


import math



def 			lowerCAmelCase (		lowerCAmelCase_ )-> bool:
				lowerCAmelCase_ :      int    				=				math.loga(math.sqrt(4 * positive_integer + 1 ) / 2 + 1 / 2 )

				return exponent == int(lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ = 1 / 12_345 )-> int:
				lowerCAmelCase_ :      Optional[int]    				=				0
				lowerCAmelCase_ :      List[Any]    				=				0

				lowerCAmelCase_ :      Union[str, Any]    				=				3
				while True:
								lowerCAmelCase_ :      Tuple    				=				(integer**2 - 1) / 4
								# if candidate is an integer, then there is a partition for k
								if partition_candidate == int(lowerCAmelCase_ ):
												lowerCAmelCase_ :      Dict    				=				int(lowerCAmelCase_ )
												total_partitions += 1
												if check_partition_perfect(lowerCAmelCase_ ):
																perfect_partitions += 1
								if perfect_partitions > 0:
												if perfect_partitions / total_partitions < max_proportion:
																return int(lowerCAmelCase_ )
								integer += 1


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



import copy
from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import Audio, Features, Value
from .base import TaskTemplate







@dataclass(frozen=UpperCAmelCase__							)
class 				snake_case__(							UpperCAmelCase__							):







						'''simple docstring'''




						SCREAMING_SNAKE_CASE__      :  str					=							field(default="""automatic-speech-recognition""",						metadata={"""include_in_asdict_even_if_is_default""": True}							)
						SCREAMING_SNAKE_CASE__      :  ClassVar[Features]					=							Features({"""audio""": Audio()}							)
						SCREAMING_SNAKE_CASE__      :  ClassVar[Features]					=							Features({"""transcription""": Value("""string"""							)}							)
						SCREAMING_SNAKE_CASE__      :  str					=							"audio"
						SCREAMING_SNAKE_CASE__      :  str					=							"transcription"




						def 						lowercase_ (				self   ,						__lowercase							)					->    int:
										if self.audio_column not in features:
														raise ValueError(f"""Column {self.audio_column} is not present in features."""							)
										if not isinstance(features[self.audio_column]   ,						__lowercase							):
														raise ValueError(f"""Column {self.audio_column} is not an Audio type."""							)
										lowerCAmelCase_ :      List[str]    				=				copy.deepcopy(self							)
										lowerCAmelCase_ :      Optional[Any]    				=				self.input_schema.copy()
										lowerCAmelCase_ :      Optional[Any]    				=				features[self.audio_column]
										lowerCAmelCase_ :      List[str]    				=				input_schema
										return task_template




						@property
						def 						lowercase_ (				self							)					->    Dict[str, str]:
										return {self.audio_column: "audio", self.transcription_column: "transcription"}