

from __future__ import annotations


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


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__       ):
						snake_case_   =	len(SCREAMING_SNAKE_CASE__       )
						# Final check point.
						if i == j == (size - 1):
												snake_case_   =	1
												return True

						snake_case_   =	(not i < 0) and (not j < 0)  # Check lower bounds
						snake_case_   =	(i < size) and (j < size)  # Check upper bounds

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

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

																		snake_case_   =	0
																		return False
						return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__       ):
						snake_case_   =	[]
						if len(SCREAMING_SNAKE_CASE__       ) == 1:
												return [nums.copy()]
						for _ in range(len(SCREAMING_SNAKE_CASE__       )       ):
												snake_case_   =	nums.pop(0       )
												snake_case_   =	permute(SCREAMING_SNAKE_CASE__       )
												for perm in permutations:
																		perm.append(SCREAMING_SNAKE_CASE__       )
												result.extend(SCREAMING_SNAKE_CASE__       )
												nums.append(SCREAMING_SNAKE_CASE__       )
						return result


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__       ):

						def backtrack(SCREAMING_SNAKE_CASE__       ):
												if start == len(SCREAMING_SNAKE_CASE__       ) - 1:
																		output.append(nums[:]       )
												else:
																		for i in range(SCREAMING_SNAKE_CASE__  ,		len(SCREAMING_SNAKE_CASE__       )       ):
																								snake_case_,    snake_case_   =	nums[i], nums[start]
																								backtrack(start + 1       )
																								snake_case_,    snake_case_   =	nums[i], nums[start]  # backtrack

						snake_case_   =	[]
						backtrack(0       )
						return output


if __name__ == "__main__":
					import doctest

					# use res to print the data in permute2 function
					lowerCAmelCase_       	=	permutea([1, 2, 3])
					print(res)
					doctest.testmod()