



from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


snake_case    :						Dict  =						logging.get_logger(__name__)


snake_case    :						Optional[Any]  =						TypeVar('DatasetType', Dataset, IterableDataset)
def 	snake_case__       (					__lowercase							,     __lowercase = None							,     __lowercase = None							,     __lowercase = None							,     __lowercase = None							,     __lowercase = "first_exhausted"							,     )		->		DatasetType:







						"""simple docstring"""

						from .arrow_dataset import Dataset
						from .iterable_dataset import IterableDataset

						if not datasets:
												raise ValueError("Unable to interleave an empty list of datasets."       )
						for i, dataset in enumerate(__lowercase       ):
												if not isinstance(__lowercase							,     (Dataset, IterableDataset)       ):
																		if isinstance(__lowercase							,     (DatasetDict, IterableDatasetDict)       ):
																								if not dataset:
																														raise ValueError(
																														    F'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '
																														    "is an empty dataset dictionary."       )
																								raise ValueError(
																								    F'Dataset at position {i} has at least one split: {list(__lowercase       )}\n'
																								    F'Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(__lowercase       )       )}\']'       )
																		raise ValueError(
																		    F'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__lowercase       ).__name__}.'       )
												if i == 0:
																		A__    ,       A__	:							Dict						    = (
																		    (Dataset, IterableDataset) if isinstance(__lowercase							,     __lowercase       ) else (IterableDataset, Dataset)
																		)
												elif not isinstance(__lowercase							,     __lowercase       ):
																		raise ValueError(
																		    F'Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'       )
						if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
												raise ValueError(F'{stopping_strategy} is not supported. Please enter a valid stopping_strategy.'       )
						if dataset_type is Dataset:
												return _interleave_map_style_datasets(
												    __lowercase							,     __lowercase							,     __lowercase							,     info=__lowercase							,     split=__lowercase							,     stopping_strategy=__lowercase       )
						else:
												return _interleave_iterable_datasets(
												    __lowercase							,     __lowercase							,     __lowercase							,     info=__lowercase							,     split=__lowercase							,     stopping_strategy=__lowercase       )




def 	snake_case__       (					__lowercase							,     __lowercase = None							,     __lowercase = None							,     __lowercase = 0							,     )		->		DatasetType:







						"""simple docstring"""

						if not dsets:
												raise ValueError("Unable to concatenate an empty list of datasets."       )
						for i, dataset in enumerate(__lowercase       ):
												if not isinstance(__lowercase							,     (Dataset, IterableDataset)       ):
																		if isinstance(__lowercase							,     (DatasetDict, IterableDatasetDict)       ):
																								if not dataset:
																														raise ValueError(
																														    F'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} '
																														    "is an empty dataset dictionary."       )
																								raise ValueError(
																								    F'Dataset at position {i} has at least one split: {list(__lowercase       )}\n'
																								    F'Please pick one to interleave with the other datasets, for example: dataset[\'{next(iter(__lowercase       )       )}\']'       )
																		raise ValueError(
																		    F'Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(__lowercase       ).__name__}.'       )
												if i == 0:
																		A__    ,       A__	:							int						    = (
																		    (Dataset, IterableDataset) if isinstance(__lowercase							,     __lowercase       ) else (IterableDataset, Dataset)
																		)
												elif not isinstance(__lowercase							,     __lowercase       ):
																		raise ValueError(
																		    F'Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects.'       )
						if dataset_type is Dataset:
												return _concatenate_map_style_datasets(__lowercase							,     info=__lowercase							,     split=__lowercase							,     axis=__lowercase       )
						else:
												return _concatenate_iterable_datasets(__lowercase							,     info=__lowercase							,     split=__lowercase							,     axis=__lowercase       )




from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt
def 	snake_case__       (					__lowercase       )		->		bool:







						"""simple docstring"""

						A__	:							int						    = int(number**0.5       )
						return number == sq * sq
def 	snake_case__       (					__lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )		->		tuple[int, int]:







						"""simple docstring"""

						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(__lowercase							,     __lowercase       )
						top //= hcf
						bottom //= hcf
						return top, bottom
def 	snake_case__       (					__lowercase = 3_5       )		->		int:







						"""simple docstring"""

						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__	:							Any						    = x_num * y_den + x_den * y_num
																														A__	:							List[Any]						    = x_den * y_den
																														A__	:							List[Any]						    = gcd(__lowercase							,     __lowercase       )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																				A__	:							List[Any]						    = add_three(
																																				    __lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )
																																				unique_s.add(__lowercase       )

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

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

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

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

						return total.denominator + total.numerator


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