




import random

def    UpperCAmelCase_				( __UpperCAmelCase		:      list     ,     __UpperCAmelCase		:      Dict				)   ->					tuple:
      SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_      		=     [], [], []
      for element in data:
            if element < pivot:
                  less.append(__UpperCAmelCase				)
            elif element > pivot:
                  greater.append(__UpperCAmelCase				)
            else:
                  equal.append(__UpperCAmelCase				)
      return less, equal, greater





def    UpperCAmelCase_				( __UpperCAmelCase		:      list     ,     __UpperCAmelCase		:      int				)   ->					List[str]:
      # index = len(items) // 2 when trying to find the median
      #   (value of index when items is sorted)

      # invalid input
      if index >= len(__UpperCAmelCase				) or index < 0:
            return None

      SCREAMING_SNAKE_CASE_      		=     items[random.randint(0     ,     len(__UpperCAmelCase				) - 1				)]
      SCREAMING_SNAKE_CASE_      		=     0
      SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_      		=     _partition(__UpperCAmelCase     ,     __UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     len(__UpperCAmelCase				)
      SCREAMING_SNAKE_CASE_      		=     len(__UpperCAmelCase				)

      # index is the pivot
      if m <= index < m + count:
            return pivot
      # must be in smaller
      elif m > index:
            return quick_select(__UpperCAmelCase     ,     __UpperCAmelCase				)
      # must be in larger
      else:
            return quick_select(__UpperCAmelCase     ,     index - (m + count)				)





from __future__ import annotations

from collections.abc import Generator

def    UpperCAmelCase_				( )   ->					Generator[int, None, None]:
      SCREAMING_SNAKE_CASE_      		=     {}
      SCREAMING_SNAKE_CASE_      		=     2
      while True:
            SCREAMING_SNAKE_CASE_      		=     factor_map.pop(__UpperCAmelCase     ,     __UpperCAmelCase				)
            if factor:
                  SCREAMING_SNAKE_CASE_      		=     factor + prime
                  while x in factor_map:
                        x += factor
                  SCREAMING_SNAKE_CASE_      		=     factor
            else:
                  SCREAMING_SNAKE_CASE_      		=     prime
                  yield prime
            prime += 1

def    UpperCAmelCase_				( __UpperCAmelCase		:      float = 1E10				)   ->					int:
      SCREAMING_SNAKE_CASE_      		=     sieve()

      SCREAMING_SNAKE_CASE_      		=     1
      while True:
            SCREAMING_SNAKE_CASE_      		=     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())