraint
					__snake_case	,							__snake_case	:						List[str]						=				self.add(a_					)

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



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

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

			__snake_case	,							__snake_case	:						Dict						=				False, False

			if self.completed:
				__snake_case	:						Dict						=				True
				__snake_case	:						Optional[Any]						=				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

				__snake_case	,							__snake_case	,							__snake_case	:						Tuple						=				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_					)					)
					__snake_case	:						str						=				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					)
					__snake_case	:						List[str]						=				None

					if len(self.pending_constraints					) == 0:
						# we're done!
						__snake_case	:						int						=				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_					):
						__snake_case	,							__snake_case	,							__snake_case	:						Any						=				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_					)
							__snake_case	:						List[Any]						=				None

						if not complete and stepped:
							__snake_case	:						Tuple						=				pending_constraint

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

							__snake_case	:						str						=				(
							    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.

								__snake_case	:						Optional[Any]						=				True

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

			return complete, stepped



		def 				SCREAMING_SNAKE_CASE  (self				,       a_=True					):





			'''simple docstring'''

			__snake_case	:						List[Any]						=				ConstraintListState(self.constraints					)  # we actually never though self.constraints objects
			# throughout this process. So it's at initialization state.

			if stateful:
				__snake_case	:						List[str]						=				[
				    constraint.copy(stateful=a_					) for constraint in self.complete_constraints
				]
				if self.inprogress_constraint is not None:
					__snake_case	:						int						=				self.inprogress_constraint.copy(stateful=a_					)
				__snake_case	:						Optional[Any]						=				[constraint.copy() for constraint in self.pending_constraints]

			return new_state









"""simple docstring"""
from math import factorial, radians






def 		lowercase							(     _snake_case						:      float     ,   _snake_case						:      int = 18     ,   _snake_case						:      int = 10     )     ->float:
	"""simple docstring"""





	__snake_case	:						Any						=				angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)

	# Converting from degrees to radians
	__snake_case	:						int						=				radians(_snake_case     )

	__snake_case	:						str						=				angle_in_radians
	__snake_case	:						Optional[int]						=				3
	__snake_case	:						List[Any]						=				-1

	for _ in range(_snake_case     ):
		result += (b * (angle_in_radians**a)) / factorial(_snake_case     )

		__snake_case	:						int						=				-b  # One positive term and the next will be negative and so on...
		a += 2  # Increased by 2 for every term.

	return round(_snake_case     ,   _snake_case     )


if __name__ == "__main__":
			__import__("""doctest""").testmod()





