


"""simple docstring"""


from __future__ import annotations

from collections.abc import Generator


def _lowerCamelCase			(	):

			'''simple docstring'''




			__lowerCAmelCase       					=    {}
			__lowerCAmelCase       					=    2
			while True:
						__lowerCAmelCase       					=    factor_map.pop(_UpperCamelCase					,				_UpperCamelCase   )
						if factor:
									__lowerCAmelCase       					=    factor + prime
									while x in factor_map:
												x += factor
									__lowerCAmelCase       					=    factor
						else:
									__lowerCAmelCase       					=    prime
									yield prime
						prime += 1


def _lowerCamelCase			(	_UpperCamelCase = 1e10   ):

			'''simple docstring'''




			__lowerCAmelCase       					=    sieve()

			__lowerCAmelCase       					=    1
			while True:
						__lowerCAmelCase       					=    next(_UpperCamelCase   )
						if (2 * prime * n) > limit:
									return n
						# Ignore the next prime as the reminder will be 2.
						next(_UpperCamelCase   )
						n += 2


if __name__ == "__main__":
	print(solution())








"""simple docstring"""


A  :     List[Any]    					=    [4, 1, 7, 4, 2, 6, 4, 1, 5, 3, 7, 5]
A  :     Optional[int]    					=    [3, 7, 7, 4, 2, 6, 4, 1, 5, 3, 7, 5]
A  :     Optional[int]    					=    {
    0: "Sunday",
    1: "Monday",
    2: "Tuesday",
    3: "Wednesday",
    4: "Thursday",
    5: "Friday",
    6: "Saturday",
}


def _lowerCamelCase			(	_UpperCamelCase					,				_UpperCamelCase					,				_UpperCamelCase   ):

			'''simple docstring'''




			assert len(str(_UpperCamelCase   )   ) > 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:
			__lowerCAmelCase       					=    year // 100
			__lowerCAmelCase       					=    (5 * (century % 4) + 2) % 7
			__lowerCAmelCase       					=    year % 100
			__lowerCAmelCase       					=    centurian % 12
			__lowerCAmelCase       					=    (
			    (centurian // 12) + centurian_m + (centurian_m // 4) + century_anchor
			) % 7
			__lowerCAmelCase       					=    (
			    DOOMSDAY_NOT_LEAP[month - 1]
			    if (year % 4 != 0) or (centurian == 0 and (year % 400) == 0)
			    else DOOMSDAY_LEAP[month - 1]
			)
			__lowerCAmelCase       					=    (dooms_day + day - day_anchor) % 7
			return WEEK_DAY_NAMES[week_day]


if __name__ == "__main__":
	import doctest

	doctest.testmod()




