



'''simple docstring'''






def        snake_case_   (	lowerCAmelCase_ = 10**6						)->						int:





       '''simple docstring'''


       if n <= 0:
              raise ValueError("""Please enter an integer greater than 0"""						)

       _UpperCAmelCase    :		Union[str, Any]     	=					list(range(n + 1						)						)
       for number in range(2			,  n + 1						):
              if phi[number] == number:
                     phi[number] -= 1
                     for multiple in range(number * 2			,  n + 1			,  lowerCAmelCase_						):
                            _UpperCAmelCase    :		Any     	=					(phi[multiple] // number) * (number - 1)

       _UpperCAmelCase    :		int     	=					1
       for number in range(1			,  n + 1						):
              if (answer / phi[answer]) < (number / phi[number]):
                     _UpperCAmelCase    :		str     	=					number

       return answer


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




'''simple docstring'''

import os
import pickle
import unittest
from collections import UserDict, namedtuple

import torch

from accelerate.test_utils.testing import require_cuda, require_torch_min_version
from accelerate.test_utils.training import RegressionModel
from accelerate.utils import (
    convert_outputs_to_fpaa,
    extract_model_from_parallel,
    find_device,
    listify,
    patch_environment,
    recursively_apply,
    send_to_device,
)


lowercase_  		=			namedtuple('''ExampleNamedTuple''', '''a b c''')
class 	SCREAMING_SNAKE_CASE      (    unittest.TestCase):







		"""simple docstring"""






		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =torch.randn(5		,    2					)
								_lowerCAmelCase					    =torch.device('cuda'					) if torch.cuda.is_available() else torch.device('cpu'					)

								_lowerCAmelCase					    =send_to_device(__A		,    __A					)
								self.assertTrue(torch.equal(resulta.cpu()		,    __A					)					)

								_lowerCAmelCase					    =send_to_device((tensor, [tensor, tensor], 1)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta[0].cpu()		,    __A					)					)
								self.assertIsInstance(resulta[1]		,    __A					)
								self.assertTrue(torch.equal(resulta[1][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta[1][1].cpu()		,    __A					)					)
								self.assertEqual(resulta[2]		,    1					)

								_lowerCAmelCase					    =send_to_device({'a': tensor, 'b': [tensor, tensor], 'c': 1}		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta['a'].cpu()		,    __A					)					)
								self.assertIsInstance(resulta['b']		,    __A					)
								self.assertTrue(torch.equal(resulta['b'][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta['b'][1].cpu()		,    __A					)					)
								self.assertEqual(resulta['c']		,    1					)

								_lowerCAmelCase					    =send_to_device(ExampleNamedTuple(a=__A		,    b=[tensor, tensor]		,    c=1					)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta.a.cpu()		,    __A					)					)
								self.assertIsInstance(resulta.b		,    __A					)
								self.assertTrue(torch.equal(resulta.b[0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta.b[1].cpu()		,    __A					)					)
								self.assertEqual(resulta.c		,    1					)

								_lowerCAmelCase					    =send_to_device(UserDict({'a': tensor, 'b': [tensor, tensor], 'c': 1}					)		,    __A					)
								self.assertIsInstance(__A		,    __A					)
								self.assertTrue(torch.equal(resulta['a'].cpu()		,    __A					)					)
								self.assertIsInstance(resulta['b']		,    __A					)
								self.assertTrue(torch.equal(resulta['b'][0].cpu()		,    __A					)					)
								self.assertTrue(torch.equal(resulta['b'][1].cpu()		,    __A					)					)
								self.assertEqual(resulta['c']		,    1					)






		def 		UpperCamelCase__							( self					)			->  Optional[int]:
								with self.assertRaises(__A					) as cm:
														_lowerCAmelCase					    =recursively_apply(torch.tensor		,    (torch.tensor(1					), 1)		,    error_on_other_type=__A					)
								self.assertEqual(
								    str(cm.exception					)		,    'Unsupported types (<class \'int\'>) passed to `tensor`. Only nested list/tuple/dicts of objects that are valid for `is_torch_tensor` should be passed.'		,    )






		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =torch.tensor([1, 2, 3, 4, 5]					)
								self.assertEqual(listify(__A					)		,    [1, 2, 3, 4, 5]					)

								_lowerCAmelCase					    =torch.tensor([[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]					)
								self.assertEqual(listify(__A					)		,    [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]					)

								_lowerCAmelCase					    =torch.tensor([[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]					)
								self.assertEqual(
								    listify(__A					)		,    [[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]], [[11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]]					)






		def 		UpperCamelCase__							( self					)			->  List[Any]:
								with patch_environment(aa=1		,    BB=2					):
														self.assertEqual(os.environ.get('AA'					)		,    '1'					)
														self.assertEqual(os.environ.get('BB'					)		,    '2'					)

								self.assertNotIn('AA'		,    os.environ					)
								self.assertNotIn('BB'		,    os.environ					)






		def 		UpperCamelCase__							( self					)			->  Union[str, Any]:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A		,    keep_fpaa_wrapper=__A					)
								_lowerCAmelCase					    =pickle.dumps(__A					)






		@require_cuda
		def 		UpperCamelCase__							( self					)			->  Dict:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =torch.cuda.amp.autocast(dtype=torch.floataa					)(model.forward					)
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A		,    keep_fpaa_wrapper=__A					)
								_lowerCAmelCase					    =pickle.dumps(__A					)






		@require_cuda
		@require_torch_min_version(version='2.0'					)
		def 		UpperCamelCase__							( self					)			->  int:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =model.forward
								_lowerCAmelCase					    =torch.cuda.amp.autocast(dtype=torch.floataa					)(model.forward					)
								_lowerCAmelCase					    =convert_outputs_to_fpaa(model.forward					)
								_lowerCAmelCase					    =torch.compile(model.forward		,    backend='inductor'					)
								_lowerCAmelCase					    =torch.randn(4		,    10					).cuda()
								_lowerCAmelCase					    =model(__A					)






		def 		UpperCamelCase__							( self					)			->  Optional[int]:
								_lowerCAmelCase					    =RegressionModel()
								# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
								_lowerCAmelCase					    =torch.nn.parallel.DataParallel(__A					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A					)

								self.assertEqual(__A		,    __A					)






		@require_torch_min_version(version='2.0'					)
		def 		UpperCamelCase__							( self					)			->  str:
								_lowerCAmelCase					    =RegressionModel()
								_lowerCAmelCase					    =torch.compile(__A					)

								# could also do a test with DistributedDataParallel, but difficult to run on CPU or single GPU
								_lowerCAmelCase					    =torch.nn.parallel.DataParallel(__A					)
								_lowerCAmelCase					    =torch.compile(__A					)
								_lowerCAmelCase					    =extract_model_from_parallel(__A					)

								self.assertEqual(compiled_model._orig_mod		,    compiled_model_unwrapped._orig_mod					)






		def 		UpperCamelCase__							( self					)			->  Tuple:
								self.assertEqual(find_device([1, 'a', torch.tensor([1, 2, 3]					)]					)		,    torch.device('cpu'					)					)
								self.assertEqual(find_device({'a': 1, 'b': torch.tensor([1, 2, 3]					)}					)		,    torch.device('cpu'					)					)
								self.assertIsNone(find_device([1, 'a']					)					)





