






from __future__ import annotations
def 					snake_case_						(   lowerCAmelCase_				:  list[int | str]					):
							create_state_space_tree(lowerCAmelCase_				,				[]				,				0				,				[0 for i in range(len(lowerCAmelCase_					)					)]					)
def 					snake_case_						(   lowerCAmelCase_				:  list[int | str]				,				lowerCAmelCase_				:  list[int | str]				,				lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  list[int]				,				):

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

							for i in range(len(lowerCAmelCase_					)					):
														if not index_used[i]:
																					current_sequence.append(sequence[i]					)
																					__lowercase					:							str			=   True
																					create_state_space_tree(lowerCAmelCase_				,				lowerCAmelCase_				,				index + 1				,				lowerCAmelCase_					)
																					current_sequence.pop()
																					__lowercase					:							Optional[int]			=   False
lowerCamelCase       :       list[int | str]        =				[3, 1, 2, 4]
generate_all_permutations(sequence)

lowerCamelCase       :       list[int | str]        =				["A", "B", "C"]



generate_all_permutations(sequence_a)







import math
def 					snake_case_						(   lowerCAmelCase_				:  int					):

							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 					snake_case_						(   lowerCAmelCase_				:  int = 10001					):

							try:
														__lowercase					:							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."""					)
							__lowercase					:							list[int]			=   []
							__lowercase					:							str			=   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() = }''')