






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_		:		List[str]		     =			10

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  for i in range(UpperCAmelCase__     ,   UpperCAmelCase__  ):
    if array[i] == target:
      return i
  return -1

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  UpperCamelCase_: List[str]   				=    0
  UpperCamelCase_: List[str]   				=    len(UpperCAmelCase__  )
  while left <= right:
    if right - left < precision:
      return lin_search(UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )

    UpperCamelCase_: Any   				=    (left + right) // 3 + 1
    UpperCamelCase_: Optional[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]:
      UpperCamelCase_: List[str]   				=    one_third - 1
    elif array[two_third] < target:
      UpperCamelCase_: Union[str, Any]   				=    two_third + 1

    else:
      UpperCamelCase_: Any   				=    one_third + 1
      UpperCamelCase_: List[str]   				=    two_third - 1
  else:
    return -1

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )	->    int:
  if left < right:
    if right - left < precision:
      return lin_search(UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )
    UpperCamelCase_: int   				=    (left + right) // 3 + 1
    UpperCamelCase_: Union[str, 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]:
      return rec_ternary_search(UpperCAmelCase__     ,   one_third - 1     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )
    elif array[two_third] < target:
      return rec_ternary_search(two_third + 1     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )
    else:
      return rec_ternary_search(one_third + 1     ,   two_third - 1     ,   UpperCAmelCase__     ,   UpperCAmelCase__  )
  else:
    return -1


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   A_		:		Any		     =			input('Enter numbers separated by comma:\n').strip()
   A_		:		Any		     =			[int(item.strip()) for item in user_input.split(',')]
   assert collection == sorted(collection), F"List must be ordered.\n{collection}."
   A_		:		Dict		     =			int(input('Enter the number to be found in the list:\n').strip())
   A_		:		Optional[Any]		     =			ite_ternary_search(collection, target)
   A_		:		Union[str, Any]		     =			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')







def   snake_case (UpperCAmelCase__  )	->    int:
  assert isinstance(UpperCAmelCase__     ,   UpperCAmelCase__  ), F'''The input value of [n={number}] is not an integer'''

  if number == 1:
    return 2
  elif number < 1:
    UpperCamelCase_: List[Any]   				=    F'''The input value of [n={number}] has to be > 0'''
    raise ValueError(UpperCAmelCase__  )
  else:
    UpperCamelCase_: str   				=    sylvester(number - 1  )
    UpperCamelCase_: str   				=    num - 1
    UpperCamelCase_: Any   				=    num
    return lower * upper + 1


if __name__ == "__main__":
   print(F'''The 8th number in Sylvester\'s sequence: {sylvester(8)}''')