
from __future__ import annotations

import bisect





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__ = 0      ,					lowerCamelCase__ = -1       ):
				if hi < 0:
								lowerCamelCase_         =     len(lowerCamelCase__       )

				while lo < hi:
								lowerCamelCase_         =     lo + (hi - lo) // 2
								if sorted_collection[mid] < item:
												lowerCamelCase_         =     mid + 1
								else:
												lowerCamelCase_         =     mid

				return lo





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__ = 0      ,					lowerCamelCase__ = -1       ):
				if hi < 0:
								lowerCamelCase_         =     len(lowerCamelCase__       )

				while lo < hi:
								lowerCamelCase_         =     lo + (hi - lo) // 2
								if sorted_collection[mid] <= item:
												lowerCamelCase_         =     mid + 1
								else:
												lowerCamelCase_         =     mid

				return lo





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__ = 0      ,					lowerCamelCase__ = -1       ):
				sorted_collection.insert(bisect_left(lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__       )      ,					lowerCamelCase__       )





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__ = 0      ,					lowerCamelCase__ = -1       ):
				sorted_collection.insert(bisect_right(lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__       )      ,					lowerCamelCase__       )





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__       ):
				lowerCamelCase_         =     0
				lowerCamelCase_         =     len(lowerCamelCase__       ) - 1

				while left <= right:
								lowerCamelCase_         =     left + (right - left) // 2
								lowerCamelCase_         =     sorted_collection[midpoint]
								if current_item == item:
												return midpoint
								elif item < current_item:
												lowerCamelCase_         =     midpoint - 1
								else:
												lowerCamelCase_         =     midpoint + 1
				return None





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__       ):
				lowerCamelCase_         =     bisect.bisect_left(lowerCamelCase__      ,					lowerCamelCase__       )
				if index != len(lowerCamelCase__       ) and sorted_collection[index] == item:
								return index
				return None





def      lowerCamelCase_					(							lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__       ):
				if right < left:
								return None

				lowerCamelCase_         =     left + (right - left) // 2

				if sorted_collection[midpoint] == item:
								return midpoint
				elif sorted_collection[midpoint] > item:
								return binary_search_by_recursion(lowerCamelCase__      ,					lowerCamelCase__      ,					lowerCamelCase__      ,					midpoint - 1       )
				else:
								return binary_search_by_recursion(lowerCamelCase__      ,					lowerCamelCase__      ,					midpoint + 1      ,					lowerCamelCase__       )


if __name__ == "__main__":
			__A							=input('''Enter numbers separated by comma:\n''').strip()
			__A							=sorted(int(item) for item in user_input.split(''','''))
			__A							=int(input('''Enter a single number to be found in the list:\n'''))
			__A							=binary_search(collection, target)
			if result is None:
						print(F"""{target} was not found in {collection}.""")
			else:
						print(F"""{target} was found at position {result} in {collection}.""")




from __future__ import annotations

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


__A							=[num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]





def      lowerCamelCase_					(							lowerCamelCase__       ):
				if not isinstance(lowerCamelCase__      ,					lowerCamelCase__       ):
								raise ValueError("n must be an integer"       )
				if n <= 0:
								raise ValueError("n must be >= 0"       )

				lowerCamelCase_         =     []
				for num in range(len(lowerCamelCase__       )       ):
								lowerCamelCase_         =     0
								while 2 * i * i <= odd_composites[num]:
												lowerCamelCase_         =     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      lowerCamelCase_					(							):
				return compute_nums(1       )[0]


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


