





def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int   ,				UpperCamelCase__:							int      ):
		if a < b:
				return gcd(UpperCamelCase__   ,				UpperCamelCase__      )
		if a % b == 0:
				return b
		return gcd(UpperCamelCase__   ,				a % b      )






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int   ,				UpperCamelCase__:							int   ,				UpperCamelCase__:							int      ):
		if y == 0:
				return 1
		SCREAMING_SNAKE_CASE__								= power(UpperCamelCase__   ,				y // 2   ,				UpperCamelCase__      ) % mod
		SCREAMING_SNAKE_CASE__								= (temp * temp) % mod
		if y % 2 == 1:
				SCREAMING_SNAKE_CASE__								= (temp * x) % mod
		return temp






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):
		SCREAMING_SNAKE_CASE__								= 2
		while b < n:
				if gcd(UpperCamelCase__   ,				UpperCamelCase__      ) == 1 and power(UpperCamelCase__   ,				n - 1   ,				UpperCamelCase__      ) != 1:
						return False
				b += 1
		return True


if __name__ == "__main__":
	UpperCamelCase_							=     int(input('Enter number: ').strip())
	if is_carmichael_number(number):
		print(F'''{number} is a Carmichael Number.''')
	else:
		print(F'''{number} is not a Carmichael Number.''')






import os
import pickle
import tempfile
import unittest
from typing import Callable, Optional

import numpy as np

from transformers import (
    BatchEncoding,
    BertTokenizer,
    BertTokenizerFast,
    PreTrainedTokenizer,
    PreTrainedTokenizerFast,
    TensorType,
    TokenSpan,
    is_tokenizers_available,
)
from transformers.models.gpta.tokenization_gpta import GPTaTokenizer
from transformers.testing_utils import CaptureStderr, require_flax, require_tf, require_tokenizers, require_torch, slow


if is_tokenizers_available():
	from tokenizers import Tokenizer
	from tokenizers.models import WordPiece




class 					UpperCamelCase_    (       unittest.TestCase      ):


							def        _snake_case					(							self      :str							,			__A      :str						)				->				Optional[int]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= list(tokenizer_class.max_model_input_sizes.keys()						)
									for model_name in sa_models[:1]:
											SCREAMING_SNAKE_CASE__								= tokenizer_class.from_pretrained(__A						)
											self.assertIsNotNone(__A						)
											self.assertIsInstance(__A							,			__A						)
											self.assertIsInstance(__A							,			__A						)

											for special_tok in tokenizer.all_special_tokens:
													self.assertIsInstance(__A							,			__A						)
													SCREAMING_SNAKE_CASE__								= tokenizer.convert_tokens_to_ids(__A						)
													self.assertIsInstance(__A							,			__A						)


							def        _snake_case					(							self      :List[str]							,			__A      :BatchEncoding							,			__A      :Optional[Callable] = None						)				->				Tuple:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= pickle.dumps(__A						)
									self.assertIsNotNone(__A						)

									SCREAMING_SNAKE_CASE__								= pickle.loads(__A						)

									# Ensure is_fast is correctly restored
									self.assertEqual(be_restored.is_fast							,			be_original.is_fast						)

									# Ensure encodings are potentially correctly restored
									if be_original.is_fast:
											self.assertIsNotNone(be_restored.encodings						)
									else:
											self.assertIsNone(be_restored.encodings						)

									# Ensure the keys are the same
									for original_v, restored_v in zip(be_original.values()							,			be_restored.values()						):
											if equal_op:
													self.assertTrue(equal_op(__A							,			__A						)						)
											else:
													self.assertEqual(__A							,			__A						)


							@slow
							def        _snake_case					(							self      :Dict						)				->				Optional[int]:



									"""simple docstring"""



									self.check_tokenizer_from_pretrained(__A						)


							def        _snake_case					(							self      :List[Any]						)				->				Dict:



									"""simple docstring"""



									self.assertEqual(TensorType("""tf"""						)							,			TensorType.TENSORFLOW						)
									self.assertEqual(TensorType("""pt"""						)							,			TensorType.PYTORCH						)
									self.assertEqual(TensorType("""np"""						)							,			TensorType.NUMPY						)


							@require_tokenizers
							def        _snake_case					(							self      :Optional[Any]						)				->				List[Any]:



									"""simple docstring"""



									import numpy as np

									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)
									SCREAMING_SNAKE_CASE__								= BertTokenizerFast.from_pretrained("""bert-base-cased"""						)

									# Python no tensor
									with self.subTest("""BatchEncoding (Python, return_tensors=None)"""						):
											self.assert_dump_and_restore(tokenizer_p("""Small example to encode"""						)						)

									with self.subTest("""BatchEncoding (Python, return_tensors=NUMPY)"""						):
											self.assert_dump_and_restore(
											    tokenizer_p("""Small example to encode"""							,			return_tensors=TensorType.NUMPY						)							,			np.array_equal						)

									with self.subTest("""BatchEncoding (Rust, return_tensors=None)"""						):
											self.assert_dump_and_restore(tokenizer_r("""Small example to encode"""						)						)

									with self.subTest("""BatchEncoding (Rust, return_tensors=NUMPY)"""						):
											self.assert_dump_and_restore(
											    tokenizer_r("""Small example to encode"""							,			return_tensors=TensorType.NUMPY						)							,			np.array_equal						)


							@require_tf
							@require_tokenizers
							def        _snake_case					(							self      :Optional[Any]						)				->				Optional[Any]:



									"""simple docstring"""



									import tensorflow as tf

									def tf_array_equals(__A      :Union[str, Any]							,			__A      :Any						):
											return tf.reduce_all(tf.equal(__A							,			__A						)						)

									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)
									SCREAMING_SNAKE_CASE__								= BertTokenizerFast.from_pretrained("""bert-base-cased"""						)

									with self.subTest("""BatchEncoding (Python, return_tensors=TENSORFLOW)"""						):
											self.assert_dump_and_restore(
											    tokenizer_p("""Small example to encode"""							,			return_tensors=TensorType.TENSORFLOW						)							,			__A						)

									with self.subTest("""BatchEncoding (Rust, return_tensors=TENSORFLOW)"""						):
											self.assert_dump_and_restore(
											    tokenizer_r("""Small example to encode"""							,			return_tensors=TensorType.TENSORFLOW						)							,			__A						)


							@require_torch
							@require_tokenizers
							def        _snake_case					(							self      :List[Any]						)				->				int:



									"""simple docstring"""



									import torch

									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)
									SCREAMING_SNAKE_CASE__								= BertTokenizerFast.from_pretrained("""bert-base-cased"""						)

									with self.subTest("""BatchEncoding (Python, return_tensors=PYTORCH)"""						):
											self.assert_dump_and_restore(
											    tokenizer_p("""Small example to encode"""							,			return_tensors=TensorType.PYTORCH						)							,			torch.equal						)

									with self.subTest("""BatchEncoding (Rust, return_tensors=PYTORCH)"""						):
											self.assert_dump_and_restore(
											    tokenizer_r("""Small example to encode"""							,			return_tensors=TensorType.PYTORCH						)							,			torch.equal						)


							@require_tokenizers
							def        _snake_case					(							self      :Optional[Any]						)				->				str:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)
									SCREAMING_SNAKE_CASE__								= BertTokenizerFast.from_pretrained("""bert-base-cased"""						)

									with self.subTest("""Python Tokenizer"""						):
											self.assertFalse(tokenizer_p("""Small example to_encode"""						).is_fast						)

									with self.subTest("""Rust Tokenizer"""						):
											self.assertTrue(tokenizer_r("""Small example to_encode"""						).is_fast						)


							@require_tokenizers
							def        _snake_case					(							self      :List[str]						)				->				str:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BertTokenizerFast.from_pretrained("""bert-base-cased"""						)
									SCREAMING_SNAKE_CASE__								= tokenizer_r(["""Test""", """\xad""", """test"""]							,			is_split_into_words=__A						)

									self.assertEqual(encoded.word_to_tokens(0						)							,			TokenSpan(start=1							,			end=2						)						)
									self.assertEqual(encoded.word_to_tokens(1						)							,			__A						)
									self.assertEqual(encoded.word_to_tokens(2						)							,			TokenSpan(start=2							,			end=3						)						)


							def        _snake_case					(							self      :Tuple						)				->				int:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""np"""						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(2, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(2,)						)
									# test converting the converted
									with CaptureStderr() as cs:
											SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""np"""						)
									self.assertFalse(len(cs.err						)							,			msg=f'''should have no warning, but got {cs.err}'''						)

									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""np"""							,			prepend_batch_axis=__A						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(1, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(1,)						)


							@require_torch
							def        _snake_case					(							self      :int						)				->				int:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""pt"""						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(2, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(2,)						)
									# test converting the converted
									with CaptureStderr() as cs:
											SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""pt"""						)
									self.assertFalse(len(cs.err						)							,			msg=f'''should have no warning, but got {cs.err}'''						)

									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""pt"""							,			prepend_batch_axis=__A						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(1, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(1,)						)


							@require_tf
							def        _snake_case					(							self      :Optional[Any]						)				->				Dict:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""tf"""						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(2, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(2,)						)
									# test converting the converted
									with CaptureStderr() as cs:
											SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""tf"""						)
									self.assertFalse(len(cs.err						)							,			msg=f'''should have no warning, but got {cs.err}'''						)

									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""tf"""							,			prepend_batch_axis=__A						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(1, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(1,)						)


							@require_flax
							def        _snake_case					(							self      :Dict						)				->				Union[str, Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [[1, 2, 3], [4, 5, 6]], """labels""": [0, 1]}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""jax"""						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(2, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(2,)						)
									# test converting the converted
									with CaptureStderr() as cs:
											SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""jax"""						)
									self.assertFalse(len(cs.err						)							,			msg=f'''should have no warning, but got {cs.err}'''						)

									SCREAMING_SNAKE_CASE__								= BatchEncoding({"""inputs""": [1, 2, 3], """labels""": 0}						)
									SCREAMING_SNAKE_CASE__								= batch.convert_to_tensors(tensor_type="""jax"""							,			prepend_batch_axis=__A						)
									self.assertEqual(tensor_batch["""inputs"""].shape							,			(1, 3)						)
									self.assertEqual(tensor_batch["""labels"""].shape							,			(1,)						)


							def        _snake_case					(							self      :List[Any]						)				->				Optional[int]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= [{"""input_ids""": np.array([0, 1, 2]						)}, {"""input_ids""": np.array([0, 1, 2, 3]						)}]
									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)

									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			np.ndarray						)						)
									self.assertEqual(batch["""input_ids"""].tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)
									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A							,			return_tensors="""np"""						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			np.ndarray						)						)
									self.assertEqual(batch["""input_ids"""].tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)


							@require_torch
							def        _snake_case					(							self      :int						)				->				Dict:



									"""simple docstring"""



									import torch

									SCREAMING_SNAKE_CASE__								= [{"""input_ids""": torch.tensor([0, 1, 2]						)}, {"""input_ids""": torch.tensor([0, 1, 2, 3]						)}]
									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)

									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			torch.Tensor						)						)
									self.assertEqual(batch["""input_ids"""].tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)
									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A							,			return_tensors="""pt"""						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			torch.Tensor						)						)
									self.assertEqual(batch["""input_ids"""].tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)


							@require_tf
							def        _snake_case					(							self      :int						)				->				int:



									"""simple docstring"""



									import tensorflow as tf

									SCREAMING_SNAKE_CASE__								= [{"""input_ids""": tf.constant([0, 1, 2]						)}, {"""input_ids""": tf.constant([0, 1, 2, 3]						)}]
									SCREAMING_SNAKE_CASE__								= BertTokenizer.from_pretrained("""bert-base-cased"""						)

									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			tf.Tensor						)						)
									self.assertEqual(batch["""input_ids"""].numpy().tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)
									SCREAMING_SNAKE_CASE__								= tokenizer.pad(__A							,			padding=__A							,			return_tensors="""tf"""						)
									self.assertTrue(isinstance(batch["""input_ids"""]							,			tf.Tensor						)						)
									self.assertEqual(batch["""input_ids"""].numpy().tolist()							,			[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]						)


							@require_tokenizers
							def        _snake_case					(							self      :Tuple						)				->				Any:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= Tokenizer(WordPiece(unk_token="""[UNK]"""						)						)
									PreTrainedTokenizerFast(tokenizer_object=__A						)


							@require_tokenizers
							def        _snake_case					(							self      :Any						)				->				Union[str, Any]:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								= Tokenizer(WordPiece(unk_token="""[UNK]"""						)						)
									with tempfile.TemporaryDirectory() as tmpdirname:
											bert_tokenizer.save(os.path.join(__A							,			"""tokenizer.json"""						)						)
											PreTrainedTokenizerFast(tokenizer_file=os.path.join(__A							,			"""tokenizer.json"""						)						)