
'''simple docstring'''







import math



def       _a		(						_SCREAMING_SNAKE_CASE		: int	):

						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		: int = 200_0000	):
						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() = }")

from __future__ import annotations
def lowerCamelCase_       (			A			:      list[int]						):




      """simple docstring"""
      if not list_of_ints:
            return []

      if min(A						) < 0:
            raise ValueError('''All numbers must be positive'''						)

      lowerCAmelCase_						=      max(len(bin(A						)[2:]						) for x in list_of_ints						)
      return _msd_radix_sort(A		,					A						)
def lowerCamelCase_       (			A			:      list[int]		,					A			:      int						):




      """simple docstring"""
      if bit_position == 0 or len(A						) in [0, 1]:
            return list_of_ints

      lowerCAmelCase_						=      []
      lowerCAmelCase_						=      []
      # Split numbers based on bit at bit_position from the right
      for number in list_of_ints:
            if (number >> (bit_position - 1)) & 1:
                  # number has a one at bit bit_position
                  ones.append(A						)
            else:
                  # number has a zero at bit bit_position
                  zeros.append(A						)

    # recursively split both lists further
      lowerCAmelCase_						=      _msd_radix_sort(A		,					bit_position - 1						)
      lowerCAmelCase_						=      _msd_radix_sort(A		,					bit_position - 1						)

      # recombine lists
      lowerCAmelCase_						=      zeros
      res.extend(A						)

      return res
def lowerCamelCase_       (			A			:      list[int]						):




      """simple docstring"""
      lowerCAmelCase_						=      len(A						)
      if not list_of_ints or length == 1:
            return

      if min(A						) < 0:
            raise ValueError('''All numbers must be positive'''						)

      lowerCAmelCase_						=      max(len(bin(A						)[2:]						) for x in list_of_ints						)
      _msd_radix_sort_inplace(A		,					A		,					0		,					A						)
def lowerCamelCase_       (			A			:      list[int]		,					A			:      int		,					A			:      int		,					A			:      int						):




      """simple docstring"""
      if bit_position == 0 or end_index - begin_index <= 1:
            return

      bit_position -= 1

      lowerCAmelCase_						=      begin_index
      lowerCAmelCase_						=      end_index - 1
      while i <= j:
            lowerCAmelCase_						=      False
            if not (list_of_ints[i] >> bit_position) & 1:
                  # found zero at the beginning
                  i += 1
                  lowerCAmelCase_						=      True
            if (list_of_ints[j] >> bit_position) & 1:
                  # found one at the end
                  j -= 1
                  lowerCAmelCase_						=      True

            if changed:
                  continue

            lowerCAmelCase_			,		lowerCAmelCase_						=      list_of_ints[j], list_of_ints[i]
            j -= 1
            if j != i:
                  i += 1

      _msd_radix_sort_inplace(A		,					A		,					A		,					A						)
      _msd_radix_sort_inplace(A		,					A		,					A		,					A						)


if __name__ == "__main__":
 import doctest

 doctest.testmod()



