
'''simple docstring'''
from math import isqrt







def 		A_(     A						:		int):
							UpperCamelCase   			=     [True] * max_number
							for i in range(2		,     isqrt(max_number - 1) + 1):
														if is_prime[i]:
																					for j in range(i**2		,     A		,     A):
																												UpperCamelCase   			=     False

							return [i for i in range(2		,     A) if is_prime[i]]







def 		A_(     A						:		int = 10**8):
							UpperCamelCase   			=     calculate_prime_numbers(max_number // 2)

							UpperCamelCase   			=     0
							UpperCamelCase   			=     0
							UpperCamelCase   			=     len(A) - 1
							while left <= right:
														while prime_numbers[left] * prime_numbers[right] >= max_number:
																					right -= 1
														semiprimes_count += right - left + 1
														left += 1

							return semiprimes_count


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






'''simple docstring'''
def 		A_(     A						:		list[int]):
							UpperCamelCase   			=     []
							if len(A) == 1:
														return [nums.copy()]
							for _ in range(len(A)):
														UpperCamelCase   			=     nums.pop(0)
														UpperCamelCase   			=     permute(A)
														for perm in permutations:
																					perm.append(A)
														result.extend(A)
														nums.append(A)
							return result







def 		A_(     A						:		str):

							def backtrack(A						:		str):
														if start == len(A) - 1:
																					output.append(nums[:])
														else:
																					for i in range(A		,     len(A)):
																												UpperCamelCase			,	UpperCamelCase   			=     nums[i], nums[start]
																												backtrack(start + 1)
																												UpperCamelCase			,	UpperCamelCase   			=     nums[i], nums[start]  # backtrack

							UpperCamelCase   			=     []
							backtrack(0)
							return output


if __name__ == "__main__":
						import doctest

						# use res to print the data in permute2 function
						lowerCAmelCase					:    Dict           = permutea([1, 2, 3])
						print(res)
						doctest.testmod()




