
"""simple docstring"""







import math
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     int:







							"""simple docstring"""


							if not isinstance(SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ):
														__snake_case     			=       F'''Input value of [number={number}] must be an integer'''
														raise TypeError(SCREAMING_SNAKE_CASE )

							if number < 1:
														__snake_case     			=       F'''Input value of [number={number}] must be > 0'''
														raise ValueError(SCREAMING_SNAKE_CASE )
							elif number == 1:
														return 3
							elif number == 2:
														return 5
							else:
														__snake_case     			=       int(math.log(number // 3							,    2 ) ) + 2

														__snake_case     			=       [3, 5]
														__snake_case     			=       2
														__snake_case     			=       3
														for block in range(1							,    SCREAMING_SNAKE_CASE ):
																					for _ in range(SCREAMING_SNAKE_CASE ):
																												proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1] )
																												proth_index += 1
																					increment *= 2

							return proth_list[number - 1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		for number in range(11):
				_SCREAMING_SNAKE_CASE	       =      0
				try:
						_SCREAMING_SNAKE_CASE	       =      proth(number)
				except ValueError:
						print(F"""ValueError: there is no {number}th Proth number""")
						continue

				print(F"""The {number}th Proth number: {value}""")


"""simple docstring"""







from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat
def   __UpperCamelCase   (					)  ->     tuple[list[int], int]:







							"""simple docstring"""


							__snake_case     			=       [randint(-10_00							,    10_00 ) for i in range(10 )]
							__snake_case     			=       randint(-50_00							,    50_00 )
							return (arr, r)


_SCREAMING_SNAKE_CASE	       =      make_dataset()
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE )  ->     tuple[int, ...]:







							"""simple docstring"""


							for triplet in permutations(SCREAMING_SNAKE_CASE							,    3 ):
														if sum(SCREAMING_SNAKE_CASE ) == target:
																					return tuple(sorted(SCREAMING_SNAKE_CASE ) )
							return (0, 0, 0)
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE )  ->     tuple[int, int, int]:







							"""simple docstring"""


							arr.sort()
							__snake_case     			=       len(SCREAMING_SNAKE_CASE )
							for i in range(n - 1 ):
														__snake_case			,   __snake_case     			=       i + 1, n - 1
														while left < right:
																					if arr[i] + arr[left] + arr[right] == target:
																												return (arr[i], arr[left], arr[right])
																					elif arr[i] + arr[left] + arr[right] < target:
																												left += 1
																					elif arr[i] + arr[left] + arr[right] > target:
																												right -= 1
							return (0, 0, 0)
def   __UpperCamelCase   (					)  ->     tuple[float, float]:







							"""simple docstring"""


							__snake_case     			=       "\nfrom __main__ import dataset, triplet_sum1, triplet_sum2\n"
							__snake_case     			=       "\ntriplet_sum1(*dataset)\n"
							__snake_case     			=       "\ntriplet_sum2(*dataset)\n"
							__snake_case     			=       repeat(setup=SCREAMING_SNAKE_CASE							,    stmt=SCREAMING_SNAKE_CASE							,    repeat=5							,    number=1_00_00 )
							__snake_case     			=       repeat(setup=SCREAMING_SNAKE_CASE							,    stmt=SCREAMING_SNAKE_CASE							,    repeat=5							,    number=1_00_00 )
							return (min(SCREAMING_SNAKE_CASE ), min(SCREAMING_SNAKE_CASE ))


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		_SCREAMING_SNAKE_CASE	       =      solution_times()
		print(F"""The time for naive implementation is {times[0]}.""")
		print(F"""The time for optimized implementation is {times[1]}.""")
