






"""simple docstring"""







def _a			(		_snake_case = 10**12							):







      """simple docstring"""






      UpperCAmelCase          =	1
      UpperCAmelCase          =	0

      UpperCAmelCase          =	1
      UpperCAmelCase          =	1

      while numerator <= 2 * min_total - 1:
            prev_numerator += 2 * numerator
            numerator += 2 * prev_numerator

            prev_denominator += 2 * denominator
            denominator += 2 * prev_denominator

      return (denominator + 1) // 2


if __name__ == "__main__":
  print(F"""{solution() = }""")











"""simple docstring"""







from pathlib import Path
from typing import List

from transformers import is_torch_available, is_vision_available
from transformers.testing_utils import get_tests_dir, is_tool_test
from transformers.tools.agent_types import AGENT_TYPE_MAPPING, AgentAudio, AgentImage, AgentText


if is_torch_available():
  import torch

if is_vision_available():
  from PIL import Image


_UpperCamelCase					      =  ["""text""", """image""", """audio"""]

def _a			(		_snake_case							):







      """simple docstring"""






      UpperCAmelCase          =	[]

      for input_type in input_types:
            if input_type == "text":
                  inputs.append("""Text input"""							)
            elif input_type == "image":
                  inputs.append(
                      Image.open(Path(get_tests_dir("""fixtures/tests_samples/COCO"""							)							) / """000000039769.png"""							).resize((512, 512)							)							)
            elif input_type == "audio":
                  inputs.append(torch.ones(3000							)							)
            elif isinstance(_snake_case				,	_snake_case							):
                  inputs.append(create_inputs(_snake_case							)							)
            else:
                  raise ValueError(F'''Invalid type requested: {input_type}'''							)

      return inputs

def _a			(		_snake_case							):







      """simple docstring"""






      UpperCAmelCase          =	[]

      for output in outputs:
            if isinstance(_snake_case				,	(str, AgentText)							):
                  output_types.append("""text"""							)
            elif isinstance(_snake_case				,	(Image.Image, AgentImage)							):
                  output_types.append("""image"""							)
            elif isinstance(_snake_case				,	(torch.Tensor, AgentAudio)							):
                  output_types.append("""audio"""							)
            else:
                  raise ValueError(F'''Invalid output: {output}'''							)

      return output_types







@is_tool_test
class  lowerCamelCase__ :






    def     _UpperCamelCase							(			self ):
          self.assertTrue(hasattr(self.tool     ,"""inputs""" ) )
          self.assertTrue(hasattr(self.tool     ,"""outputs""" ) )

          UpperCAmelCase          =	self.tool.inputs
          for _input in inputs:
                if isinstance(_input     ,A ):
                      for __input in _input:
                            self.assertTrue(__input in authorized_types )
                else:
                      self.assertTrue(_input in authorized_types )

          UpperCAmelCase          =	self.tool.outputs
          for _output in outputs:
                self.assertTrue(_output in authorized_types )






    def     _UpperCamelCase							(			self ):
          UpperCAmelCase          =	create_inputs(self.tool.inputs )
          UpperCAmelCase          =	self.tool(*A )

          # There is a single output
          if len(self.tool.outputs ) == 1:
                UpperCAmelCase          =	[outputs]

          self.assertListEqual(output_types(A )     ,self.tool.outputs )






    def     _UpperCamelCase							(			self ):
          self.assertTrue(hasattr(self.tool     ,"""description""" ) )
          self.assertTrue(hasattr(self.tool     ,"""default_checkpoint""" ) )
          self.assertTrue(self.tool.description.startswith("""This is a tool that""" ) )






    def     _UpperCamelCase							(			self ):
          UpperCAmelCase          =	create_inputs(self.tool.inputs )
          UpperCAmelCase          =	self.tool(*A )

          if not isinstance(A     ,A ):
                UpperCAmelCase          =	[outputs]

          self.assertEqual(len(A )     ,len(self.tool.outputs ) )

          for output, output_type in zip(A     ,self.tool.outputs ):
                UpperCAmelCase          =	AGENT_TYPE_MAPPING[output_type]
                self.assertTrue(isinstance(A     ,A ) )






    def     _UpperCamelCase							(			self ):
          UpperCAmelCase          =	create_inputs(self.tool.inputs )

          UpperCAmelCase          =	[]

          for _input, input_type in zip(A     ,self.tool.inputs ):
                if isinstance(A     ,A ):
                      _inputs.append([AGENT_TYPE_MAPPING[_input_type](_input ) for _input_type in input_type] )
                else:
                      _inputs.append(AGENT_TYPE_MAPPING[input_type](_input ) )

        # Should not raise an error
          UpperCAmelCase          =	self.tool(*A )

          if not isinstance(A     ,A ):
                UpperCAmelCase          =	[outputs]

          self.assertEqual(len(A )     ,len(self.tool.outputs ) )



