






'''simple docstring'''

import unittest

from transformers import PegasusConfig, PegasusTokenizer, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor


if is_flax_available():
     import os

     # The slow tests are often failing with OOM error on GPU
     # This makes JAX allocate exactly what is needed on demand, and deallocate memory that is no longer needed
     # but will be slower as stated here https://jax.readthedocs.io/en/latest/gpu_memory_allocation.html
     SCREAMING_SNAKE_CASE__											=     'platform'
     import jax
     import jax.numpy as jnp
     import numpy as np

     from transformers import FlaxPegasusForConditionalGeneration, FlaxPegasusModel






@require_flax
class        a_		:
  lowercase  	=   PegasusConfig
  lowercase  	=   {}
  lowercase  	=   """gelu"""

  def __init__(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE=13    ,	_SCREAMING_SNAKE_CASE=7    ,	_SCREAMING_SNAKE_CASE=True    ,	_SCREAMING_SNAKE_CASE=False    ,	_SCREAMING_SNAKE_CASE=99    ,	_SCREAMING_SNAKE_CASE=32    ,	_SCREAMING_SNAKE_CASE=5    ,	_SCREAMING_SNAKE_CASE=4    ,	_SCREAMING_SNAKE_CASE=37    ,	_SCREAMING_SNAKE_CASE=0.1    ,	_SCREAMING_SNAKE_CASE=0.1    ,	_SCREAMING_SNAKE_CASE=20    ,	_SCREAMING_SNAKE_CASE=2    ,	_SCREAMING_SNAKE_CASE=1    ,	_SCREAMING_SNAKE_CASE=0    ,	)						->   int:



        """simple docstring"""






        UpperCamelCase       						=      parent
        UpperCamelCase       						=      batch_size
        UpperCamelCase       						=      seq_length
        UpperCamelCase       						=      is_training
        UpperCamelCase       						=      use_labels
        UpperCamelCase       						=      vocab_size
        UpperCamelCase       						=      hidden_size
        UpperCamelCase       						=      num_hidden_layers
        UpperCamelCase       						=      num_attention_heads
        UpperCamelCase       						=      intermediate_size

        UpperCamelCase       						=      hidden_dropout_prob
        UpperCamelCase       						=      attention_probs_dropout_prob
        UpperCamelCase       						=      max_position_embeddings
        UpperCamelCase       						=      eos_token_id
        UpperCamelCase       						=      pad_token_id
        UpperCamelCase       						=      bos_token_id

  def 						A__		(   self   )						->   Any:



        """simple docstring"""






        UpperCamelCase       						=      ids_tensor([self.batch_size, self.seq_length - 1]    ,	self.vocab_size   ).clip(3    ,	self.vocab_size   )
        UpperCamelCase       						=      np.expand_dims(np.array([self.eos_token_id] * self.batch_size   )    ,	1   )
        UpperCamelCase       						=      np.concatenate([input_ids, eos_tensor]    ,	axis=1   )

        UpperCamelCase       						=      ids_tensor([self.batch_size, self.seq_length]    ,	self.vocab_size   )

        UpperCamelCase       						=      self.config_cls(
            vocab_size=self.vocab_size    ,	d_model=self.hidden_size    ,	encoder_layers=self.num_hidden_layers    ,	decoder_layers=self.num_hidden_layers    ,	encoder_attention_heads=self.num_attention_heads    ,	decoder_attention_heads=self.num_attention_heads    ,	encoder_ffn_dim=self.intermediate_size    ,	decoder_ffn_dim=self.intermediate_size    ,	dropout=self.hidden_dropout_prob    ,	attention_dropout=self.attention_probs_dropout_prob    ,	max_position_embeddings=self.max_position_embeddings    ,	eos_token_ids=[2]    ,	bos_token_id=self.bos_token_id    ,	pad_token_id=self.pad_token_id    ,	decoder_start_token_id=self.pad_token_id    ,	**self.config_updates    ,	)
        UpperCamelCase       						=      prepare_pegasus_inputs_dict(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )
        return config, inputs_dict

  def 						A__		(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )						->   Optional[int]:



        """simple docstring"""






        UpperCamelCase       						=      20
        UpperCamelCase       						=      model_class_name(_SCREAMING_SNAKE_CASE   )

        UpperCamelCase       						=      model.encode(inputs_dict["""input_ids"""]   )

        UpperCamelCase						,UpperCamelCase       						=      (
            inputs_dict["""decoder_input_ids"""],
            inputs_dict["""decoder_attention_mask"""],
        )

        UpperCamelCase       						=      model.init_cache(decoder_input_ids.shape[0]    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      jnp.ones((decoder_input_ids.shape[0], max_decoder_length)    ,	dtype="""i4"""   )

        UpperCamelCase       						=      jnp.broadcast_to(
            jnp.arange(decoder_input_ids.shape[-1] - 1   )[None, :]    ,	(decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)    ,	)
        UpperCamelCase       						=      model.decode(
            decoder_input_ids[:, :-1]    ,	_SCREAMING_SNAKE_CASE    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE    ,	past_key_values=_SCREAMING_SNAKE_CASE    ,	decoder_position_ids=_SCREAMING_SNAKE_CASE    ,	)

        UpperCamelCase       						=      jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]    ,	dtype="""i4"""   )
        UpperCamelCase       						=      model.decode(
            decoder_input_ids[:, -1:]    ,	_SCREAMING_SNAKE_CASE    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE    ,	past_key_values=outputs_cache.past_key_values    ,	decoder_position_ids=_SCREAMING_SNAKE_CASE    ,	)

        UpperCamelCase       						=      model.decode(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )

        UpperCamelCase       						=      np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])   )   )
        self.parent.assertTrue(diff < 1e-3    ,	msg=F"Max diff is {diff}"   )


  def 						A__		(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )						->   Optional[Any]:



        """simple docstring"""






        UpperCamelCase       						=      20
        UpperCamelCase       						=      model_class_name(_SCREAMING_SNAKE_CASE   )

        UpperCamelCase       						=      model.encode(inputs_dict["""input_ids"""]   )

        UpperCamelCase						,UpperCamelCase       						=      (
            inputs_dict["""decoder_input_ids"""],
            inputs_dict["""decoder_attention_mask"""],
        )

        UpperCamelCase       						=      jnp.concatenate(
            [
                decoder_attention_mask,
                jnp.zeros((decoder_attention_mask.shape[0], max_decoder_length - decoder_attention_mask.shape[1])   ),
            ]    ,	axis=-1    ,	)

        UpperCamelCase       						=      model.init_cache(decoder_input_ids.shape[0]    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      jnp.broadcast_to(
            jnp.arange(decoder_input_ids.shape[-1] - 1   )[None, :]    ,	(decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)    ,	)

        UpperCamelCase       						=      model.decode(
            decoder_input_ids[:, :-1]    ,	_SCREAMING_SNAKE_CASE    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE    ,	past_key_values=_SCREAMING_SNAKE_CASE    ,	decoder_position_ids=_SCREAMING_SNAKE_CASE    ,	)
        UpperCamelCase       						=      jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]    ,	dtype="""i4"""   )
        UpperCamelCase       						=      model.decode(
            decoder_input_ids[:, -1:]    ,	_SCREAMING_SNAKE_CASE    ,	past_key_values=outputs_cache.past_key_values    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE    ,	decoder_position_ids=_SCREAMING_SNAKE_CASE    ,	)

        UpperCamelCase       						=      model.decode(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE   )

        UpperCamelCase       						=      np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])   )   )
        self.parent.assertTrue(diff < 1e-3    ,	msg=F"Max diff is {diff}"   )







def 					lowercase__				(   __UpperCamelCase	,		__UpperCamelCase	,		__UpperCamelCase	,		__UpperCamelCase=None	,		__UpperCamelCase=None	,		)->				Tuple:
      if attention_mask is None:
            UpperCamelCase       						=      np.not_equal(__UpperCamelCase	,		config.pad_token_id					).astype(np.inta					)
      if decoder_attention_mask is None:
            UpperCamelCase       						=      np.concatenate(
                [
                    np.ones(decoder_input_ids[:, :1].shape	,		dtype=np.inta					),
                    np.not_equal(decoder_input_ids[:, 1:]	,		config.pad_token_id					).astype(np.inta					),
                ]	,		axis=-1	,		)
      return {
          "input_ids": input_ids,
          "decoder_input_ids": decoder_input_ids,
          "attention_mask": attention_mask,
          "decoder_attention_mask": decoder_attention_mask,
      }






@require_flax
class        a_		(    lowerCamelCase			, unittest.TestCase       ):
  lowercase  	=   (
      (
          FlaxPegasusForConditionalGeneration,
          FlaxPegasusModel,
      )
      if is_flax_available()
      else ()
  )
  lowercase  	=   (FlaxPegasusForConditionalGeneration,) if is_flax_available() else ()
  lowercase  	=   True
  lowercase  	=   False
  lowercase  	=   False
  lowercase  	=   False

  def 						A__		(   self   )						->   List[Any]:



        """simple docstring"""






        UpperCamelCase       						=      FlaxPegasusModelTester(self   )
        UpperCamelCase       						=      ConfigTester(self    ,	config_class=_SCREAMING_SNAKE_CASE   )

  def 						A__		(   self   )						->   Dict:



        """simple docstring"""






        self.config_tester.run_common_tests()

  def 						A__		(   self   )						->   Tuple:



        """simple docstring"""






        UpperCamelCase						,UpperCamelCase       						=      self.model_tester.prepare_config_and_inputs_for_common()
        for model_class in self.all_model_classes:
              self.model_tester.check_use_cache_forward(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )

  def 						A__		(   self   )						->   str:



        """simple docstring"""






        UpperCamelCase						,UpperCamelCase       						=      self.model_tester.prepare_config_and_inputs_for_common()
        for model_class in self.all_model_classes:
              self.model_tester.check_use_cache_forward_with_attn_mask(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )

  def 						A__		(   self   )						->   Optional[int]:



        """simple docstring"""






        UpperCamelCase						,UpperCamelCase       						=      self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
              with self.subTest(model_class.__name__   ):
                    UpperCamelCase       						=      self._prepare_for_class(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )
                    UpperCamelCase       						=      model_class(_SCREAMING_SNAKE_CASE   )

                    @jax.jit
                    def encode_jitted(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE=None    ,	**_SCREAMING_SNAKE_CASE   ):
                          return model.encode(input_ids=_SCREAMING_SNAKE_CASE    ,	attention_mask=_SCREAMING_SNAKE_CASE   )

                    with self.subTest("""JIT Enabled"""   ):
                          UpperCamelCase       						=      encode_jitted(**_SCREAMING_SNAKE_CASE   ).to_tuple()

                    with self.subTest("""JIT Disabled"""   ):
                          with jax.disable_jit():
                                UpperCamelCase       						=      encode_jitted(**_SCREAMING_SNAKE_CASE   ).to_tuple()

                    self.assertEqual(len(_SCREAMING_SNAKE_CASE   )    ,	len(_SCREAMING_SNAKE_CASE   )   )
                    for jitted_output, output in zip(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ):
                          self.assertEqual(jitted_output.shape    ,	output.shape   )

  def 						A__		(   self   )						->   Optional[int]:



        """simple docstring"""






        UpperCamelCase						,UpperCamelCase       						=      self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
              with self.subTest(model_class.__name__   ):
                    UpperCamelCase       						=      model_class(_SCREAMING_SNAKE_CASE   )
                    UpperCamelCase       						=      model.encode(inputs_dict["""input_ids"""]    ,	inputs_dict["""attention_mask"""]   )

                    UpperCamelCase       						=      {
                        """decoder_input_ids""": inputs_dict["""decoder_input_ids"""],
                        """decoder_attention_mask""": inputs_dict["""decoder_attention_mask"""],
                        """encoder_outputs""": encoder_outputs,
                    }

                    @jax.jit
                    def decode_jitted(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ):
                          return model.decode(
                              decoder_input_ids=_SCREAMING_SNAKE_CASE    ,	decoder_attention_mask=_SCREAMING_SNAKE_CASE    ,	encoder_outputs=_SCREAMING_SNAKE_CASE    ,	)

                    with self.subTest("""JIT Enabled"""   ):
                          UpperCamelCase       						=      decode_jitted(**_SCREAMING_SNAKE_CASE   ).to_tuple()

                    with self.subTest("""JIT Disabled"""   ):
                          with jax.disable_jit():
                                UpperCamelCase       						=      decode_jitted(**_SCREAMING_SNAKE_CASE   ).to_tuple()

                    self.assertEqual(len(_SCREAMING_SNAKE_CASE   )    ,	len(_SCREAMING_SNAKE_CASE   )   )
                    for jitted_output, output in zip(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ):
                          self.assertEqual(jitted_output.shape    ,	output.shape   )

  @slow
  def 						A__		(   self   )						->   Union[str, Any]:



        """simple docstring"""






        for model_class_name in self.all_model_classes:
              UpperCamelCase       						=      model_class_name.from_pretrained("""google/pegasus-large"""    ,	from_pt=_SCREAMING_SNAKE_CASE   )
              UpperCamelCase       						=      np.ones((1, 1)   )
              UpperCamelCase       						=      model(_SCREAMING_SNAKE_CASE   )
              self.assertIsNotNone(_SCREAMING_SNAKE_CASE   )


  @slow
  def 						A__		(   self   )						->   str:



        """simple docstring"""






        UpperCamelCase       						=      FlaxPegasusForConditionalGeneration.from_pretrained("""google/pegasus-xsum"""   )
        UpperCamelCase       						=      PegasusTokenizer.from_pretrained("""google/pegasus-xsum"""   )

        UpperCamelCase       						=      [
            """ PG&E stated it scheduled the blackouts in response to forecasts for high winds amid dry conditions. The aim is to reduce the risk of wildfires. Nearly 800 thousand customers were scheduled to be affected by the shutoffs which were expected to last through at least midday tomorrow.""",
            """ The London trio are up for best UK act and best album, as well as getting two nominations in the best song category.\"We got told like this morning 'Oh I think you're nominated'\", said Dappy.\"And I was like 'Oh yeah, which one?' And now we've got nominated for four awards. I mean, wow!\"Bandmate Fazer added: \"We thought it's best of us to come down and mingle with everyone and say hello to the cameras. And now we find we've got four nominations.\"The band have two shots at the best song prize, getting the nod for their Tynchy Stryder collaboration Number One, and single Strong Again.Their album Uncle B will also go up against records by the likes of Beyonce and Kanye West.N-Dubz picked up the best newcomer Mobo in 2007, but female member Tulisa said they wouldn't be too disappointed if they didn't win this time around.\"At the end of the day we're grateful to be where we are in our careers.\"If it don't happen then it don't happen - live to fight another day and keep on making albums and hits for the fans.\"Dappy also revealed they could be performing live several times on the night.The group will be doing Number One and also a possible rendition of the War Child single, I Got Soul.The charity song is a  re-working of The Killers' All These Things That I've Done and is set to feature artists like Chipmunk, Ironik and Pixie Lott.This year's Mobos will be held outside of London for the first time, in Glasgow on 30 September.N-Dubz said they were looking forward to performing for their Scottish fans and boasted about their recent shows north of the border.\"We just done Edinburgh the other day,\" said Dappy.\"We smashed up an N-Dubz show over there. We done Aberdeen about three or four months ago - we smashed up that show over there! Everywhere we go we smash it up!\" """,
        ]

        UpperCamelCase       						=      [
            """California's largest electricity provider has turned off power to hundreds of thousands of customers.""",
            """Pop group N-Dubz have revealed they were surprised to get four nominations for this year's Mobo Awards.""",
        ]

        UpperCamelCase       						=      tokenizer(_SCREAMING_SNAKE_CASE    ,	return_tensors="""np"""    ,	truncation=_SCREAMING_SNAKE_CASE    ,	max_length=512    ,	padding=_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      model.generate(**_SCREAMING_SNAKE_CASE    ,	num_beams=2   ).sequences
        UpperCamelCase       						=      tokenizer.batch_decode(_SCREAMING_SNAKE_CASE    ,	skip_special_tokens=_SCREAMING_SNAKE_CASE   )
        assert tgt_text == decoded








'''simple docstring'''

from math import sqrt







def 					lowercase__				(   __UpperCamelCase					)->				int:
      UpperCamelCase       						=      0
      for i in range(1	,		int(sqrt(__UpperCamelCase					) + 1					)					):
            if n % i == 0 and i != sqrt(__UpperCamelCase					):
                  total += i + n // i
            elif i == sqrt(__UpperCamelCase					):
                  total += i
      return total - n







def 					lowercase__				(   __UpperCamelCase = 10000					)->				int:
      UpperCamelCase       						=      sum(
          i
          for i in range(1	,		__UpperCamelCase					)
          if sum_of_divisors(sum_of_divisors(__UpperCamelCase					)					) == i and sum_of_divisors(__UpperCamelCase					) != i					)
      return total


if __name__ == "__main__":
     print(solution(int(str(input()).strip())))
