





"""simple docstring"""






from __future__ import annotations

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


__UpperCAmelCase						=			[num for num in range(3, 10_0001, 2) if not is_prime(num)]






def      lowercase__ (					lowerCAmelCase__   :			int			)    ->			list[int]:



			'''simple docstring'''
			if not isinstance(lowerCAmelCase__							,			lowerCAmelCase__			):
						raise ValueError("n must be an integer"			)
			if n <= 0:
						raise ValueError("n must be >= 0"			)

			a__  :	Dict		 =			[]
			for num in range(len(lowerCAmelCase__			)			):
						a__  :	Dict		 =			0
						while 2 * i * i <= odd_composites[num]:
									a__  :	Union[str, Any]		 =			odd_composites[num] - 2 * i * i
									if is_prime(lowerCAmelCase__			):
												break
									i += 1
						else:
									list_nums.append(odd_composites[num]			)
									if len(lowerCAmelCase__			) == n:
												return list_nums

			return []






def      lowercase__ (					)    ->			int:



			'''simple docstring'''
			return compute_nums(1			)[0]


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






"""simple docstring"""






import functools






def      lowercase__ (					lowerCAmelCase__   :			str							,			lowerCAmelCase__   :			str			)    ->			int:



			'''simple docstring'''
			a__  :	Any		 =			len(lowerCAmelCase__			)
			a__  :	Optional[int]		 =			len(lowerCAmelCase__			)

			@functools.cache
			def min_distance(lowerCAmelCase__   :			int							,			lowerCAmelCase__   :			int			) -> int:
						# if first word index is overflow - delete all from the second word
						if indexa >= len_worda:
									return len_worda - indexa
						# if second word index is overflow - delete all from the first word
						if indexa >= len_worda:
									return len_worda - indexa
						a__  :	List[Any]		 =			int(worda[indexa] != worda[indexa]			)  # current letters not identical
						return min(
						    1 + min_distance(indexa + 1							,			lowerCAmelCase__			)							,			1 + min_distance(lowerCAmelCase__							,			indexa + 1			)							,			diff + min_distance(indexa + 1							,			indexa + 1			)							,			)

			return min_distance(0							,			0			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()