



'''simple docstring'''

def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )     -> bool:

		# 1. Validate that path exists between current and next vertices
		if graph[path[curr_ind - 1]][next_ver] == 0:
				return False

		# 2. Validate that next vertex is not already in path
		return not any(vertex == next_ver for vertex in path    )



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )     -> bool:

		# Base Case
		if curr_ind == len(lowerCAmelCase_    ):
				# return whether path exists between current and starting vertices
				return graph[path[curr_ind - 1]][path[0]] == 1

		# Recursive Step
		for next_ver in range(0		,     len(lowerCAmelCase_    )    ):
				if valid_connection(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    ):
						# Insert current vertex  into path as next transition
						_a	: Tuple								=				next_ver
						# Validate created path
						if util_hamilton_cycle(lowerCAmelCase_		,     lowerCAmelCase_		,     curr_ind + 1    ):
								return True
						# Backtrack
						_a	: Tuple								=				-1
		return False



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_ = 0    )     -> list[int]:
		_a	: str								=				[-1] * (len(lowerCAmelCase_    ) + 1)
		# initialize start and end of path with starting index
		_a	: int								=				start_index
		# evaluate and if we find answer return path either return empty array
		return path if util_hamilton_cycle(lowerCAmelCase_		,     lowerCAmelCase_		,     1    ) else []









'''simple docstring'''

import re

from filelock import FileLock


try:
							import nltk

							__lowerCAmelCase		     =  True
except (ImportError, ModuleNotFoundError):
							__lowerCAmelCase		     =  False

if NLTK_AVAILABLE:
							with FileLock('''.lock''') as lock:
														nltk.download('''punkt''', quiet=True)



def 	__lowerCamelCase	( lowerCAmelCase_    )     -> str:
		re.sub('<n>'		,     ''		,     lowerCAmelCase_    )  # remove pegasus newline char
		assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
		return "\n".join(nltk.sent_tokenize(lowerCAmelCase_    )    )




