
def     a						(							snake_case__: Optional[int] ):


				'''simple docstring'''
				lowercase_					  = len(snake_case__ )
				for _ in range(
				    0						,       int(((no_of_elements - 1) / 2) + 1 ) ):  # we don't need to traverse to end of list as
								for j in range(0						,       no_of_elements - 1 ):
												if (
												    lst[j + 1] < lst[j]
												):  # applying bubble sort algorithm from left to right (or forwards)
																lowercase_					  = lst[j + 1]
																lowercase_					  = lst[j]
																lowercase_					  = temp
												if (
												    lst[no_of_elements - 1 - j] < lst[no_of_elements - 2 - j]
												):  # applying bubble sort algorithm from right to left (or backwards)
																lowercase_					  = lst[no_of_elements - 1 - j]
																lowercase_					  = lst[no_of_elements - 2 - j]
																lowercase_					  = temp
				return lst


if __name__ == "__main__":
						print('enter the list to be sorted')
						__a        = [int(x) for x in input().split()]  # inputing elements of the list in one line
						__a        = double_sort(lst)
						print('the sorted list is')
						print(sorted_lst)






from __future__ import annotations

__a        = 'Alexander Joslin'




def     a						(							snake_case__: int ):


				'''simple docstring'''

				if number <= 0:
								lowercase_					  = F'''n must be greater than 0. Got n = {number}'''
								raise ValueError(snake_case__ )

				lowercase_					  = [number + 1] * (number + 1)

				# starting position
				lowercase_					  = 0
				for i in range(1						,       snake_case__ ):
								lowercase_					  = min(table[i + 1]						,       table[i] + 1 )
								# check if out of bounds
								if i * 2 <= number:
												lowercase_					  = min(table[i * 2]						,       table[i] + 1 )
								# check if out of bounds
								if i * 3 <= number:
												lowercase_					  = min(table[i * 3]						,       table[i] + 1 )
				return table[number]


if __name__ == "__main__":
						import doctest

						doctest.testmod()




