


from __future__ import annotations

def        lowerCAmelCase__ (			a__:		Tuple       )  ->		list[int]:  # This function is recursive


							'''simple docstring'''





							_UpperCAmelCase 		=			len(_SCREAMING_SNAKE_CASE       )
							# If the array contains only one element, we return it (it's the stop condition of
							# recursion)
							if array_length <= 1:
														return array
														# Else
							_UpperCAmelCase 		=			array[0]
							_UpperCAmelCase 		=			False
							_UpperCAmelCase 		=			1
							_UpperCAmelCase 		=			[]
							while not is_found and i < array_length:
														if array[i] < pivot:
																					_UpperCAmelCase 		=			True
																					_UpperCAmelCase 		=			[element for element in array[i:] if element >= array[i]]
																					_UpperCAmelCase 		=			longest_subsequence(_SCREAMING_SNAKE_CASE       )
																					if len(_SCREAMING_SNAKE_CASE       ) > len(_SCREAMING_SNAKE_CASE       ):
																												_UpperCAmelCase 		=			temp_array
														else:
																					i += 1

							_UpperCAmelCase 		=			[element for element in array[1:] if element >= pivot]
							_UpperCAmelCase 		=			[pivot, *longest_subsequence(_SCREAMING_SNAKE_CASE       )]
							if len(_SCREAMING_SNAKE_CASE       ) > len(_SCREAMING_SNAKE_CASE       ):
														return temp_array
							else:
														return longest_subseq


if __name__ == "__main__":
		import doctest

		doctest.testmod()

"""simple docstring"""
import math







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->bool:

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5		,     int(math.sqrt(_SCREAMING_SNAKE_CASE   ) + 1   )		,     6   ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True







def 						__a   (	_SCREAMING_SNAKE_CASE = 0.1   )	->int:
  a__:     str										=	3
  a__:     Optional[Any]										=	3

  while primes / (2 * j - 1) >= ratio:
    for i in range(j * j + j + 1		,     (j + 2) * (j + 2)		,     j + 1   ):
      primes += is_prime(_SCREAMING_SNAKE_CASE   )
    j += 2
  return j


if __name__ == "__main__":
 import doctest

 doctest.testmod()


