


"""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 = 2_000_000					)     ->					int:
							return sum(num for num in range(3					,			_SCREAMING_SNAKE_CASE					,			2					) if is_prime(_SCREAMING_SNAKE_CASE					)					) + 2 if n > 2 else 0


if __name__ == "__main__":
				print(f"""{solution() = }""")







"""simple docstring"""
from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize





class   __A  (snake_case__):





							'''simple docstring'''

							__lowercase:		Dict				   =     1
							__lowercase:		List[str]				   =     2
							__lowercase:		int				   =     3



							def __repr__(					self				:   Optional[Any]							)       ->Optional[int]:



														"""simple docstring"""



														return F"""{self.__class__.__name__}.{self.name}"""







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					float:
							snake_case_							,    snake_case_     							=		point
							return degrees(atana(y - miny					,			x - minx					)					)







def     _a					(   _SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)     ->					Direction:
							snake_case_							,    snake_case_     							=		starting
							snake_case_							,    snake_case_     							=		via
							snake_case_							,    snake_case_     							=		target
							snake_case_     							=		degrees(atana(ya - ya					,			xa - xa					)					)
							via_angle %= 360
							snake_case_     							=		degrees(atana(ya - ya					,			xa - xa					)					)
							target_angle %= 360
							# t-
							#  \ \
							#   \ v
							#    \|
							#     s
							# via_angle is always lower than target_angle, if direction is left.
							# If they are same, it means they are on a same line of convex hull.
							if target_angle > via_angle:
														return Direction.left
							elif target_angle == via_angle:
														return Direction.straight
							else:
														return Direction.right







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[tuple[int, int]]:

							if len(_SCREAMING_SNAKE_CASE					) <= 2:
														# There is no convex hull
														raise ValueError("""graham_scan: argument must contain more than 3 points."""					)
							if len(_SCREAMING_SNAKE_CASE					) == 3:
														return points
							# find the lowest and the most left point
							snake_case_     							=		0
							snake_case_							,    snake_case_     							=		maxsize, maxsize
							for i, point in enumerate(_SCREAMING_SNAKE_CASE					):
														snake_case_     							=		point[0]
														snake_case_     							=		point[1]
														if y < miny:
																					snake_case_     							=		y
																					snake_case_     							=		x
																					snake_case_     							=		i
														if y == miny and x < minx:
																					snake_case_     							=		x
																					snake_case_     							=		i

    # remove the lowest and the most left point from points for preparing for sort
							points.pop(_SCREAMING_SNAKE_CASE					)

							snake_case_     							=		sorted(_SCREAMING_SNAKE_CASE					,			key=lambda _SCREAMING_SNAKE_CASE					: angle_comparer(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)					)
							# This insert actually costs complexity,
							# and you should instead add (minx, miny) into stack later.
							# I'm using insert just for easy understanding.
							sorted_points.insert(0					,			(minx, miny)					)

							snake_case_     							=		deque()
							stack.append(sorted_points[0]					)
							stack.append(sorted_points[1]					)
							stack.append(sorted_points[2]					)
							# In any ways, the first 3 points line are towards left.
							# Because we sort them the angle from minx, miny.
							snake_case_     							=		Direction.left

							for i in range(3					,			len(_SCREAMING_SNAKE_CASE					)					):
														while True:
																					snake_case_     							=		stack[-2]
																					snake_case_     							=		stack[-1]
																					snake_case_     							=		sorted_points[i]
																					snake_case_     							=		check_direction(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					)

																					if next_direction == Direction.left:
																												snake_case_     							=		Direction.left
																												break
																					if next_direction == Direction.straight:
																												if current_direction == Direction.left:
																																			# We keep current_direction as left.
																																			# Because if the straight line keeps as straight,
																																			# we want to know if this straight line is towards left.
																																			break
																												elif current_direction == Direction.right:
																																			# If the straight line is towards right,
																																			# every previous points on those straigh line is not convex hull.
																																			stack.pop()
																					if next_direction == Direction.right:
																												stack.pop()
														stack.append(sorted_points[i]					)
							return list(_SCREAMING_SNAKE_CASE					)



