


'''simple docstring'''
from __future__ import annotations


def       a				(      __a       )  ->     bool:



					'''simple docstring'''






					UpperCamelCase__       :Tuple							 =			len(__a       )
					# We need to create solution object to save path.
					UpperCamelCase__       :List[str]							 =			[[0 for _ in range(__a       )] for _ in range(__a       )]
					UpperCamelCase__       :Optional[int]							 =			run_maze(__a			, 0			, 0			, __a       )
					if solved:
										print('''\n'''.join(str(__a       ) for row in solutions       )       )
					else:
										print('''No solution exists!'''       )
					return solved


def       a				(      __a			, __a			, __a			, __a       )  ->     bool:



					'''simple docstring'''






					UpperCamelCase__       :Optional[Any]							 =			len(__a       )
					# Final check point.
					if i == j == (size - 1):
										UpperCamelCase__       :Tuple							 =			1
										return True

					UpperCamelCase__       :Any							 =			(not i < 0) and (not j < 0)  # Check lower bounds
					UpperCamelCase__       :List[Any]							 =			(i < size) and (j < size)  # Check upper bounds

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

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

															UpperCamelCase__       :Tuple							 =			0
															return False
					return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''
from __future__ import annotations

__snake_case											=					[True] * 1000001
__snake_case											=					2
while i * i <= 1000000:
		if seive[i]:
				for j in range(i * i, 1000001, i):
						__snake_case											=					False
		i += 1


def       a				(      __a       )  ->     bool:



					'''simple docstring'''






					return seive[n]


def       a				(      __a       )  ->     bool:



					'''simple docstring'''






					return any(digit in '''02468''' for digit in str(__a       )       )


def       a				(      __a = 1000000       )  ->     list[int]:



					'''simple docstring'''






					UpperCamelCase__       :Any							 =			[2]  # result already includes the number 2.
					for num in range(3			, limit + 1			, 2       ):
										if is_prime(__a       ) and not contains_an_even_digit(__a       ):
															UpperCamelCase__       :str							 =			str(__a       )
															UpperCamelCase__       :List[str]							 =			[int(str_num[j:] + str_num[:j]       ) for j in range(len(__a       )       )]
															if all(is_prime(__a       ) for i in list_nums       ):
																				result.append(__a       )
					return result


def       a				(      )  ->     int:



					'''simple docstring'''






					return len(find_circular_primes()       )


if __name__ == "__main__":
		print(F"""{len(find_circular_primes()) = }""")