code: 
  
  
  
  
  """simple docstring"""
  
  from __future__ import annotations
  
  
  
  def   UpperCamelCase__     (		lowercase__  :     int   ):
  		snake_case		:						int								=				{1}
  		snake_case		:						Optional[Any]								=				[1]
  		for _ in range(2       ,     depth + 1   ):
  				snake_case		:						Optional[int]								=				[*previous_coefficients, 0]
  				snake_case		:						List[str]								=				[0, *previous_coefficients]
  				snake_case		:						Dict								=				[]
  				for x, y in zip(lowercase__       ,     lowercase__   ):
  						coefficients.add(x + y   )
  						previous_coefficients.append(x + y   )
  		return coefficients
  
  
  
  def   UpperCamelCase__     (		lowercase__  :     set[int]   ):
  		snake_case		:						Tuple								=				set()
  		for number in unique_coefficients:
  				snake_case		:						List[Any]								=				2
  				snake_case		:						Optional[Any]								=				number
  				while divisor**2 <= copy_number:
  						snake_case		:						Tuple								=				0
  						while copy_number % divisor == 0:
  								copy_number //= divisor
  								multiplicity += 1
  						if multiplicity >= 2:
  								non_squarefrees.add(lowercase__   )
  								break
  						divisor += 1
  
  		return unique_coefficients.difference(lowercase__   )
  
  
  
  def   UpperCamelCase__     (		lowercase__  :     int = 51   ):
  		snake_case		:						Union[str, Any]								=				get_pascal_triangle_unique_coefficients(lowercase__   )
  		snake_case		:						str								=				get_squarefrees(lowercase__   )
  		return sum(lowercase__   )
  
  
  if __name__ == "__main__":
  							print(f'{solution() = }')
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  import tempfile
  import unittest
  
  from diffusers import (
      DDIMScheduler,
      DDPMScheduler,
      DPMSolverMultistepScheduler,
      EulerAncestralDiscreteScheduler,
      EulerDiscreteScheduler,
      PNDMScheduler,
      logging,
  )
  from diffusers.configuration_utils import ConfigMixin, register_to_config
  from diffusers.utils.testing_utils import CaptureLogger
  class 			lowerCamelCase__    (  lowerCamelCase_			):
  			a__ :      int								=     """config.json"""
  
  
  			@register_to_config
  			def __init__(     self				, SCREAMING_SNAKE_CASE=2				, SCREAMING_SNAKE_CASE=5				, SCREAMING_SNAKE_CASE=(2, 5)				, SCREAMING_SNAKE_CASE="for diffusion"				, SCREAMING_SNAKE_CASE=[1, 3]				, ):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  class 			lowerCamelCase__    (  lowerCamelCase_			):
  			a__ :      Dict								=     """config.json"""
  
  
  			@register_to_config
  			def __init__(     self				, SCREAMING_SNAKE_CASE=2				, SCREAMING_SNAKE_CASE=5				, SCREAMING_SNAKE_CASE=(2, 5)				, SCREAMING_SNAKE_CASE="for diffusion"				, SCREAMING_SNAKE_CASE=[1, 3]				, ):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  class 			lowerCamelCase__    (  lowerCamelCase_			):
  			a__ :      Union[str, Any]								=     """config.json"""
  
  
  			@register_to_config
  			def __init__(     self				, SCREAMING_SNAKE_CASE=2				, SCREAMING_SNAKE_CASE=5				, SCREAMING_SNAKE_CASE=(2, 5)				, SCREAMING_SNAKE_CASE="for diffusion"				, SCREAMING_SNAKE_CASE=[1, 3]				, SCREAMING_SNAKE_CASE=[1, 3]				, ):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  class 			lowerCamelCase__    (  lowerCamelCase_			):
  			a__ :      Tuple								=     """config.json"""
  
  
  			@register_to_config
  			def __init__(     self				, SCREAMING_SNAKE_CASE=2				, SCREAMING_SNAKE_CASE=5				, SCREAMING_SNAKE_CASE=(2, 5)				, SCREAMING_SNAKE_CASE="for diffusion"				, SCREAMING_SNAKE_CASE=[1, 5]				, SCREAMING_SNAKE_CASE=[5, 4]				, ):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					pass
  
  
  
  
  
  
  
  class 			lowerCamelCase__    (  unittest.TestCase			):
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					with self.assertRaises(SCREAMING_SNAKE_CASE							):
  							ConfigMixin.load_config("dummy_path"							)
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Dict								=				SampleObject()
  					snake_case		:						Dict								=				obj.config
  					assert config["a"] == 2
  					assert config["b"] == 5
  					assert config["c"] == (2, 5)
  					assert config["d"] == "for diffusion"
  					assert config["e"] == [1, 3]
  
  					# init ignore private arguments
  					snake_case		:						Dict								=				SampleObject(_name_or_path="lalala"							)
  					snake_case		:						List[Any]								=				obj.config
  					assert config["a"] == 2
  					assert config["b"] == 5
  					assert config["c"] == (2, 5)
  					assert config["d"] == "for diffusion"
  					assert config["e"] == [1, 3]
  
  					# can override default
  					snake_case		:						str								=				SampleObject(c=6							)
  					snake_case		:						Any								=				obj.config
  					assert config["a"] == 2
  					assert config["b"] == 5
  					assert config["c"] == 6
  					assert config["d"] == "for diffusion"
  					assert config["e"] == [1, 3]
  
  					# can use positional arguments.
  					snake_case		:						int								=				SampleObject(1				, c=6							)
  					snake_case		:						Dict								=				obj.config
  					assert config["a"] == 1
  					assert config["b"] == 5
  					assert config["c"] == 6
  					assert config["d"] == "for diffusion"
  					assert config["e"] == [1, 3]
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						str								=				SampleObject()
  					snake_case		:						List[str]								=				obj.config
  
  					assert config["a"] == 2
  					assert config["b"] == 5
  					assert config["c"] == (2, 5)
  					assert config["d"] == "for diffusion"
  					assert config["e"] == [1, 3]
  
  					with tempfile.TemporaryDirectory() as tmpdirname:
  							obj.save_config(SCREAMING_SNAKE_CASE							)
  							snake_case		:						Union[str, Any]								=				SampleObject.from_config(SampleObject.load_config(SCREAMING_SNAKE_CASE							)							)
  							snake_case		:						Union[str, Any]								=				new_obj.config
  
  					# unfreeze configs
  					snake_case		:						List[str]								=				dict(SCREAMING_SNAKE_CASE							)
  					snake_case		:						Union[str, Any]								=				dict(SCREAMING_SNAKE_CASE							)
  
  					assert config.pop("c"							) == (2, 5)  # instantiated as tuple
  					assert new_config.pop("c"							) == [2, 5]  # saved & loaded as list because of json
  					config.pop("_use_default_values"							)
  					assert config == new_config
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						List[Any]								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						Any								=				DDIMScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"							)
  
  					assert ddim.__class__ == DDIMScheduler
  					# no warning should be thrown
  					assert cap_logger.out == ""
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						int								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						Optional[int]								=				EulerDiscreteScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"							)
  
  					assert euler.__class__ == EulerDiscreteScheduler
  					# no warning should be thrown
  					assert cap_logger.out == ""
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Any								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						Union[str, Any]								=				EulerAncestralDiscreteScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"							)
  
  					assert euler.__class__ == EulerAncestralDiscreteScheduler
  					# no warning should be thrown
  					assert cap_logger.out == ""
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Union[str, Any]								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						List[Any]								=				PNDMScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"							)
  
  					assert pndm.__class__ == PNDMScheduler
  					# no warning should be thrown
  					assert cap_logger.out == ""
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						str								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						List[Any]								=				DDPMScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"				, prediction_type="sample"				, beta_end=8				, )
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger_a:
  							snake_case		:						Optional[int]								=				DDPMScheduler.from_pretrained("google/ddpm-celebahq-256"				, beta_start=88							)
  
  					assert ddpm.__class__ == DDPMScheduler
  					assert ddpm.config.prediction_type == "sample"
  					assert ddpm.config.beta_end == 8
  					assert ddpm_a.config.beta_start == 88
  
  					# no warning should be thrown
  					assert cap_logger.out == ""
  					assert cap_logger_a.out == ""
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Dict								=				logging.get_logger("diffusers.configuration_utils"							)
  					# 30 for warning
  					logger.setLevel(30							)
  
  					with CaptureLogger(SCREAMING_SNAKE_CASE							) as cap_logger:
  							snake_case		:						Union[str, Any]								=				DPMSolverMultistepScheduler.from_pretrained(
  							    "hf-internal-testing/tiny-stable-diffusion-torch"				, subfolder="scheduler"							)
  
  					assert dpm.__class__ == DPMSolverMultistepScheduler
  					# no warning should be thrown
  					assert cap_logger.out == ""
  
  
  
  			def 							lowerCamelCase_				(     self							):
  
  
  
  					"""simple docstring"""
  
  
  
  
  
  
  
  					snake_case		:						Optional[Any]								=				SampleObject()
  
  					snake_case		:						str								=				{k: v for k, v in config.config.items() if not k.startswith("_"							)}
  
  					# make sure that default config has all keys in `_use_default_values`
  					assert set(config_dict.keys()							) == set(config.config._use_default_values							)
  
  					with tempfile.TemporaryDirectory() as tmpdirname:
  							config.save_config(SCREAMING_SNAKE_CASE							)
  
  							# now loading it with SampleObject2 should put f into `_use_default_values`
  							snake_case		:						Optional[int]								=				SampleObjecta.from_config(SCREAMING_SNAKE_CASE							)
  
  							assert "f" in config._use_default_values
  							assert config.f == [1, 3]
  
  					# now loading the config, should **NOT** use [1, 3] for `f`, but the default [1, 4] value
  					# **BECAUSE** it is part of `config._use_default_values`
  					snake_case		:						Tuple								=				SampleObjecta.from_config(config.config							)
  					assert new_config.f == [5, 4]
  
  					config.config._use_default_values.pop()
  					snake_case		:						List[Any]								=				SampleObjecta.from_config(config.config							)
  					assert new_config_a.f == [1, 3]
  
  					# Nevertheless "e" should still be correctly loaded to [1, 3] from SampleObject2 instead of defaulting to [1, 5]
  					assert new_config_a.e == [1, 3]
  
  