



def  _lowerCAmelCase     (_lowerCAmelCase ,						_lowerCAmelCase):
					UpperCamelCase_			= []
					UpperCamelCase_			= len(_lowerCAmelCase)
					for i in range(_lowerCAmelCase):
										UpperCamelCase_			= []
										for j in range(_lowerCAmelCase):
															UpperCamelCase_			= 0
															for k in range(_lowerCAmelCase):
																				UpperCamelCase_			= val + matrix_a[i][k] * matrix_b[k][j]
															list_a.append(_lowerCAmelCase)
										matrix_c.append(_lowerCAmelCase)
					return matrix_c



def  _lowerCAmelCase     (_lowerCAmelCase):
					return [[int(row == column) for column in range(_lowerCAmelCase)] for row in range(_lowerCAmelCase)]



def  _lowerCAmelCase     (_lowerCAmelCase):
					if n <= 1:
										return n
					UpperCamelCase_			= identity(2)
					UpperCamelCase_			= [[1, 1], [1, 0]]
					UpperCamelCase_			= n - 1
					while n > 0:
										if n % 2 == 1:
															UpperCamelCase_			= multiply(_lowerCAmelCase ,						_lowerCAmelCase)
										UpperCamelCase_			= multiply(_lowerCAmelCase ,						_lowerCAmelCase)
										UpperCamelCase_			= int(n / 2)
					return res_matrix[0][0]



def  _lowerCAmelCase     (_lowerCAmelCase):
					if n <= 1:
										return n
					UpperCamelCase_			= 0
					UpperCamelCase_			= 1
					for _ in range(2 ,						n + 1):
										UpperCamelCase_	,     UpperCamelCase_			= fiba, fiba + fiba
					return fiba



def  _lowerCAmelCase     ():
					for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
										UpperCamelCase_			= int("".join(c for c in ordinal if c in "0123456789"))  # 1000th --> 1000
										print(
										    f"""{ordinal} fibonacci number using matrix exponentiation is """
										    f"""{nth_fibonacci_matrix(_lowerCAmelCase)} and using bruteforce is """
										    f"""{nth_fibonacci_bruteforce(_lowerCAmelCase)}\n""")
					# from timeit import timeit
					# print(timeit("nth_fibonacci_matrix(1000000)",
					#              "from main import nth_fibonacci_matrix", number=5))
					# print(timeit("nth_fibonacci_bruteforce(1000000)",
					#              "from main import nth_fibonacci_bruteforce", number=5))
					# 2.3342058970001744
					# 57.256506615000035


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()

import torch

from accelerate import Accelerator, DistributedType



class 			UpperCamelCase					:

     '''simple docstring'''

     def __enter__(       self    )			->					int:






           """simple docstring"""
           if self.enabled:
                 _lowerCamelCase           =					self.model.no_sync()
                 self.model_sync_obj.__enter__()

           return self



     def __exit__(       self					,					A_					,					A_					,					A_    )			->					Union[str, Any]:






           """simple docstring"""
           if self.enabled:
                 # Average all models on exit
                 self._sync_and_avg_model_params()
                 self.model_sync_obj.__exit__(A_					,					A_					,					A_    )



     def __init__(       self					,					A_					,					A_					,					A_					,					A_ = True    )			->					List[str]:






           """simple docstring"""
           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)'''    )
           _lowerCamelCase           =					enabled and accelerator.distributed_type != DistributedType.NO
           _lowerCamelCase           =					0
           if self.enabled:
                 _lowerCamelCase           =					accelerator
                 _lowerCamelCase           =					model
                 _lowerCamelCase           =					local_sgd_steps



     def 		UpperCamelCase_    (       self    )			->					Optional[Any]:






           """simple docstring"""
           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 		UpperCamelCase_    (       self    )			->					Union[str, Any]:






           """simple docstring"""
           self.accelerator.wait_for_everyone()
           with self.accelerator.autocast():
                 for param in self.model.parameters():
                       _lowerCamelCase           =					self.accelerator.reduce(param.data					,					reduction='''mean'''    )