






from __future__ import annotations




def      __A					(     _lowercase					,			_lowercase					,			_lowercase					,			_lowercase ):  # noqa: E741

					'''simple docstring'''







					while r - l > 1:
										_A								= (l + r) // 2
										if v[m] >= key:
															_A								= m
										else:
															_A								= m  # noqa: E741
					return r




def      __A					(     _lowercase ):

					'''simple docstring'''







					if len(_lowercase ) == 0:
										return 0

					_A								= [0] * len(_lowercase )
					_A								= 1

					_A								= v[0]

					for i in range(1					,			len(_lowercase ) ):
										if v[i] < tail[0]:
															_A								= v[i]
										elif v[i] > tail[length - 1]:
															_A								= v[i]
															length += 1
										else:
															_A								= v[i]

					return length


if __name__ == "__main__":
				import doctest

				doctest.testmod()











import math




def      __A					(     _lowercase ):

					'''simple docstring'''







					_A								= []
					_A								= 2
					_A								= int(math.sqrt(_lowercase ) )  # Size of every segment
					_A								= [True] * (end + 1)
					_A								= []

					while start <= end:
										if temp[start] is True:
															in_prime.append(_lowercase )
															for i in range(start * start					,			end + 1					,			_lowercase ):
																				_A								= False
										start += 1
					prime += in_prime

					_A								= end + 1
					_A								= min(2 * end					,			_lowercase )

					while low <= n:
										_A								= [True] * (high - low + 1)
										for each in in_prime:
															_A								= math.floor(low / each ) * each
															if t < low:
																				t += each

															for j in range(_lowercase					,			high + 1					,			_lowercase ):
																				_A								= False

										for j in range(len(_lowercase ) ):
															if temp[j] is True:
																				prime.append(j + low )

										_A								= high + 1
										_A								= min(high + end					,			_lowercase )

					return prime


print(sieve(10**6))



