


'''simple docstring'''


import itertools
import math






def  __lowerCAmelCase (__lowerCAmelCase   ):

		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  __lowerCAmelCase ():
		_UpperCAmelCase		:       Any								=      2
		while True:
				if is_prime(__lowerCAmelCase   ):
						yield num
				num += 1






def  __lowerCAmelCase (__lowerCAmelCase = 10_001   ):
		return next(itertools.islice(prime_generator()      , nth - 1      , __lowerCAmelCase   )   )


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







'''simple docstring'''


def  __lowerCAmelCase (__lowerCAmelCase   ):  # noqa: E741
		_UpperCAmelCase		:       List[str]								=      len(__lowerCAmelCase   )
		_UpperCAmelCase		:       str								=      0
		_UpperCAmelCase		:       List[str]								=      [0] * n
		_UpperCAmelCase		:       int								=      [False] * n
		_UpperCAmelCase		:       Dict								=      [False] * n

		def dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   ):
				if parent == root:
						out_edge_count += 1
				_UpperCAmelCase		:       List[Any]								=      True
				_UpperCAmelCase		:       str								=      at

				for to in l[at]:
						if to == parent:
								pass
						elif not visited[to]:
								_UpperCAmelCase		:       List[str]								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase   )
								_UpperCAmelCase		:       Tuple								=      min(low[at]      , low[to]   )

								# AP found via bridge
								if at < low[to]:
										_UpperCAmelCase		:       Dict								=      True
								# AP found via cycle
								if at == low[to]:
										_UpperCAmelCase		:       Dict								=      True
						else:
								_UpperCAmelCase		:       Optional[int]								=      min(low[at]      , __lowerCAmelCase   )
				return out_edge_count

		for i in range(__lowerCAmelCase   ):
				if not visited[i]:
						_UpperCAmelCase		:       str								=      0
						_UpperCAmelCase		:       Tuple								=      dfs(__lowerCAmelCase      , __lowerCAmelCase      , -1      , __lowerCAmelCase   )
						_UpperCAmelCase		:       Optional[int]								=      out_edge_count > 1

		for x in range(len(__lowerCAmelCase   )   ):
				if is_art[x] is True:
						print(__lowerCAmelCase   )


# Adjacency list of graph
lowerCamelCase__    	=     {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}





compute_ap(data)



