
"""simple docstring"""


# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


A_    							=					{
    """configuration_vivit""": ["""VIVIT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """VivitConfig"""],
}
try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_    							=					["""VivitImageProcessor"""]


try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_    							=					[
						    """VIVIT_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """VivitModel""",
						    """VivitPreTrainedModel""",
						    """VivitForVideoClassification""",
						]


if TYPE_CHECKING:
						from .configuration_vivit import VIVIT_PRETRAINED_CONFIG_ARCHIVE_MAP, VivitConfig

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .image_processing_vivit import VivitImageProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_vivit import (
												    VIVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
												    VivitForVideoClassification,
												    VivitModel,
												    VivitPreTrainedModel,
												)


else:
						import sys

						A_    							=					_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





"""simple docstring"""


import math






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  [True] * n
			lowerCamelCase_					=  False
			lowerCamelCase_					=  False
			lowerCamelCase_					=  True

			for i in range(3	,int(n**0.5 + 1						)	,2						):
						lowerCamelCase_					=  i * 2
						while index < n:
									lowerCamelCase_					=  False
									lowerCamelCase_					=  index + i

			lowerCamelCase_					=  [2]

			for i in range(3	,lowerCAmelCase__	,2						):
						if is_prime[i]:
									primes.append(lowerCAmelCase__						)

			return primes






def  lowercase						(	lowerCAmelCase__ = 999_966_663_333						):
			lowerCamelCase_					=  math.floor(math.sqrt(lowerCAmelCase__						)						) + 100
			lowerCamelCase_					=  prime_sieve(lowerCAmelCase__						)

			lowerCamelCase_					=  0
			lowerCamelCase_					=  0
			lowerCamelCase_					=  primes[prime_index]

			while (last_prime**2) <= limit:
						lowerCamelCase_					=  primes[prime_index + 1]

						lowerCamelCase_					=  last_prime**2
						lowerCamelCase_					=  next_prime**2

						# Get numbers divisible by lps(current)
						lowerCamelCase_					=  lower_bound + last_prime
						while upper_bound > current <= limit:
									matches_sum += current
									current += last_prime

						# Reset the upper_bound
						while (upper_bound - next_prime) > limit:
									upper_bound -= next_prime

						# Add the numbers divisible by ups(current)
						lowerCamelCase_					=  upper_bound - next_prime
						while current > lower_bound:
									matches_sum += current
									current -= next_prime

						# Remove the numbers divisible by both ups and lps
						lowerCamelCase_					=  0
						while upper_bound > current <= limit:
									if current <= lower_bound:
												# Increment the current number
												current += last_prime * next_prime
												continue

									if current > limit:
												break

									# Remove twice since it was added by both ups and lps
									matches_sum -= current * 2

									# Increment the current number
									current += last_prime * next_prime

						# Setup for next pair
						lowerCamelCase_					=  next_prime
						prime_index += 1

			return matches_sum


if __name__ == "__main__":
						print(solution())



