'''simple docstring'''
import torch

from accelerate import Accelerator, DistributedType






class       __lowercase		:







     """simple docstring"""






     def __enter__(		self     ):
         if self.enabled:
             __UpperCamelCase						:						Dict		     =	self.model.no_sync()
             self.model_sync_obj.__enter__()

         return self







     def __exit__(		self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase     ):
         if self.enabled:
             # Average all models on exit
             self._sync_and_avg_model_params()
             self.model_sync_obj.__exit__(lowercase_  ,      lowercase_  ,      lowercase_     )







     def __init__(		self  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase  ,      _lowerCamelCase = True     ):
         if accelerator.distributed_type not in [
             DistributedType.NO,
             DistributedType.MULTI_CPU,
             DistributedType.MULTI_GPU,
         ]:
             raise NotImplementedError('LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'     )
         __UpperCamelCase						:						Any		     =	enabled and accelerator.distributed_type != DistributedType.NO
         __UpperCamelCase						:						List[Any]		     =	0
         if self.enabled:
             __UpperCamelCase						:						Optional[int]		     =	accelerator
             __UpperCamelCase						:						Tuple		     =	model
             __UpperCamelCase						:						Union[str, Any]		     =	local_sgd_steps







     def lowerCAmelCase  (		self     ):
         self.num_steps += 1
         if not self.enabled:
             return

         if self.num_steps % self.local_sgd_steps == 0:
             self._sync_and_avg_model_params()







     def lowerCAmelCase  (		self     ):
         self.accelerator.wait_for_everyone()
         with self.accelerator.autocast():
             for param in self.model.parameters():
                 __UpperCamelCase						:						Any		     =	self.accelerator.reduce(param.data  ,      reduction='mean'     )








"""simple docstring"""


from itertools import permutations

def 					_lowerCAmelCase (  lowercase_ = 5		):
						if gon_side < 3 or gon_side > 5:
												raise ValueError('gon_side must be in the range [3, 5]'		)

						# Since it's 16, we know 10 is on the outer ring
						# Put the big numbers at the end so that they are never the first number
						UpperCAmelCase			 =					list(range(gon_side + 1						,      0						,      -1		)		)
						UpperCAmelCase			 =					list(range(gon_side + 2						,      gon_side * 2 + 1		)		)

						for perm in permutations(small_numbers + big_numbers		):
												UpperCAmelCase			 =					generate_gon_ring(lowercase_						,      list(lowercase_		)		)
												if is_magic_gon(lowercase_		):
																		return int(''.join(str(lowercase_		) for n in numbers		)		)

						UpperCAmelCase			 =					F"""Magic {gon_side}-gon ring is impossible"""
						raise ValueError(lowercase_		)

def 					_lowerCAmelCase (  lowercase_						,      lowercase_		):
						UpperCAmelCase			 =					[0] * (gon_side * 3)
						UpperCAmelCase			 =					perm[0:3]
						perm.append(perm[1]		)

						UpperCAmelCase			 =					1 if gon_side < 5 else 2

						for i in range(1						,      len(lowercase_		) // 3 + magic_number		):
												UpperCAmelCase			 =					perm[2 * i + 1]
												UpperCAmelCase			 =					result[3 * i - 1]
												UpperCAmelCase			 =					perm[2 * i + 2]

						return result

def 					_lowerCAmelCase (  lowercase_		):
						if len(lowercase_		) % 3 != 0:
												raise ValueError('a gon ring should have a length that is a multiple of 3'		)

						if min(numbers[::3]		) != numbers[0]:
												return False

						UpperCAmelCase			 =					sum(numbers[:3]		)

						return all(sum(numbers[i : i + 3]		) == total for i in range(3						,      len(lowercase_		)						,      3		)		)


if __name__ == "__main__":
				print(solution())





