



'''simple docstring'''

from __future__ import annotations



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				bool:
		_a					:				Tuple				=							len(lowerCAmelCase_  )
		# We need to create solution object to save path.
		_a					:				str				=							[[0 for _ in range(lowerCAmelCase_  )] for _ in range(lowerCAmelCase_  )]
		_a					:				str				=							run_maze(lowerCAmelCase_						,      0						,      0						,      lowerCAmelCase_  )
		if solved:
				print('\n'.join(str(lowerCAmelCase_  ) for row in solutions  )  )
		else:
				print('No solution exists!'  )
		return solved



def 					__lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_  )      ->				bool:
		_a					:				Union[str, Any]				=							len(lowerCAmelCase_  )
		# Final check point.
		if i == j == (size - 1):
				_a					:				Optional[int]				=							1
				return True

		_a					:				List[str]				=							(not i < 0) and (not j < 0)  # Check lower bounds
		_a					:				int				=							(i < size) and (j < size)  # Check upper bounds

		if lower_flag and upper_flag:
				# check for already visited and block points.
				_a					:				List[Any]				=							(not solutions[i][j]) and (not maze[i][j])
				if block_flag:
						# check visited
						_a					:				List[str]				=							1

						# check for directions
						if (
						    run_maze(lowerCAmelCase_						,      i + 1						,      lowerCAmelCase_						,      lowerCAmelCase_  )
						    or run_maze(lowerCAmelCase_						,      lowerCAmelCase_						,      j + 1						,      lowerCAmelCase_  )
						    or run_maze(lowerCAmelCase_						,      i - 1						,      lowerCAmelCase_						,      lowerCAmelCase_  )
						    or run_maze(lowerCAmelCase_						,      lowerCAmelCase_						,      j - 1						,      lowerCAmelCase_  )
						):
								return True

						_a					:				int				=							0
						return False
		return False


if __name__ == "__main__":
							import doctest

							doctest.testmod()









'''simple docstring'''

def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				list:
		if any(not isinstance(lowerCAmelCase_						,      lowerCAmelCase_  ) or x < 0 for x in sequence  ):
				raise TypeError('Sequence must be list of non-negative integers'  )
		for _ in range(len(lowerCAmelCase_  )  ):
				for i, (rod_upper, rod_lower) in enumerate(zip(lowerCAmelCase_						,      sequence[1:]  )  ):
						if rod_upper > rod_lower:
								sequence[i] -= rod_upper - rod_lower
								sequence[i + 1] += rod_upper - rod_lower
		return sequence


if __name__ == "__main__":
							assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
							assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]




