"""simple docstring"""






import inspect
import tempfile
from collections import OrderedDict, UserDict
from collections.abc import MutableMapping
from contextlib import ExitStack, contextmanager
from dataclasses import fields
from enum import Enum
from typing import Any, ContextManager, List, Tuple

import numpy as np

from .import_utils import is_flax_available, is_tf_available, is_torch_available, is_torch_fx_proxy


if is_flax_available():
						import jax.numpy as jnp
class 				snake_case       ( __UpperCAmelCase				):




					"""simple docstring"""

					def __get__(				self   :	str    ,lowerCamelCase__   :	Any    ,lowerCamelCase__   :	List[str]=None			):
									# See docs.python.org/3/howto/descriptor.html#properties
									if obj is None:
													return self
									if self.fget is None:
													raise AttributeError('unreadable attribute'			)
									UpperCAmelCase__             =							'__cached_' + self.fget.__name__
									UpperCAmelCase__             =							getattr(lowerCamelCase__    ,lowerCamelCase__    ,lowerCamelCase__			)
									if cached is None:
													UpperCAmelCase__             =							self.fget(lowerCamelCase__			)
													setattr(lowerCamelCase__    ,lowerCamelCase__    ,lowerCamelCase__			)
									return cached






def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__             =							val.lower()
				if val in {"y", "yes", "t", "true", "on", "1"}:
								return 1
				if val in {"n", "no", "f", "false", "off", "0"}:
								return 0
				raise ValueError(f'''invalid truth value {val!r}'''       )



def   a_						(					lowerCamelCase       ):
				if is_torch_fx_proxy(lowerCamelCase       ):
								return True
				if is_torch_available():
								import torch

								if isinstance(lowerCamelCase					,			torch.Tensor       ):
												return True
				if is_tf_available():
								import tensorflow as tf

								if isinstance(lowerCamelCase					,			tf.Tensor       ):
												return True

				if is_flax_available():
								import jax.numpy as jnp
								from jax.core import Tracer

								if isinstance(lowerCamelCase					,			(jnp.ndarray, Tracer)       ):
												return True

				return isinstance(lowerCamelCase					,			np.ndarray       )



def   a_						(					lowerCamelCase       ):
				return isinstance(lowerCamelCase					,			np.ndarray       )



def   a_						(					lowerCamelCase       ):
				return _is_numpy(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import torch

				return isinstance(lowerCamelCase					,			torch.Tensor       )



def   a_						(					lowerCamelCase       ):
				return False if not is_torch_available() else _is_torch(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import torch

				return isinstance(lowerCamelCase					,			torch.device       )



def   a_						(					lowerCamelCase       ):
				return False if not is_torch_available() else _is_torch_device(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import torch

				if isinstance(lowerCamelCase					,			lowerCamelCase       ):
								if hasattr(lowerCamelCase					,			lowerCamelCase       ):
												UpperCAmelCase__             =							getattr(lowerCamelCase					,			lowerCamelCase       )
								else:
												return False
				return isinstance(lowerCamelCase					,			torch.dtype       )



def   a_						(					lowerCamelCase       ):
				return False if not is_torch_available() else _is_torch_dtype(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import tensorflow as tf

				return isinstance(lowerCamelCase					,			tf.Tensor       )



def   a_						(					lowerCamelCase       ):
				return False if not is_tf_available() else _is_tensorflow(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import tensorflow as tf

				# the `is_symbolic_tensor` predicate is only available starting with TF 2.14
				if hasattr(lowerCamelCase					,			'is_symbolic_tensor'       ):
								return tf.is_symbolic_tensor(lowerCamelCase       )
				return type(lowerCamelCase       ) == tf.Tensor



def   a_						(					lowerCamelCase       ):
				return False if not is_tf_available() else _is_tf_symbolic_tensor(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				import jax.numpy as jnp  # noqa: F811

				return isinstance(lowerCamelCase					,			jnp.ndarray       )



def   a_						(					lowerCamelCase       ):
				return False if not is_flax_available() else _is_jax(lowerCamelCase       )



def   a_						(					lowerCamelCase       ):
				if isinstance(lowerCamelCase					,			(dict, UserDict)       ):
								return {k: to_py_obj(lowerCamelCase       ) for k, v in obj.items()}
				elif isinstance(lowerCamelCase					,			(list, tuple)       ):
								return [to_py_obj(lowerCamelCase       ) for o in obj]
				elif is_tf_tensor(lowerCamelCase       ):
								return obj.numpy().tolist()
				elif is_torch_tensor(lowerCamelCase       ):
								return obj.detach().cpu().tolist()
				elif is_jax_tensor(lowerCamelCase       ):
								return np.asarray(lowerCamelCase       ).tolist()
				elif isinstance(lowerCamelCase					,			(np.ndarray, np.number)       ):  # tolist also works on 0d np arrays
								return obj.tolist()
				else:
								return obj



def   a_						(					lowerCamelCase       ):
				if isinstance(lowerCamelCase					,			(dict, UserDict)       ):
								return {k: to_numpy(lowerCamelCase       ) for k, v in obj.items()}
				elif isinstance(lowerCamelCase					,			(list, tuple)       ):
								return np.array(lowerCamelCase       )
				elif is_tf_tensor(lowerCamelCase       ):
								return obj.numpy()
				elif is_torch_tensor(lowerCamelCase       ):
								return obj.detach().cpu().numpy()
				elif is_jax_tensor(lowerCamelCase       ):
								return np.asarray(lowerCamelCase       )
				else:
								return obj
class 				snake_case       ( __UpperCAmelCase				):




					"""simple docstring"""

					def 		__lowerCAmelCase						(				self   :	List[Any]			):
									UpperCAmelCase__             =							fields(self			)

									# Safety and consistency checks
									if not len(lowerCamelCase__			):
													raise ValueError(f'''{self.__class__.__name__} has no fields.'''			)
									if not all(field.default is None for field in class_fields[1:]			):
													raise ValueError(f'''{self.__class__.__name__} should not have more than one required field.'''			)

									UpperCAmelCase__             =							getattr(self    ,class_fields[0].name			)
									UpperCAmelCase__             =							all(getattr(self    ,field.name			) is None for field in class_fields[1:]			)

									if other_fields_are_none and not is_tensor(lowerCamelCase__			):
													if isinstance(lowerCamelCase__    ,lowerCamelCase__			):
																	UpperCAmelCase__             =							first_field.items()
																	UpperCAmelCase__             =							True
													else:
																	try:
																					UpperCAmelCase__             =							iter(lowerCamelCase__			)
																					UpperCAmelCase__             =							True
																	except TypeError:
																					UpperCAmelCase__             =							False

            # if we provided an iterator as first field and the iterator is a (key, value) iterator
            # set the associated fields
													if first_field_iterator:
																	for idx, element in enumerate(lowerCamelCase__			):
																					if (
																					    not isinstance(lowerCamelCase__    ,(list, tuple)			)
																					    or not len(lowerCamelCase__			) == 2
																					    or not isinstance(element[0]    ,lowerCamelCase__			)
																					):
																									if idx == 0:
																													# If we do not have an iterator of key/values, set it as attribute
																													UpperCAmelCase__             =							first_field
																									else:
																													# If we have a mixed iterator, raise an error
																													raise ValueError(
																													    f'''Cannot set key/value for {element}. It needs to be a tuple (key, value).'''			)
																									break
																					setattr(self    ,element[0]    ,element[1]			)
																					if element[1] is not None:
																									UpperCAmelCase__             =							element[1]
													elif first_field is not None:
																	UpperCAmelCase__             =							first_field
									else:
													for field in class_fields:
																	UpperCAmelCase__             =							getattr(self    ,field.name			)
																	if v is not None:
																					UpperCAmelCase__             =							v







					def __delitem__(				self   :	Union[str, Any]    ,*lowerCamelCase__   :	List[str]    ,**lowerCamelCase__   :	Dict			):
									raise Exception(f'''You cannot use ``__delitem__`` on a {self.__class__.__name__} instance.'''			)







					def 		__lowerCAmelCase						(				self   :	Optional[int]    ,*lowerCamelCase__   :	List[str]    ,**lowerCamelCase__   :	str			):
									raise Exception(f'''You cannot use ``setdefault`` on a {self.__class__.__name__} instance.'''			)







					def 		__lowerCAmelCase						(				self   :	str    ,*lowerCamelCase__   :	Any    ,**lowerCamelCase__   :	Union[str, Any]			):
									raise Exception(f'''You cannot use ``pop`` on a {self.__class__.__name__} instance.'''			)







					def 		__lowerCAmelCase						(				self   :	str    ,*lowerCamelCase__   :	Optional[Any]    ,**lowerCamelCase__   :	List[Any]			):
									raise Exception(f'''You cannot use ``update`` on a {self.__class__.__name__} instance.'''			)







					def __getitem__(				self   :	List[str]    ,lowerCamelCase__   :	List[Any]			):
									if isinstance(lowerCamelCase__    ,lowerCamelCase__			):
													UpperCAmelCase__             =							dict(self.items()			)
													return inner_dict[k]
									else:
													return self.to_tuple()[k]







					def __setattr__(				self   :	Optional[int]    ,lowerCamelCase__   :	str    ,lowerCamelCase__   :	Optional[int]			):
									if name in self.keys() and value is not None:
													# Don't call self.__setitem__ to avoid recursion errors
													super().__setitem__(lowerCamelCase__    ,lowerCamelCase__			)
									super().__setattr__(lowerCamelCase__    ,lowerCamelCase__			)







					def __setitem__(				self   :	Optional[Any]    ,lowerCamelCase__   :	str    ,lowerCamelCase__   :	Dict			):
									# Will raise a KeyException if needed
									super().__setitem__(lowerCamelCase__    ,lowerCamelCase__			)
									# Don't call self.__setattr__ to avoid recursion errors
									super().__setattr__(lowerCamelCase__    ,lowerCamelCase__			)







					def 		__lowerCAmelCase						(				self   :	Optional[int]			):
									return tuple(self[k] for k in self.keys()			)






class 				snake_case       ( __UpperCAmelCase      ,    __UpperCAmelCase				):




					"""simple docstring"""

					@classmethod
					def 		__lowerCAmelCase						(				cls   :	List[str]    ,lowerCamelCase__   :	List[Any]			):
									raise ValueError(
									    f'''{value} is not a valid {cls.__name__}, please select one of {list(cls._valueamember_map_.keys()			)}'''			)






class 				snake_case       ( __UpperCAmelCase				):




					"""simple docstring"""

					snake_case__				    = "longest"
					snake_case__				    = "max_length"
					snake_case__				    = "do_not_pad"






class 				snake_case       ( __UpperCAmelCase				):




					"""simple docstring"""

					snake_case__				    = "pt"
					snake_case__				    = "tf"
					snake_case__				    = "np"
					snake_case__				    = "jax"






class 				snake_case       :




					"""simple docstring"""

					def __init__(				self   :	Tuple    ,lowerCamelCase__   :	List[ContextManager]			):
									UpperCAmelCase__             =							context_managers
									UpperCAmelCase__             =							ExitStack()







					def __enter__(				self   :	Union[str, Any]			):
									for context_manager in self.context_managers:
													self.stack.enter_context(lowerCamelCase__			)







					def __exit__(				self   :	Union[str, Any]    ,*lowerCamelCase__   :	Optional[Any]    ,**lowerCamelCase__   :	Dict			):
									self.stack.__exit__(*lowerCamelCase__    ,**lowerCamelCase__			)






def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__             =							infer_framework(lowerCamelCase       )
				if framework == "tf":
								UpperCAmelCase__             =							inspect.signature(model_class.call       )  # TensorFlow models
				elif framework == "pt":
								UpperCAmelCase__             =							inspect.signature(model_class.forward       )  # PyTorch models
				else:
								UpperCAmelCase__             =							inspect.signature(model_class.__call__       )  # Flax models

				for p in signature.parameters:
								if p == "return_loss" and signature.parameters[p].default is True:
												return True

				return False



def   a_						(					lowerCamelCase       ):
				UpperCAmelCase__             =							model_class.__name__
				UpperCAmelCase__             =							infer_framework(lowerCamelCase       )
				if framework == "tf":
								UpperCAmelCase__             =							inspect.signature(model_class.call       )  # TensorFlow models
				elif framework == "pt":
								UpperCAmelCase__             =							inspect.signature(model_class.forward       )  # PyTorch models
				else:
								UpperCAmelCase__             =							inspect.signature(model_class.__call__       )  # Flax models

				if "QuestionAnswering" in model_name:
								return [p for p in signature.parameters if "label" in p or p in ("start_positions", "end_positions")]
				else:
								return [p for p in signature.parameters if "label" in p]



def   a_						(					lowerCamelCase					,			lowerCamelCase = ""					,			lowerCamelCase = "."       ):

				def _flatten_dict(lowerCamelCase					,			lowerCamelCase=""					,			lowerCamelCase="."       ):
								for k, v in d.items():
												UpperCAmelCase__             =							str(lowerCamelCase       ) + delimiter + str(lowerCamelCase       ) if parent_key else k
												if v and isinstance(lowerCamelCase					,			lowerCamelCase       ):
																yield from flatten_dict(lowerCamelCase					,			lowerCamelCase					,			delimiter=lowerCamelCase       ).items()
												else:
																yield key, v

				return dict(_flatten_dict(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )       )



@contextmanager
def   a_						(					lowerCamelCase					,			lowerCamelCase = False       ):
				if use_temp_dir:
								with tempfile.TemporaryDirectory() as tmp_dir:
												yield tmp_dir
				else:
								yield working_dir



def   a_						(					lowerCamelCase					,			lowerCamelCase=None       ):
				if is_numpy_array(lowerCamelCase       ):
								return np.transpose(lowerCamelCase					,			axes=lowerCamelCase       )
				elif is_torch_tensor(lowerCamelCase       ):
								return array.T if axes is None else array.permute(*lowerCamelCase       )
				elif is_tf_tensor(lowerCamelCase       ):
								import tensorflow as tf

								return tf.transpose(lowerCamelCase					,			perm=lowerCamelCase       )
				elif is_jax_tensor(lowerCamelCase       ):
								return jnp.transpose(lowerCamelCase					,			axes=lowerCamelCase       )
				else:
								raise ValueError(f'''Type not supported for transpose: {type(lowerCamelCase       )}.'''       )



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if is_numpy_array(lowerCamelCase       ):
								return np.reshape(lowerCamelCase					,			lowerCamelCase       )
				elif is_torch_tensor(lowerCamelCase       ):
								return array.reshape(*lowerCamelCase       )
				elif is_tf_tensor(lowerCamelCase       ):
								import tensorflow as tf

								return tf.reshape(lowerCamelCase					,			lowerCamelCase       )
				elif is_jax_tensor(lowerCamelCase       ):
								return jnp.reshape(lowerCamelCase					,			lowerCamelCase       )
				else:
								raise ValueError(f'''Type not supported for reshape: {type(lowerCamelCase       )}.'''       )



def   a_						(					lowerCamelCase					,			lowerCamelCase=None       ):
				if is_numpy_array(lowerCamelCase       ):
								return np.squeeze(lowerCamelCase					,			axis=lowerCamelCase       )
				elif is_torch_tensor(lowerCamelCase       ):
								return array.squeeze() if axis is None else array.squeeze(dim=lowerCamelCase       )
				elif is_tf_tensor(lowerCamelCase       ):
								import tensorflow as tf

								return tf.squeeze(lowerCamelCase					,			axis=lowerCamelCase       )
				elif is_jax_tensor(lowerCamelCase       ):
								return jnp.squeeze(lowerCamelCase					,			axis=lowerCamelCase       )
				else:
								raise ValueError(f'''Type not supported for squeeze: {type(lowerCamelCase       )}.'''       )



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if is_numpy_array(lowerCamelCase       ):
								return np.expand_dims(lowerCamelCase					,			lowerCamelCase       )
				elif is_torch_tensor(lowerCamelCase       ):
								return array.unsqueeze(dim=lowerCamelCase       )
				elif is_tf_tensor(lowerCamelCase       ):
								import tensorflow as tf

								return tf.expand_dims(lowerCamelCase					,			axis=lowerCamelCase       )
				elif is_jax_tensor(lowerCamelCase       ):
								return jnp.expand_dims(lowerCamelCase					,			axis=lowerCamelCase       )
				else:
								raise ValueError(f'''Type not supported for expand_dims: {type(lowerCamelCase       )}.'''       )



def   a_						(					lowerCamelCase       ):
				if is_numpy_array(lowerCamelCase       ):
								return np.size(lowerCamelCase       )
				elif is_torch_tensor(lowerCamelCase       ):
								return array.numel()
				elif is_tf_tensor(lowerCamelCase       ):
								import tensorflow as tf

								return tf.size(lowerCamelCase       )
				elif is_jax_tensor(lowerCamelCase       ):
								return array.size
				else:
								raise ValueError(f'''Type not supported for expand_dims: {type(lowerCamelCase       )}.'''       )



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				for key, value in auto_map.items():
								if isinstance(lowerCamelCase					,			(tuple, list)       ):
												UpperCAmelCase__             =							[f'''{repo_id}--{v}''' if (v is not None and '--' not in v) else v for v in value]
								elif value is not None and "--" not in value:
												UpperCAmelCase__             =							f'''{repo_id}--{value}'''

				return auto_map







def   a_						(					lowerCamelCase       ):
				for base_class in inspect.getmro(lowerCamelCase       ):
								UpperCAmelCase__             =							base_class.__module__
								UpperCAmelCase__             =							base_class.__name__
								if module.startswith('tensorflow'       ) or module.startswith('keras'       ) or name == "TFPreTrainedModel":
												return "tf"
								elif module.startswith('torch'       ) or name == "PreTrainedModel":
												return "pt"
								elif module.startswith('flax'       ) or module.startswith('jax'       ) or name == "FlaxPreTrainedModel":
												return "flax"
				else:
								raise TypeError(f'''Could not infer framework from class {model_class}.'''       )







'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  int(number**0.5   )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a			:       int					    =  x_den * y_den * z_den
					__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 35   ):
					__a			:       set					    =  set()
					__a			:       int
					__a			:       Fraction					    =  Fraction(0   )
					__a			:       tuple[int, int]

					for x_num in range(1						,      order + 1   ):
										for x_den in range(x_num + 1						,      order + 1   ):
															for y_num in range(1						,      order + 1   ):
																				for y_den in range(y_num + 1						,      order + 1   ):
																									# n=1
																									__a			:       Union[str, Any]					    =  x_num * y_den + x_den * y_num
																									__a			:       Optional[Any]					    =  x_den * y_den
																									__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       Optional[int]					    =  (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									__a			:       Union[str, Any]					    =  x_den * x_den * y_den * y_den
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       List[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Any					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Optional[int]					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[Any]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

                    # n=-1
																									__a			:       int					    =  x_num * y_num
																									__a			:       Optional[Any]					    =  x_den * y_num + x_num * y_den
																									__a			:       Tuple					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       List[Any]					    =  x_num * x_num * y_num * y_num
																									__a			:       List[Any]					    =  (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       Optional[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Union[str, Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[str]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

					for num, den in unique_s:
										total += Fraction(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )

					return total.denominator + total.numerator


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



