

"""simple docstring"""




from __future__ import annotations

from collections.abc import Generator
def 	lowerCAmelCase    (       ):
 '''simple docstring'''





 UpperCAmelCase__       :	dict[int, int]        =       {}
 UpperCAmelCase__       :	Optional[int]        =       2
 while True:
  UpperCAmelCase__       :	Dict        =       factor_map.pop(__UpperCamelCase				,     __UpperCamelCase   )
  if factor:
   UpperCAmelCase__       :	Tuple        =       factor + prime
   while x in factor_map:
    x += factor
   UpperCAmelCase__       :	int        =       factor
  else:
   UpperCAmelCase__       :	Optional[Any]        =       prime
   yield prime
  prime += 1
def 	lowerCAmelCase    (       __UpperCamelCase = 1e10   ):
 '''simple docstring'''





 UpperCAmelCase__       :	Any        =       sieve()

 UpperCAmelCase__       :	Any        =       1
 while True:
  UpperCAmelCase__       :	List[Any]        =       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())











from __future__ import annotations

from typing import Any

def lowercase    (  SCREAMING_SNAKE_CASE )			->							None:


			'''simple docstring'''







			create_state_space_tree(SCREAMING_SNAKE_CASE       ,    []       ,    0 )

def lowercase    (  SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )			->							None:


			'''simple docstring'''







			if index == len(SCREAMING_SNAKE_CASE ):
						print(SCREAMING_SNAKE_CASE )
						return

			create_state_space_tree(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    index + 1 )
			current_subsequence.append(sequence[index] )
			create_state_space_tree(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE       ,    index + 1 )
			current_subsequence.pop()


if __name__ == "__main__":
				SCREAMING_SNAKE_CASE__     :     list[Any]		    =       [3, 1, 2, 4]
				generate_all_subsequences(seq)

				seq.clear()
				seq.extend(["A", "B", "C"])
				generate_all_subsequences(seq)
