






import math


def 	lowerCamelCase__      (  lowercase					):

  """simple docstring"""






  SCREAMING_SNAKE_CASE							:   List[Any]						    =     []
  SCREAMING_SNAKE_CASE							:   Union[str, Any]						    =     2
  SCREAMING_SNAKE_CASE							:   List[str]						    =     int(math.sqrt(lowercase					)					)  # Size of every segment
  SCREAMING_SNAKE_CASE							:   str						    =     [True] * (end + 1)
  SCREAMING_SNAKE_CASE							:   Dict						    =     []

  while start <= end:
    if temp[start] is True:
      in_prime.append(lowercase					)
      for i in range(start * start    ,  end + 1    ,  lowercase					):
        SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     False
    start += 1
  prime += in_prime

  SCREAMING_SNAKE_CASE							:   Union[str, Any]						    =     end + 1
  SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     min(2 * end    ,  lowercase					)

  while low <= n:
    SCREAMING_SNAKE_CASE							:   Dict						    =     [True] * (high - low + 1)
    for each in in_prime:
      SCREAMING_SNAKE_CASE							:   Tuple						    =     math.floor(low / each					) * each
      if t < low:
        t += each

      for j in range(lowercase    ,  high + 1    ,  lowercase					):
        SCREAMING_SNAKE_CASE							:   Union[str, Any]						    =     False

    for j in range(len(lowercase					)					):
      if temp[j] is True:
        prime.append(j + low					)

    SCREAMING_SNAKE_CASE							:   str						    =     high + 1
    SCREAMING_SNAKE_CASE							:   List[Any]						    =     min(high + end    ,  lowercase					)

  return prime

print(sieve(10**6))










'''simple docstring'''






from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
__A   :    Tuple											= 10







def 							UpperCamelCase_     (       A__   :  int				,       A__   :  int				,       A__   :  list[int]				,       A__   :  int   ):
  '''simple docstring'''





  for i in range(A__				,       A__   ):
    if array[i] == target:
      return i
  return -1







def 							UpperCamelCase_     (       A__   :  list[int]				,       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Optional[int]     =  0
  lowerCAmelCase_     : Union[str, Any]     =  len(A__   )
  while left <= right:
    if right - left < precision:
      return lin_search(A__				,       A__				,       A__				,       A__   )

    lowerCAmelCase_     : Dict     =  (left + right) // 3 + 1
    lowerCAmelCase_     : List[Any]     =  2 * (left + right) // 3 + 1

    if array[one_third] == target:
      return one_third
    elif array[two_third] == target:
      return two_third

    elif target < array[one_third]:
      lowerCAmelCase_     : List[str]     =  one_third - 1
    elif array[two_third] < target:
      lowerCAmelCase_     : Tuple     =  two_third + 1

    else:
      lowerCAmelCase_     : Tuple     =  one_third + 1
      lowerCAmelCase_     : Any     =  two_third - 1
  else:
    return -1







def 							UpperCamelCase_     (       A__   :  int				,       A__   :  int				,       A__   :  list[int]				,       A__   :  int   ):
  '''simple docstring'''





  if left < right:
    if right - left < precision:
      return lin_search(A__				,       A__				,       A__				,       A__   )
    lowerCAmelCase_     : Dict     =  (left + right) // 3 + 1
    lowerCAmelCase_     : Dict     =  2 * (left + right) // 3 + 1

    if array[one_third] == target:
      return one_third
    elif array[two_third] == target:
      return two_third

    elif target < array[one_third]:
      return rec_ternary_search(A__				,       one_third - 1				,       A__				,       A__   )
    elif array[two_third] < target:
      return rec_ternary_search(two_third + 1				,       A__				,       A__				,       A__   )
    else:
      return rec_ternary_search(one_third + 1				,       two_third - 1				,       A__				,       A__   )
  else:
    return -1


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __A   :    List[Any]											= input("Enter numbers separated by comma:\n").strip()
  __A   :    Union[str, Any]											= [int(item.strip()) for item in user_input.split(",")]
  assert collection == sorted(collection), F"List must be ordered.\n{collection}."
  __A   :    List[Any]											= int(input("Enter the number to be found in the list:\n").strip())
  __A   :    str											= ite_ternary_search(collection, target)
  __A   :    Dict											= rec_ternary_search(0, len(collection) - 1, collection, target)
  if resulta != -1:
    print(F'''Iterative search: {target} found at positions: {resulta}''')
    print(F'''Recursive search: {target} found at positions: {resulta}''')
  else:
    print("Not found")



