






import tempfile
import unittest

import numpy as np

import transformers
from transformers import GPTaConfig, GPTaTokenizer, is_flax_available, is_torch_available
from transformers.testing_utils import is_pt_flax_cross_test, require_flax, slow

from ...generation.test_flax_utils import FlaxGenerationTesterMixin
from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
  import jax
  import jax.numpy as jnp

  from transformers.modeling_flax_pytorch_utils import (
      convert_pytorch_state_dict_to_flax,
      load_flax_weights_in_pytorch_model,
  )
  from transformers.models.gpta.modeling_flax_gpta import FlaxGPTaLMHeadModel, FlaxGPTaModel

if is_torch_available():
  import torch






class 							A_				:


     def __init__(							self    :	Dict    ,						UpperCAmelCase    :	Optional[int]    ,						UpperCAmelCase    :	Dict=1_4    ,						UpperCAmelCase    :	str=7    ,						UpperCAmelCase    :	Tuple=True    ,						UpperCAmelCase    :	Dict=True    ,						UpperCAmelCase    :	Dict=False    ,						UpperCAmelCase    :	Tuple=True    ,						UpperCAmelCase    :	Dict=9_9    ,						UpperCAmelCase    :	List[Any]=3_2    ,						UpperCAmelCase    :	Tuple=5    ,						UpperCAmelCase    :	int=4    ,						UpperCAmelCase    :	Optional[int]=3_7    ,						UpperCAmelCase    :	str="gelu"    ,						UpperCAmelCase    :	List[str]=0.1    ,						UpperCAmelCase    :	Any=0.1    ,						UpperCAmelCase    :	List[str]=5_1_2    ,						UpperCAmelCase    :	Any=0.02    ,						)							->			Tuple:
      __lowerCAmelCase:     Union[str, Any]     			=   parent
      __lowerCAmelCase:     Optional[int]     			=   batch_size
      __lowerCAmelCase:     List[Any]     			=   seq_length
      __lowerCAmelCase:     Dict     			=   is_training
      __lowerCAmelCase:     Optional[Any]     			=   use_input_mask
      __lowerCAmelCase:     Tuple     			=   use_token_type_ids
      __lowerCAmelCase:     Optional[int]     			=   use_labels
      __lowerCAmelCase:     Optional[Any]     			=   vocab_size
      __lowerCAmelCase:     Dict     			=   hidden_size
      __lowerCAmelCase:     str     			=   num_hidden_layers
      __lowerCAmelCase:     Union[str, Any]     			=   num_attention_heads
      __lowerCAmelCase:     List[Any]     			=   intermediate_size
      __lowerCAmelCase:     Optional[int]     			=   hidden_act
      __lowerCAmelCase:     Optional[Any]     			=   hidden_dropout_prob
      __lowerCAmelCase:     Union[str, Any]     			=   attention_probs_dropout_prob
      __lowerCAmelCase:     Any     			=   max_position_embeddings
      __lowerCAmelCase:     Dict     			=   initializer_range
      __lowerCAmelCase:     Tuple     			=   None
      __lowerCAmelCase:     Union[str, Any]     			=   vocab_size - 1
      __lowerCAmelCase:     List[Any]     			=   vocab_size - 1
      __lowerCAmelCase:     str     			=   vocab_size - 1


     def 						UpperCAmelCase						(							self    :	Dict      )							->			List[Any]:
      __lowerCAmelCase:     Union[str, Any]     			=   ids_tensor([self.batch_size, self.seq_length]    ,						self.vocab_size      )

      __lowerCAmelCase:     Optional[Any]     			=   None
      if self.use_input_mask:
       __lowerCAmelCase:     Tuple     			=   random_attention_mask([self.batch_size, self.seq_length]      )

      __lowerCAmelCase:     Optional[int]     			=   GPTaConfig(
          vocab_size=self.vocab_size    ,						n_embd=self.hidden_size    ,						n_layer=self.num_hidden_layers    ,						n_head=self.num_attention_heads    ,						n_positions=self.max_position_embeddings    ,						use_cache=UpperCAmelCase    ,						bos_token_id=self.bos_token_id    ,						eos_token_id=self.eos_token_id    ,						pad_token_id=self.pad_token_id    ,						)

      return (config, input_ids, input_mask)


     def 						UpperCAmelCase						(							self    :	Optional[int]      )							->			Tuple:
      __lowerCAmelCase:     str     			=   self.prepare_config_and_inputs()
      __lowerCAmelCase:     List[Any]     			=   config_and_inputs
      __lowerCAmelCase:     int     			=   {'input_ids': input_ids, 'attention_mask': attention_mask}
      return config, inputs_dict


     def 						UpperCAmelCase						(							self    :	Optional[Any]      )							->			Optional[int]:
      __lowerCAmelCase:     List[str]     			=   self.prepare_config_and_inputs()

      __lowerCAmelCase:     int     			=   floats_tensor([self.batch_size, self.seq_length, self.hidden_size]      )
      __lowerCAmelCase:     str     			=   ids_tensor([self.batch_size, self.seq_length]    ,						vocab_size=2      )

      return (
          config,
          input_ids,
          attention_mask,
          encoder_hidden_states,
          encoder_attention_mask,
      )


     def 						UpperCAmelCase						(							self    :	List[Any]    ,						UpperCAmelCase    :	Tuple    ,						UpperCAmelCase    :	Tuple    ,						UpperCAmelCase    :	List[str]    ,						UpperCAmelCase    :	Optional[Any]      )							->			Any:
      __lowerCAmelCase:     Dict     			=   2_0
      __lowerCAmelCase:     Tuple     			=   model_class_name(UpperCAmelCase      )

      __lowerCAmelCase:     Dict     			=   model.init_cache(input_ids.shape[0]    ,						UpperCAmelCase      )
      __lowerCAmelCase:     Optional[Any]     			=   jnp.ones((input_ids.shape[0], max_decoder_length)    ,						dtype='i4'      )

      __lowerCAmelCase:     Union[str, Any]     			=   jnp.broadcast_to(
          jnp.arange(input_ids.shape[-1] - 1      )[None, :]    ,						(input_ids.shape[0], input_ids.shape[-1] - 1)      )
      __lowerCAmelCase:     int     			=   model(
          input_ids[:, :-1]    ,						attention_mask=UpperCAmelCase    ,						past_key_values=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						)

      __lowerCAmelCase:     Tuple     			=   jnp.array(input_ids.shape[0] * [[input_ids.shape[-1] - 1]]    ,						dtype='i4'      )
      __lowerCAmelCase:     Any     			=   model(
          input_ids[:, -1:]    ,						attention_mask=UpperCAmelCase    ,						past_key_values=outputs_cache.past_key_values    ,						position_ids=UpperCAmelCase    ,						)

      __lowerCAmelCase:     int     			=   model(UpperCAmelCase      )

      __lowerCAmelCase:     Optional[Any]     			=   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 						UpperCAmelCase						(							self    :	List[str]    ,						UpperCAmelCase    :	Union[str, Any]    ,						UpperCAmelCase    :	List[str]    ,						UpperCAmelCase    :	Tuple    ,						UpperCAmelCase    :	Any      )							->			Union[str, Any]:
      __lowerCAmelCase:     str     			=   2_0
      __lowerCAmelCase:     Any     			=   model_class_name(UpperCAmelCase      )

      __lowerCAmelCase:     List[Any]     			=   jnp.concatenate(
          [attention_mask, jnp.zeros((attention_mask.shape[0], max_decoder_length - attention_mask.shape[1])      )]    ,						axis=-1    ,						)

      __lowerCAmelCase:     List[Any]     			=   model.init_cache(input_ids.shape[0]    ,						UpperCAmelCase      )
      __lowerCAmelCase:     str     			=   jnp.broadcast_to(
          jnp.arange(input_ids.shape[-1] - 1      )[None, :]    ,						(input_ids.shape[0], input_ids.shape[-1] - 1)      )

      __lowerCAmelCase:     Union[str, Any]     			=   model(
          input_ids[:, :-1]    ,						attention_mask=UpperCAmelCase    ,						past_key_values=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						)
      __lowerCAmelCase:     Tuple     			=   jnp.array(input_ids.shape[0] * [[input_ids.shape[-1] - 1]]    ,						dtype='i4'      )
      __lowerCAmelCase:     List[Any]     			=   model(
          input_ids[:, -1:]    ,						past_key_values=outputs_cache.past_key_values    ,						attention_mask=UpperCAmelCase    ,						position_ids=UpperCAmelCase    ,						)

      __lowerCAmelCase:     List[Any]     			=   model(UpperCAmelCase    ,						attention_mask=UpperCAmelCase      )

      __lowerCAmelCase:     Dict     			=   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}'''      )







@require_flax
class 							A_				(	snake_case__							,			snake_case__							,			unittest.TestCase      ):
     _lowercase    :  str          =			(FlaxGPTaModel, FlaxGPTaLMHeadModel) if is_flax_available() else ()
     _lowercase    :  Optional[Any]          =			(FlaxGPTaLMHeadModel,) if is_flax_available() else ()


     def 						UpperCAmelCase						(							self    :	int      )							->			Optional[Any]:
      __lowerCAmelCase:     Dict     			=   FlaxGPTaModelTester(self      )


     def 						UpperCAmelCase						(							self    :	Union[str, Any]      )							->			Dict:
      for model_class_name in self.all_model_classes:
       __lowerCAmelCase:     int     			=   self.model_tester.prepare_config_and_inputs()
       self.model_tester.check_use_cache_forward(UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase      )


     def 						UpperCAmelCase						(							self    :	Union[str, Any]      )							->			Dict:
      for model_class_name in self.all_model_classes:
       __lowerCAmelCase:     Union[str, Any]     			=   self.model_tester.prepare_config_and_inputs()
       self.model_tester.check_use_cache_forward_with_attn_mask(
           UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase      )


     @slow
     def 						UpperCAmelCase						(							self    :	Any      )							->			Dict:
      __lowerCAmelCase:     Dict     			=   GPTaTokenizer.from_pretrained('gpt2'    ,						pad_token='</s>'    ,						padding_side='left'      )
      __lowerCAmelCase:     Dict     			=   tokenizer(['Hello this is a long string', 'Hey']    ,						return_tensors='np'    ,						padding=UpperCAmelCase    ,						truncation=UpperCAmelCase      )

      __lowerCAmelCase:     Dict     			=   FlaxGPTaLMHeadModel.from_pretrained('gpt2'      )
      __lowerCAmelCase:     int     			=   False
      __lowerCAmelCase:     Dict     			=   model.config.eos_token_id

      __lowerCAmelCase:     Tuple     			=   jax.jit(model.generate      )

      __lowerCAmelCase:     Tuple     			=   jit_generate(inputs['input_ids']    ,						attention_mask=inputs['attention_mask']      ).sequences

      __lowerCAmelCase:     int     			=   tokenizer.batch_decode(UpperCAmelCase    ,						skip_special_tokens=UpperCAmelCase      )

      __lowerCAmelCase:     str     			=   [
          'Hello this is a long string of words. I\'m going to start with the first one.\n',
          'Hey, I\'m not sure if I\'m going to be able to do',
      ]

      self.assertListEqual(UpperCAmelCase    ,						UpperCAmelCase      )


     @is_pt_flax_cross_test
     def 						UpperCAmelCase						(							self    :	Dict      )							->			Union[str, Any]:
      __lowerCAmelCase:     List[str]     			=   self.model_tester.prepare_config_and_inputs_for_common()

      for model_class in self.all_model_classes:
       with self.subTest(model_class.__name__      ):
        # prepare inputs
        __lowerCAmelCase:     Any     			=   self._prepare_for_class(UpperCAmelCase    ,						UpperCAmelCase      )
        __lowerCAmelCase:     List[str]     			=   {k: torch.tensor(v.tolist()      ) for k, v in prepared_inputs_dict.items()}

        # load corresponding PyTorch class
        __lowerCAmelCase:     Optional[Any]     			=   model_class.__name__[4:]  # Skip the "Flax" at the beginning
        __lowerCAmelCase:     Union[str, Any]     			=   getattr(UpperCAmelCase    ,						UpperCAmelCase      )

        __lowerCAmelCase:     Union[str, Any]     			=   pt_inputs['input_ids'].shape
        __lowerCAmelCase:     Optional[int]     			=   np.random.randint(0    ,						seq_length - 1    ,						size=(batch_size,)      )
        for batch_idx, start_index in enumerate(UpperCAmelCase      ):
         __lowerCAmelCase:     Dict     			=   0
         __lowerCAmelCase:     List[Any]     			=   1
         __lowerCAmelCase:     int     			=   0
         __lowerCAmelCase:     List[Any]     			=   1
        __lowerCAmelCase:     List[Any]     			=   pt_model_class(UpperCAmelCase      ).eval()
        __lowerCAmelCase:     int     			=   model_class(UpperCAmelCase    ,						dtype=jnp.floataa      )

        __lowerCAmelCase:     Union[str, Any]     			=   convert_pytorch_state_dict_to_flax(pt_model.state_dict()    ,						UpperCAmelCase      )
        __lowerCAmelCase:     Any     			=   fx_state

        with torch.no_grad():
         __lowerCAmelCase:     List[str]     			=   pt_model(**UpperCAmelCase      ).to_tuple()

        __lowerCAmelCase:     Dict     			=   fx_model(**UpperCAmelCase      ).to_tuple()
        self.assertEqual(len(UpperCAmelCase      )    ,						len(UpperCAmelCase      )    ,						'Output lengths differ between Flax and PyTorch'      )
        for fx_output, pt_output in zip(UpperCAmelCase    ,						UpperCAmelCase      ):
         self.assert_almost_equals(fx_output[:, -1]    ,						pt_output[:, -1].numpy()    ,						4E-2      )

        with tempfile.TemporaryDirectory() as tmpdirname:
         pt_model.save_pretrained(UpperCAmelCase      )
         __lowerCAmelCase:     List[Any]     			=   model_class.from_pretrained(UpperCAmelCase    ,						from_pt=UpperCAmelCase      )

        __lowerCAmelCase:     Optional[Any]     			=   fx_model_loaded(**UpperCAmelCase      ).to_tuple()
        self.assertEqual(
            len(UpperCAmelCase      )    ,						len(UpperCAmelCase      )    ,						'Output lengths differ between Flax and PyTorch'      )
        for fx_output_loaded, pt_output in zip(UpperCAmelCase    ,						UpperCAmelCase      ):
         self.assert_almost_equals(fx_output_loaded[:, -1]    ,						pt_output[:, -1].numpy()    ,						4E-2      )


     @is_pt_flax_cross_test
     def 						UpperCAmelCase						(							self    :	Dict      )							->			str:
      __lowerCAmelCase:     Any     			=   self.model_tester.prepare_config_and_inputs_for_common()
      for model_class in self.all_model_classes:
       with self.subTest(model_class.__name__      ):
        # prepare inputs
        __lowerCAmelCase:     int     			=   self._prepare_for_class(UpperCAmelCase    ,						UpperCAmelCase      )
        __lowerCAmelCase:     Any     			=   {k: torch.tensor(v.tolist()      ) for k, v in prepared_inputs_dict.items()}

        # load corresponding PyTorch class
        __lowerCAmelCase:     Any     			=   model_class.__name__[4:]  # Skip the "Flax" at the beginning
        __lowerCAmelCase:     Dict     			=   getattr(UpperCAmelCase    ,						UpperCAmelCase      )

        __lowerCAmelCase:     Dict     			=   pt_model_class(UpperCAmelCase      ).eval()
        __lowerCAmelCase:     str     			=   model_class(UpperCAmelCase    ,						dtype=jnp.floataa      )

        __lowerCAmelCase:     Union[str, Any]     			=   load_flax_weights_in_pytorch_model(UpperCAmelCase    ,						fx_model.params      )
        __lowerCAmelCase:     Optional[int]     			=   pt_inputs['input_ids'].shape
        __lowerCAmelCase:     Dict     			=   np.random.randint(0    ,						seq_length - 1    ,						size=(batch_size,)      )
        for batch_idx, start_index in enumerate(UpperCAmelCase      ):
         __lowerCAmelCase:     List[str]     			=   0
         __lowerCAmelCase:     Union[str, Any]     			=   1
         __lowerCAmelCase:     Tuple     			=   0
         __lowerCAmelCase:     Optional[int]     			=   1

        # make sure weights are tied in PyTorch
        pt_model.tie_weights()

        with torch.no_grad():
         __lowerCAmelCase:     Dict     			=   pt_model(**UpperCAmelCase      ).to_tuple()

        __lowerCAmelCase:     Union[str, Any]     			=   fx_model(**UpperCAmelCase      ).to_tuple()
        self.assertEqual(len(UpperCAmelCase      )    ,						len(UpperCAmelCase      )    ,						'Output lengths differ between Flax and PyTorch'      )
        for fx_output, pt_output in zip(UpperCAmelCase    ,						UpperCAmelCase      ):
         self.assert_almost_equals(fx_output[:, -1]    ,						pt_output[:, -1].numpy()    ,						4E-2      )

        with tempfile.TemporaryDirectory() as tmpdirname:
         fx_model.save_pretrained(UpperCAmelCase      )
         __lowerCAmelCase:     Tuple     			=   pt_model_class.from_pretrained(UpperCAmelCase    ,						from_flax=UpperCAmelCase      )

        with torch.no_grad():
         __lowerCAmelCase:     List[str]     			=   pt_model_loaded(**UpperCAmelCase      ).to_tuple()

        self.assertEqual(
            len(UpperCAmelCase      )    ,						len(UpperCAmelCase      )    ,						'Output lengths differ between Flax and PyTorch'      )
        for fx_output, pt_output in zip(UpperCAmelCase    ,						UpperCAmelCase      ):
         self.assert_almost_equals(fx_output[:, -1]    ,						pt_output[:, -1].numpy()    ,						4E-2      )


     @slow
     def 						UpperCAmelCase						(							self    :	Optional[int]      )							->			Optional[int]:
      for model_class_name in self.all_model_classes:
       __lowerCAmelCase:     int     			=   model_class_name.from_pretrained('gpt2'    ,						from_pt=UpperCAmelCase      )
       __lowerCAmelCase:     Optional[Any]     			=   model(np.ones((1, 1)      )      )
       self.assertIsNotNone(UpperCAmelCase      )








from math import floor, sqrt







def _a				( SCREAMING_SNAKE_CASE	:    int	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0.0
 __lowerCAmelCase:     Any     			=   1.0
 __lowerCAmelCase:     List[str]     			=   int(sqrt(SCREAMING_SNAKE_CASE	)	)
 __lowerCAmelCase:     Union[str, Any]     			=   root
 __lowerCAmelCase:     List[str]     			=   0
 while integer_part != 2 * root:
  __lowerCAmelCase:     List[str]     			=   denominator * integer_part - numerator
  __lowerCAmelCase:     Optional[int]     			=   (n - numerator**2) / denominator
  __lowerCAmelCase:     Union[str, Any]     			=   int((root + numerator) / denominator	)
  period += 1
 return period







def _a				( SCREAMING_SNAKE_CASE	:    int = 1_00_00	)					->					int:

 """simple docstring"""






 __lowerCAmelCase:     Optional[int]     			=   0
 for i in range(2					,      n + 1	):
  __lowerCAmelCase:     List[str]     			=   sqrt(SCREAMING_SNAKE_CASE	)
  if sr - floor(SCREAMING_SNAKE_CASE	) != 0 and continuous_fraction_period(SCREAMING_SNAKE_CASE	) % 2 == 1:
   count_odd_periods += 1
 return count_odd_periods


if __name__ == "__main__":
  print(f"{solution(int(input().strip()))}")





