





from .imports import is_tqdm_available


if is_tqdm_available():
					from tqdm.auto import tqdm as _tqdm

from ..state import PartialState







def        __lowerCamelCase (							__a       :bool = True   ,					*__a       :str   ,					**__a       :Optional[int]   )		->    Optional[Any]:






		"""simple docstring"""

		if not is_tqdm_available():
				raise ImportError("""Accelerate's `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`."""   )
		A__  				=       False
		if main_process_only:
				A__  				=       PartialState().local_process_index == 0
		return _tqdm(*a__   ,					**a__   ,					disable=a__   )






import math







def        __lowerCamelCase (							__a       :int   )		->    bool:






		"""simple docstring"""

		A__  				=       math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

		return exponent == int(__a   )







def        __lowerCamelCase (							__a       :float = 1 / 1_2_3_4_5   )		->    int:






		"""simple docstring"""

		A__  				=       0
		A__  				=       0

		A__  				=       3
		while True:
				A__  				=       (integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(__a   ):
						A__  				=       int(__a   )
						total_partitions += 1
						if check_partition_perfect(__a   ):
								perfect_partitions += 1
				if perfect_partitions > 0:
						if perfect_partitions / total_partitions < max_proportion:
								return int(__a   )
				integer += 1


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



