



import random

from .binary_exp_mod import bin_exp_mod



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE=1_0_0_0   ):
 if n < 2:
  return False

 if n % 2 == 0:
  return n == 2

 # this means n is odd
 __lowercase		       =			n - 1
 __lowercase		       =			0
 while d % 2 == 0:
  d /= 2
  exp += 1

 # n - 1=d*(2**exp)
 __lowercase		       =			0
 while count < prec:
  __lowercase		       =			random.randint(2  ,	n - 1   )
  __lowercase		       =			bin_exp_mod(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )
  if b != 1:
   __lowercase		       =			True
   for _ in range(_SCREAMING_SNAKE_CASE   ):
    if b == n - 1:
     __lowercase		       =			False
     break
    __lowercase		       =			b * b
    b %= n
   if flag:
    return False
   count += 1
 return True


if __name__ == "__main__":
 snake_case__					:     Dict    		=   abs(int(input("""Enter bound : """).strip()))
 print("""Here's the list of primes:""")
 print(""", """.join(str(i) for i in range(n + 1) if is_prime_big(i)))








from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

snake_case__					:     Union[str, Any]    		=   TypeVar("""T""")
snake_case__					:     Optional[int]    		=   TypeVar("""U""")

class   _A   ( Generic[T, U]	):


						'''simple docstring'''





						def __init__(	self	:							Optional[int]							,      lowerCamelCase	:							T | None							,      lowerCamelCase	:							U | None	):






							'''simple docstring'''



							__lowercase		       =			key
							__lowercase		       =			val
							__lowercase		       =			None
							__lowercase		       =			None



						def __repr__(	self	:							Any	):






							'''simple docstring'''



							return (
							    f"""Node: key: {self.key}, val: {self.val}, """
							    f"""has next: {bool(self.next	)}, has prev: {bool(self.prev	)}"""
							)

class   _A   ( Generic[T, U]	):


						'''simple docstring'''





						def __init__(	self	:							Dict	):






							'''simple docstring'''



							__lowercase		       =			DoubleLinkedListNode(lowerCamelCase							,      lowerCamelCase	)
							__lowercase		       =			DoubleLinkedListNode(lowerCamelCase							,      lowerCamelCase	)
							__lowercase       ,    __lowercase		       =			self.rear, self.head



						def __repr__(	self	:							Optional[Any]	):






							'''simple docstring'''



							__lowercase		       =			["DoubleLinkedList"]
							__lowercase		       =			self.head
							while node.next is not None:
								rep.append(str(lowerCamelCase	)	)
								__lowercase		       =			node.next
							rep.append(str(self.rear	)	)
							return ",\n    ".join(lowerCamelCase	)



						def     _snake_case	(	self	:							Union[str, Any]							,      lowerCamelCase	:							DoubleLinkedListNode[T, U]	):






							'''simple docstring'''



							__lowercase		       =			self.rear.prev

							# All nodes other than self.head are guaranteed to have non-None previous
							assert previous is not None

							__lowercase		       =			node
							__lowercase		       =			previous
							__lowercase		       =			node
							__lowercase		       =			self.rear



						def     _snake_case	(	self	:							Optional[int]							,      lowerCamelCase	:							DoubleLinkedListNode[T, U]	):






							'''simple docstring'''



							if node.prev is None or node.next is None:
								return None

							__lowercase		       =			node.next
							__lowercase		       =			node.prev
							__lowercase		       =			None
							__lowercase		       =			None
							return node

class   _A   ( Generic[T, U]	):


						'''simple docstring'''





						_snake_case			:     dict[Callable[[T], U], LRUCache[T, U]]      							=      {}



						def __init__(	self	:							List[Any]							,      lowerCamelCase	:							int	):






							'''simple docstring'''



							__lowercase		       =			DoubleLinkedList()
							__lowercase		       =			capacity
							__lowercase		       =			0
							__lowercase		       =			0
							__lowercase		       =			0
							__lowercase		       =			{}



						def __repr__(	self	:							Optional[Any]	):






							'''simple docstring'''



							return (
							    f"""CacheInfo(hits={self.hits}, misses={self.miss}, """
							    f"""capacity={self.capacity}, current size={self.num_keys})"""
							)



						def __contains__(	self	:							Dict							,      lowerCamelCase	:							T	):






							'''simple docstring'''



							return key in self.cache



						def     _snake_case	(	self	:							List[Any]							,      lowerCamelCase	:							T	):






							'''simple docstring'''



							if key in self.cache:
								self.hits += 1
								__lowercase		       =			self.cache[key]
								__lowercase		       =			self.list.remove(self.cache[key]	)
								assert node == value_node

								# node is guaranteed not None because it is in self.cache
								assert node is not None
								self.list.add(lowerCamelCase	)
								return node.val
							self.miss += 1
							return None



						def     _snake_case	(	self	:							Union[str, Any]							,      lowerCamelCase	:							T							,      lowerCamelCase	:							U	):






							'''simple docstring'''



							if key not in self.cache:
								if self.num_keys >= self.capacity:
									# delete first node (oldest) when over capacity
									__lowercase		       =			self.list.head.next

									# guaranteed to have a non-None first node when num_keys > 0
									# explain to type checker via assertions
									assert first_node is not None
									assert first_node.key is not None
									assert (
									    self.list.remove(lowerCamelCase	) is not None
									)  # node guaranteed to be in list assert node.key is not None

									del self.cache[first_node.key]
									self.num_keys -= 1
								__lowercase		       =			DoubleLinkedListNode(lowerCamelCase							,      lowerCamelCase	)
								self.list.add(self.cache[key]	)
								self.num_keys += 1

							else:
								# bump node to the end of the list, update value
								__lowercase		       =			self.list.remove(self.cache[key]	)
								assert node is not None  # node guaranteed to be in list
								__lowercase		       =			value
								self.list.add(lowerCamelCase	)



						@classmethod
						def     _snake_case	(	cls	:							Union[str, Any]							,      lowerCamelCase	:							int = 128	):






							'''simple docstring'''



							def cache_decorator_inner(lowerCamelCase	:							Callable[[T], U]	) -> Callable[..., U]:
								def cache_decorator_wrapper(*lowerCamelCase	:							T	) -> U:
									if func not in cls.decorator_function_to_instance_map:
										__lowercase		       =			LRUCache(lowerCamelCase	)

									__lowercase		       =			cls.decorator_function_to_instance_map[func].get(args[0]	)
									if result is None:
										__lowercase		       =			func(*lowerCamelCase	)
										cls.decorator_function_to_instance_map[func].put(args[0]							,      lowerCamelCase	)
									return result

								def cache_info() -> LRUCache[T, U]:
									return cls.decorator_function_to_instance_map[func]

								setattr(lowerCamelCase							,      "cache_info"							,      lowerCamelCase	)  # noqa: B010

								return cache_decorator_wrapper

							return cache_decorator_inner


if __name__ == "__main__":
	import doctest

	doctest.testmod()



