"""simple docstring"""





import math


def    lowercase_   (   _lowerCamelCase:	int      ) ->      bool:



       '''simple docstring'''

       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(_lowerCamelCase      ) + 1      )						,   6      ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True


def    lowercase_   (   _lowerCamelCase:	int = 10001      ) ->      int:



       '''simple docstring'''

       try:
              __lowerCamelCase					:		Optional[int]		   =     int(_lowerCamelCase      )
       except (TypeError, ValueError):
              raise TypeError("Parameter nth must be int or castable to int."      ) from None
       if nth <= 0:
              raise ValueError("Parameter nth must be greater than or equal to one."      )
       __lowerCamelCase					:		list[int]		   =     []
       __lowerCamelCase					:		Tuple		   =     2
       while len(_lowerCamelCase      ) < nth:
              if is_prime(_lowerCamelCase      ):
                     primes.append(_lowerCamelCase      )
                     num += 1
              else:
                     num += 1
       return primes[len(_lowerCamelCase      ) - 1]


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





from functools import lru_cache


def    lowercase_   (   _lowerCamelCase:	int      ) ->      set:



							'''simple docstring'''

							__lowerCamelCase					:		Optional[Any]		   =     2
							__lowerCamelCase					:		Tuple		   =     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    lowercase_   (   _lowerCamelCase:	int      ) ->      int:



							'''simple docstring'''

							return len(unique_prime_factors(_lowerCamelCase      )      )


def    lowercase_   (   _lowerCamelCase:	list      ) ->      bool:



							'''simple docstring'''

							return len(set(_lowerCamelCase      )      ) in (0, 1)


def    lowercase_   (   _lowerCamelCase:	int      ) ->      list:



							'''simple docstring'''

							__lowerCamelCase					:		str		   =     2

							while True:
														# Increment each value of a generated range
														__lowerCamelCase					:		int		   =     [base + i for i in range(_lowerCamelCase      )]

														# Run elements through out unique_prime_factors function
														# Append our target number to the end.
														__lowerCamelCase					:		Dict		   =     [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    lowercase_   (   _lowerCamelCase:	int = 4      ) ->      int:



							'''simple docstring'''

							__lowerCamelCase					:		Any		   =     run(_lowerCamelCase      )
							return results[0] if len(_lowerCamelCase      ) else None


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