






import random

from .binary_exp_mod import bin_exp_mod







def 			A__							(      _a  :					Dict		,  _a  :					Any=1000	):





 '''simple docstring'''







 if n < 2:
  return False

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

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

 # n - 1=d*(2**exp)
 snake_case__  :    str							       =0
 while count < prec:
  snake_case__  :    Optional[int]							       =random.randint(2		,  n - 1	)
  snake_case__  :    Optional[Any]							       =bin_exp_mod(lowerCamelCase__		,  lowerCamelCase__		,  lowerCamelCase__	)
  if b != 1:
   snake_case__  :    str							       =True
   for _ in range(lowerCamelCase__	):
    if b == n - 1:
     snake_case__  :    List[str]							       =False
     break
    snake_case__  :    List[Any]							       =b * b
    b %= n
   if flag:
    return False
   count += 1
 return True


if __name__ == "__main__":
       __lowerCamelCase	:		Tuple										=   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)))













def 			A__							(      _a  :					Optional[Any]		,  _a  :					Tuple		,  _a  :					List[str]=False	):





 '''simple docstring'''







 if isinstance(_a		,  _a	) and isinstance(_a		,  _a	):
  snake_case__  :    int							       =len(set_a.intersection(_a	)	)

  if alternative_union:
   snake_case__  :    int							       =len(_a	) + len(_a	)
  else:
   snake_case__  :    Tuple							       =len(set_a.union(_a	)	)

  return intersection / union

 if isinstance(_a		,  (list, tuple)	) and isinstance(_a		,  (list, tuple)	):
  snake_case__  :    Optional[int]							       =[element for element in set_a if element in set_b]

  if alternative_union:
   snake_case__  :    Optional[Any]							       =len(_a	) + len(_a	)
   return len(_a	) / union
  else:
   snake_case__  :    Dict							       =set_a + [element for element in set_b if element not in set_a]
   return len(_a	) / len(_a	)

  return len(_a	) / len(_a	)
 return None


if __name__ == "__main__":
       __lowerCamelCase	:		List[Any]										=   {"""a""", """b""", """c""", """d""", """e"""}
       __lowerCamelCase	:		Optional[int]										=   {"""c""", """d""", """e""", """f""", """h""", """i"""}
       print(jaccard_similarity(set_a, set_b))





