



import math



def 			_lowerCAmelCase       (					__lowerCAmelCase      )   ->					bool:


				"""simple docstring"""

				assert isinstance(__lowerCAmelCase  ,  __lowerCAmelCase      ) and (
				    number >= 0
				), "'number' must been an int and positive"

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

				snake_case__	:      Union[str, Any]     		=	range(3  ,  int(math.sqrt(__lowerCAmelCase      ) + 1      )  ,  2      )
				return not any(not number % i for i in odd_numbers      )





def 			_lowerCAmelCase       (					__lowerCAmelCase  ,  __lowerCAmelCase=1  ,  **__lowerCAmelCase      )   ->					str:


				"""simple docstring"""

				snake_case__	:      Optional[Any]     		=	factor * value
				snake_case__	:      Any     		=	value

				while not is_prime(__lowerCAmelCase      ):
								value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

				if value == first_value_val:
								return next_prime(value + 1  ,  **__lowerCAmelCase      )
				return value






A__								=						[4, 1, 7, 4, 2, 6, 4, 1, 5, 3, 7, 5]
A__								=						[3, 7, 7, 4, 2, 6, 4, 1, 5, 3, 7, 5]
A__								=						{
    0: '''Sunday''',
    1: '''Monday''',
    2: '''Tuesday''',
    3: '''Wednesday''',
    4: '''Thursday''',
    5: '''Friday''',
    6: '''Saturday''',
}



def 			_lowerCAmelCase       (					__lowerCAmelCase  ,  __lowerCAmelCase  ,  __lowerCAmelCase      )   ->					str:


				"""simple docstring"""

				assert len(str(__lowerCAmelCase      )      ) > 2, "year should be in YYYY format"
				assert 1 <= month <= 12, "month should be between 1 to 12"
				assert 1 <= day <= 31, "day should be between 1 to 31"

				# Doomsday algorithm:
				snake_case__	:      Optional[int]     		=	year // 100
				snake_case__	:      List[str]     		=	(5 * (century % 4) + 2) % 7
				snake_case__	:      Dict     		=	year % 100
				snake_case__	:      Union[str, Any]     		=	centurian % 12
				snake_case__	:      List[Any]     		=	(
				    (centurian // 12) + centurian_m + (centurian_m // 4) + century_anchor
				) % 7
				snake_case__	:      List[str]     		=	(
				    DOOMSDAY_NOT_LEAP[month - 1]
				    if (year % 4 != 0) or (centurian == 0 and (year % 400) == 0)
				    else DOOMSDAY_LEAP[month - 1]
				)
				snake_case__	:      List[str]     		=	(dooms_day + day - day_anchor) % 7
				return WEEK_DAY_NAMES[week_day]


if __name__ == "__main__":
				import doctest

				doctest.testmod()

