





from __future__ import annotations

_UpperCAmelCase       : Dict			     =       [True] * 1_00_00_01
_UpperCAmelCase       : Tuple			     =       2
while i * i <= 1_00_00_00:
    if seive[i]:
        for j in range(i * i, 1_00_00_01, i):
            _UpperCAmelCase       : List[Any]			     =       False
    i += 1


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase				)    ->  bool:
    return seive[n]


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase				)    ->  bool:
    return any(digit in '02468' for digit in str(_UpperCAmelCase				)				)


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 100_0000				)    ->  list[int]:
    lowerCamelCase__					:   Union[str, Any]      				=	[2]  # result already includes the number 2.
    for num in range(3		,			limit + 1		,			2				):
        if is_prime(_UpperCAmelCase				) and not contains_an_even_digit(_UpperCAmelCase				):
            lowerCamelCase__					:   List[Any]      				=	str(_UpperCAmelCase				)
            lowerCamelCase__					:   Dict      				=	[int(str_num[j:] + str_num[:j]				) for j in range(len(_UpperCAmelCase				)				)]
            if all(is_prime(_UpperCAmelCase				) for i in list_nums				):
                result.append(_UpperCAmelCase				)
    return result


def  SCREAMING_SNAKE_CASE   ( )    ->  int:
    return len(find_circular_primes()				)


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












from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

_UpperCAmelCase       : Union[str, Any]			     =       (3, 9, -11, 0, 7, 5, 1, -1)
_UpperCAmelCase       : Union[str, Any]			     =       (4, 6, 2, 0, 8, 10, 3, -2)

@dataclass
class      lowerCAmelCase							:
 UpperCAmelCase__									=	42
 UpperCAmelCase__									=	42


class      lowerCAmelCase							:
 def __init__(   self						:   Any    ,  UpperCAmelCase						:   Iterable[int]			)    ->			None:
     lowerCamelCase__					:   Node | None      				=	None
     for i in sorted(UpperCAmelCase    ,  reverse=UpperCAmelCase			):
         lowerCamelCase__					:   Tuple      				=	Node(UpperCAmelCase    ,  self.head			)
 def __iter__(   self						:   Optional[int]			)    ->			Iterator[int]:
     lowerCamelCase__					:   str      				=	self.head
     while node:
         yield node.data
         lowerCamelCase__					:   List[str]      				=	node.next_node
 def __len__(   self						:   List[str]			)    ->			int:
     return sum(1 for _ in self			)







 def __str__(   self						:   Any			)    ->			str:
     return " -> ".join([str(UpperCAmelCase			) for node in self]			)


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase				)    ->  SortedLinkedList:
    return SortedLinkedList(list(_UpperCAmelCase				) + list(_UpperCAmelCase				)				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    _UpperCAmelCase       : Optional[Any]			     =       SortedLinkedList
    print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))





