






def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  int = 50					)		->			int:






	"""simple docstring"""



	UpperCamelCase     :Any          =	[1] * (length + 1)

	for row_length in range(3	,			length + 1					):
		for block_length in range(3	,			row_length + 1					):
			for block_start in range(row_length - block_length					):
				ways_number[row_length] += ways_number[
				    row_length - block_start - block_length - 1
				]

			ways_number[row_length] += 1

	return ways_number[length]


if __name__ == "__main__":
	print(F'''{solution() = }''')








def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  list[list[int]]	,			__magic_name__					:  int	,			__magic_name__					:  int	,			__magic_name__					:  list[int]					)		->			bool:






	"""simple docstring"""



	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    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  list[list[int]]	,			__magic_name__					:  list[int]	,			__magic_name__					:  int					)		->			bool:






	"""simple docstring"""



	if curr_ind == len(__magic_name__					):
		# 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(__magic_name__					)					):
		if valid_connection(__magic_name__	,			__magic_name__	,			__magic_name__	,			__magic_name__					):
			# Insert current vertex  into path as next transition
			UpperCamelCase     :str          =	next_ver
			# Validate created path
			if util_hamilton_cycle(__magic_name__	,			__magic_name__	,			curr_ind + 1					):
				return True
			# Backtrack
			UpperCamelCase     :Union[str, Any]          =	-1
	return False

def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  list[list[int]]	,			__magic_name__					:  int = 0					)		->			list[int]:






	"""simple docstring"""



	UpperCamelCase     :Union[str, Any]          =	[-1] * (len(__magic_name__					) + 1)
	# initialize start and end of path with starting index
	UpperCamelCase     :Any          =	start_index
	# evaluate and if we find answer return path either return empty array
	return path if util_hamilton_cycle(__magic_name__	,			__magic_name__	,			1					) else []
