

"""simple docstring"""

from functools import lru_cache



def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						set:
 lowerCAmelCase__   :				Optional[Any] 			=				2
 lowerCAmelCase__   :				List[Any] 			=				set()
 while i * i <= n:
  if n % i:
   i += 1
  else:
   n //= i
   factors.add(_lowerCAmelCase   )
 if n > 1:
  factors.add(_lowerCAmelCase   )
 return factors



@lru_cache
def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						int:
 return len(unique_prime_factors(_lowerCAmelCase   )   )



def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						bool:
 return len(set(_lowerCAmelCase   )   ) in (0, 1)



def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						list:
 lowerCAmelCase__   :				Optional[Any] 			=				2

 while True:
  # Increment each value of a generated range
  lowerCAmelCase__   :				List[Any] 			=				[base + i for i in range(_lowerCAmelCase   )]

  # Run elements through out unique_prime_factors function
  # Append our target number to the end.
  lowerCAmelCase__   :				List[str] 			=				[upf_len(_lowerCAmelCase   ) for x in group]
  checker.append(_lowerCAmelCase   )

  # If all numbers in the list are equal, return the group variable.
  if equality(_lowerCAmelCase   ):
   return group

  # Increment our base variable by 1
  base += 1



def       SCREAMING_SNAKE_CASE							( lowercase__ = 4   )			->						int:
 lowerCAmelCase__   :				Tuple 			=				run(_lowerCAmelCase   )
 return results[0] if len(_lowerCAmelCase   ) else None


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













from math import sqrt

def   __snake_case    (       _lowerCAmelCase			:			int						)			->    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(sqrt(_lowerCAmelCase						) + 1						)					,					6						):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True

def   __snake_case    (       _lowerCAmelCase			:			int = 10001						)			->    int:
   A_       :					Any        =      0
   A_       :					Tuple        =      1
   while count != nth and number < 3:
      number += 1
      if is_prime(_lowerCAmelCase						):
         count += 1
   while count != nth:
      number += 2
      if is_prime(_lowerCAmelCase						):
         count += 1
   return number


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