code: 
  
  import math
  from decimal import Decimal, getcontext
  
  
  def       __a       (   SCREAMING_SNAKE_CASE = 4_0_0_0_0_0_0      )      ->     int:
  
  
  
  
  
  
      '''simple docstring'''
  
      try:
          __UpperCAmelCase									=			int(SCREAMING_SNAKE_CASE      )
      except (TypeError, ValueError):
          raise TypeError('''Parameter n must be int or castable to int.'''      )
      if n <= 0:
          raise ValueError('''Parameter n must be greater than or equal to one.'''      )
      __UpperCAmelCase									=			1_0_0
      __UpperCAmelCase									=			(Decimal(5      ) ** Decimal(0.5      ) + 1) / Decimal(2      )
  
      __UpperCAmelCase									=			(math.floor(math.log(n * (phi + 2)       ,   SCREAMING_SNAKE_CASE      ) - 1      ) // 3) * 3 + 2
      __UpperCAmelCase									=			Decimal(round(phi ** Decimal(index + 1      )      )      ) / (phi + 2)
      __UpperCAmelCase									=			num // 2
      return int(SCREAMING_SNAKE_CASE      )
  
  
  if __name__ == "__main__":
         print(F"""{solution() = }""")
  
  
  
  
  
style_context: 
  
  from __future__ import annotations
  
  import unittest
  
  from transformers import is_tf_available
  from transformers.testing_utils import require_tf, slow
  
  from ...test_configuration_common import ConfigTester
  from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
  from ...test_pipeline_mixin import PipelineTesterMixin
  
  
  if is_tf_available():
         import tensorflow as tf
  
         from transformers import (
             TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST,
             TFXLMForMultipleChoice,
             TFXLMForQuestionAnsweringSimple,
             TFXLMForSequenceClassification,
             TFXLMForTokenClassification,
             TFXLMModel,
             TFXLMWithLMHeadModel,
             XLMConfig,
         )
  class 					A_   :
  
  
      '''simple docstring'''
  
  
  
  
  
  
      def __init__(self     ,      lowercase__     ,      )     ->      Tuple:
          __UpperCAmelCase									=			parent
          __UpperCAmelCase									=			13
          __UpperCAmelCase									=			7
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			False
          __UpperCAmelCase									=			False
          __UpperCAmelCase									=			False
          __UpperCAmelCase									=			2
          __UpperCAmelCase									=			99
          __UpperCAmelCase									=			0
          __UpperCAmelCase									=			32
          __UpperCAmelCase									=			2
          __UpperCAmelCase									=			4
          __UpperCAmelCase									=			0.1
          __UpperCAmelCase									=			0.1
          __UpperCAmelCase									=			512
          __UpperCAmelCase									=			16
          __UpperCAmelCase									=			2
          __UpperCAmelCase									=			0.02
          __UpperCAmelCase									=			3
          __UpperCAmelCase									=			4
          __UpperCAmelCase									=			'''last'''
          __UpperCAmelCase									=			True
          __UpperCAmelCase									=			None
          __UpperCAmelCase									=			0
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[Any]:
          __UpperCAmelCase									=			ids_tensor([self.batch_size, self.seq_length]     ,      self.vocab_size  )
          __UpperCAmelCase									=			random_attention_mask([self.batch_size, self.seq_length]     ,      dtype=tf.floataa  )
  
          __UpperCAmelCase									=			None
          if self.use_input_lengths:
              __UpperCAmelCase									=			(
                  ids_tensor([self.batch_size]     ,      vocab_size=2  ) + self.seq_length - 2
              )  # small variation of seq_length
  
          __UpperCAmelCase									=			None
          if self.use_token_type_ids:
              __UpperCAmelCase									=			ids_tensor([self.batch_size, self.seq_length]     ,      self.n_langs  )
  
          __UpperCAmelCase									=			None
          __UpperCAmelCase									=			None
          __UpperCAmelCase									=			None
          if self.use_labels:
              __UpperCAmelCase									=			ids_tensor([self.batch_size]     ,      self.type_sequence_label_size  )
              __UpperCAmelCase									=			ids_tensor([self.batch_size, self.seq_length]     ,      self.num_labels  )
              __UpperCAmelCase									=			ids_tensor([self.batch_size]     ,      2     ,      dtype=tf.floataa  )
              __UpperCAmelCase									=			ids_tensor([self.batch_size]     ,      self.num_choices  )
  
          __UpperCAmelCase									=			XLMConfig(
              vocab_size=self.vocab_size     ,      n_special=self.n_special     ,      emb_dim=self.hidden_size     ,      n_layers=self.num_hidden_layers     ,      n_heads=self.num_attention_heads     ,      dropout=self.hidden_dropout_prob     ,      attention_dropout=self.attention_probs_dropout_prob     ,      gelu_activation=self.gelu_activation     ,      sinusoidal_embeddings=self.sinusoidal_embeddings     ,      asm=self.asm     ,      causal=self.causal     ,      n_langs=self.n_langs     ,      max_position_embeddings=self.max_position_embeddings     ,      initializer_range=self.initializer_range     ,      summary_type=self.summary_type     ,      use_proj=self.use_proj     ,      bos_token_id=self.bos_token_id     ,      )
  
          return (
              config,
              input_ids,
              token_type_ids,
              input_lengths,
              sequence_labels,
              token_labels,
              is_impossible_labels,
              choice_labels,
              input_mask,
          )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      List[Any]:
          __UpperCAmelCase									=			TFXLMModel(config=lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''lengths''': input_lengths, '''langs''': token_type_ids}
          __UpperCAmelCase									=			model(lowercase__  )
  
          __UpperCAmelCase									=			[input_ids, input_mask]
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.last_hidden_state.shape     ,      (self.batch_size, self.seq_length, self.hidden_size)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      List[str]:
          __UpperCAmelCase									=			TFXLMWithLMHeadModel(lowercase__  )
  
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''lengths''': input_lengths, '''langs''': token_type_ids}
          __UpperCAmelCase									=			model(lowercase__  )
  
          __UpperCAmelCase									=			outputs
  
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.seq_length, self.vocab_size)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      Optional[Any]:
          __UpperCAmelCase									=			TFXLMForQuestionAnsweringSimple(lowercase__  )
  
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''lengths''': input_lengths}
  
          __UpperCAmelCase									=			model(lowercase__  )
  
          self.parent.assertEqual(result.start_logits.shape     ,      (self.batch_size, self.seq_length)  )
          self.parent.assertEqual(result.end_logits.shape     ,      (self.batch_size, self.seq_length)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      Dict:
          __UpperCAmelCase									=			TFXLMForSequenceClassification(lowercase__  )
  
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''lengths''': input_lengths}
  
          __UpperCAmelCase									=			model(lowercase__  )
  
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.type_sequence_label_size)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      int:
          __UpperCAmelCase									=			self.num_labels
          __UpperCAmelCase									=			TFXLMForTokenClassification(config=lowercase__  )
          __UpperCAmelCase									=			{'''input_ids''': input_ids, '''attention_mask''': input_mask, '''token_type_ids''': token_type_ids}
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.seq_length, self.num_labels)  )
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      )     ->      Tuple:
          __UpperCAmelCase									=			self.num_choices
          __UpperCAmelCase									=			TFXLMForMultipleChoice(config=lowercase__  )
          __UpperCAmelCase									=			tf.tile(tf.expand_dims(lowercase__     ,      1  )     ,      (1, self.num_choices, 1)  )
          __UpperCAmelCase									=			tf.tile(tf.expand_dims(lowercase__     ,      1  )     ,      (1, self.num_choices, 1)  )
          __UpperCAmelCase									=			tf.tile(tf.expand_dims(lowercase__     ,      1  )     ,      (1, self.num_choices, 1)  )
          __UpperCAmelCase									=			{
              '''input_ids''': multiple_choice_inputs_ids,
              '''attention_mask''': multiple_choice_input_mask,
              '''token_type_ids''': multiple_choice_token_type_ids,
          }
          __UpperCAmelCase									=			model(lowercase__  )
          self.parent.assertEqual(result.logits.shape     ,      (self.batch_size, self.num_choices)  )
  
  
  
  
  
  
      def      lowerCAmelCase_						(self  )     ->      str:
          __UpperCAmelCase									=			self.prepare_config_and_inputs()
          (
              (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     (
              __UpperCAmelCase
          )					,     
          )									=			config_and_inputs
          __UpperCAmelCase									=			{
              '''input_ids''': input_ids,
              '''token_type_ids''': token_type_ids,
              '''langs''': token_type_ids,
              '''lengths''': input_lengths,
          }
          return config, inputs_dict
  
  
  
  
  
  
  @require_tf
  class 					A_   (      _a ,     _a ,     unittest.TestCase						):
  
  
      '''simple docstring'''
  
  
  
  
  
  
      a__     							=       (
          (
              TFXLMModel,
              TFXLMWithLMHeadModel,
              TFXLMForSequenceClassification,
              TFXLMForQuestionAnsweringSimple,
              TFXLMForTokenClassification,
              TFXLMForMultipleChoice,
          )
          if is_tf_available()
          else ()
      )
      a__     							=       (
          (TFXLMWithLMHeadModel,) if is_tf_available() else ()
      )  # TODO (PVP): Check other models whether language generation is also applicable
      a__     							=       (
          {
              "feature-extraction": TFXLMModel,
              "fill-mask": TFXLMWithLMHeadModel,
              "question-answering": TFXLMForQuestionAnsweringSimple,
              "text-classification": TFXLMForSequenceClassification,
              "text-generation": TFXLMWithLMHeadModel,
              "token-classification": TFXLMForTokenClassification,
              "zero-shot": TFXLMForSequenceClassification,
          }
          if is_tf_available()
          else {}
      )
      a__     							=       False
      a__     							=       False
  
  
      def      lowerCAmelCase_						(self     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__     ,      lowercase__  )     ->      Tuple:
          if (
              pipeline_test_casse_name == "QAPipelineTests"
              and tokenizer_name is not None
              and not tokenizer_name.endswith('''Fast'''  )
          ):
              # `QAPipelineTests` fails for a few models when the slower tokenizer are used.
              # (The slower tokenizers were never used for pipeline tests before the pipeline testing rework)
              # TODO: check (and possibly fix) the `QAPipelineTests` with slower tokenizer
              return True
  
          return False
  
  
      def      lowerCAmelCase_						(self  )     ->      Tuple:
          __UpperCAmelCase									=			TFXLMModelTester(self  )
          __UpperCAmelCase									=			ConfigTester(self     ,      config_class=lowercase__     ,      emb_dim=37  )
  
  
      def      lowerCAmelCase_						(self  )     ->      str:
          self.config_tester.run_common_tests()
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[int]:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_model(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Any:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_lm_head(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Dict:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_qa(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      int:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_sequence_classif(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Optional[Any]:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_for_token_classification(*lowercase__  )
  
  
      def      lowerCAmelCase_						(self  )     ->      Tuple:
          __UpperCAmelCase									=			self.model_tester.prepare_config_and_inputs()
          self.model_tester.create_and_check_xlm_for_multiple_choice(*lowercase__  )
  
  
  
  
  
  
      @slow
      def      lowerCAmelCase_						(self  )     ->      int:
          for model_name in TF_XLM_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
              __UpperCAmelCase									=			TFXLMModel.from_pretrained(lowercase__  )
              self.assertIsNotNone(lowercase__  )
  
  
  
  
  
  
  @require_tf
  class 					A_   (      unittest.TestCase						):
  
  
      '''simple docstring'''
  
  
  
  
  
  
      @slow
      def      lowerCAmelCase_						(self  )     ->      Tuple:
          __UpperCAmelCase									=			TFXLMWithLMHeadModel.from_pretrained('''xlm-mlm-en-2048'''  )
          __UpperCAmelCase									=			tf.convert_to_tensor([[14, 447]]     ,      dtype=tf.intaa  )  # the president
          __UpperCAmelCase									=			[
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
              14,
              447,
          ]  # the president the president the president the president the president the president the president the president the president the president
          # TODO(PVP): this and other input_ids I tried for generation give pretty bad results. Not sure why. Model might just not be made for auto-regressive inference
          __UpperCAmelCase									=			model.generate(lowercase__     ,      do_sample=lowercase__  )
          self.assertListEqual(output_ids[0].numpy().tolist()     ,      lowercase__  )
  
  
  
  
  